The brass statue of Goddess Ganesha you're describing typically features intricate craftsmanship and a rich cultural significance. Here are some details you might find about such a statue:

Design and Features:

1. Material: Made from high-quality brass, which is known for its durability and resistance to tarnishing. Brass gives the statue a warm, golden hue.

2. Finishing: The statue is often hand-engraved, showcasing intricate designs that highlight Ganesha's various attributes and symbols, such as his large ears, trunk, and the mouse at his feet.

3. Antique Finish: The yellow antique finish adds an aged, vintage look, enhancing the statue's aesthetic appeal and making it a beautiful decorative piece.

4. Posture and Hand Gestures: Ganesha is usually depicted with multiple arms, each holding different objects (like a modak, a lotus, or a bell), and performing mudras (hand gestures) that symbolize blessings, protection, and wisdom.

5. Size:  width 4 inches

6. depth: 2.5 inches
7. heigh:  7 inches

Cultural Significance:

• Symbolism: Ganesha is known as the remover of obstacles, the god of beginnings, and is often worshipped at the start of new ventures or projects.
• Traditional Craftsmanship: Made by skilled artisans in India, often using techniques passed down through generations, these statues represent not just religious significance but also cultural heritage.

Usage:

• Home Decor: Often placed in homes, offices, or temples as a symbol of prosperity and good fortune.
• Gift Item: An ideal gift for festivals, housewarming, or special occasions due to its auspicious nature.

If you're looking to purchase or learn more, it's best to visit local artisans or specialized stores that focus on traditional Indian handicrafts.