Defining parameters
Level: | \( N \) | = | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 18 \) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(25920\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(380))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 9000 | 4700 | 4300 |
Cusp forms | 8280 | 4492 | 3788 |
Eisenstein series | 720 | 208 | 512 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(380))\)
We only show spaces with odd parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(380))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(380)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 2}\)