Defining parameters
Level: | \( N \) | = | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 29 \) | ||
Sturm bound: | \(17280\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(304))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 6012 | 3299 | 2713 |
Cusp forms | 5508 | 3145 | 2363 |
Eisenstein series | 504 | 154 | 350 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(304))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(304))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(304)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)