Defining parameters
Level: | \( N \) | = | \( 304 = 2^{4} \cdot 19 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(23040\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(304))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 8892 | 4909 | 3983 |
Cusp forms | 8388 | 4757 | 3631 |
Eisenstein series | 504 | 152 | 352 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(304))\)
We only show spaces with even 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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(304))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(304)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 2}\)