Defining parameters
Level: | \( N \) | = | \( 464 = 2^{4} \cdot 29 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 14 \) | ||
Sturm bound: | \(53760\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(464))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20552 | 11434 | 9118 |
Cusp forms | 19768 | 11192 | 8576 |
Eisenstein series | 784 | 242 | 542 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(464))\)
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 \(S_{4}^{\mathrm{old}}(\Gamma_1(464))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(464)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 2}\)