Defining parameters
Level: | \( N \) | = | \( 476 = 2^{2} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 20 \) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(27648\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(476))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7392 | 3984 | 3408 |
Cusp forms | 6433 | 3688 | 2745 |
Eisenstein series | 959 | 296 | 663 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)
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 the newforms together with their dimension.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(476))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(476)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 2}\)