Defining parameters
Level: | \( N \) | = | \( 5312 = 2^{6} \cdot 83 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(3526656\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5312))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 887568 | 497574 | 389994 |
Cusp forms | 875761 | 494010 | 381751 |
Eisenstein series | 11807 | 3564 | 8243 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5312))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(5312))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(5312)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(166))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(332))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(664))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1328))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2656))\)\(^{\oplus 2}\)