Defining parameters
Level: | \( N \) | = | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | = | \( 1 \) |
Nonzero newspaces: | \( 5 \) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(46080\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(912))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1146 | 178 | 968 |
Cusp forms | 138 | 26 | 112 |
Eisenstein series | 1008 | 152 | 856 |
The following table gives the dimensions of subspaces with specified projective image type.
\(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
---|---|---|---|---|
Dimension | 26 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(912))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(912))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(912)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 2}\)