Defining parameters
| Level: | \( N \) | = | \( 312 = 2^{3} \cdot 3 \cdot 13 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 1 \) | ||
| Newform subspaces: | \( 1 \) | ||
| Sturm bound: | \(5376\) | ||
| Trace bound: | \(0\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(312))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 316 | 48 | 268 |
| Cusp forms | 28 | 4 | 24 |
| Eisenstein series | 288 | 44 | 244 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 4 | 0 | 0 | 0 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(312))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(312))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(312)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 2}\)