Defining parameters
| Level: | \( N \) | = | \( 3756 = 2^{2} \cdot 3 \cdot 313 \) |
| Weight: | \( k \) | = | \( 1 \) |
| Nonzero newspaces: | \( 7 \) | ||
| Newform subspaces: | \( 11 \) | ||
| Sturm bound: | \(783744\) | ||
| Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3756))\).
| Total | New | Old | |
|---|---|---|---|
| Modular forms | 3565 | 744 | 2821 |
| Cusp forms | 445 | 120 | 325 |
| Eisenstein series | 3120 | 624 | 2496 |
The following table gives the dimensions of subspaces with specified projective image type.
| \(D_n\) | \(A_4\) | \(S_4\) | \(A_5\) | |
|---|---|---|---|---|
| Dimension | 112 | 0 | 0 | 8 |
Trace form
Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3756))\)
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 \(S_{1}^{\mathrm{old}}(\Gamma_1(3756))\) into lower level spaces
\( S_{1}^{\mathrm{old}}(\Gamma_1(3756)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(313))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(626))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(939))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1878))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3756))\)\(^{\oplus 1}\)