Defining parameters
Level: | \( N \) | = | \( 891 = 3^{4} \cdot 11 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Newform subspaces: | \( 89 \) | ||
Sturm bound: | \(116640\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(891))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 30240 | 23160 | 7080 |
Cusp forms | 28081 | 22152 | 5929 |
Eisenstein series | 2159 | 1008 | 1151 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(891))\)
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.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(891))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(891)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 2}\)