Defining parameters
Level: | \( N \) | = | \( 231 = 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Newform subspaces: | \( 33 \) | ||
Sturm bound: | \(7680\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(231))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2160 | 1447 | 713 |
Cusp forms | 1681 | 1271 | 410 |
Eisenstein series | 479 | 176 | 303 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)
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 the newforms together with their dimension.
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(231))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(231)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)