Defining parameters
Level: | \( N \) | = | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 27 \) | ||
Sturm bound: | \(4032\) | ||
Trace bound: | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(156))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1464 | 606 | 858 |
Cusp forms | 1224 | 558 | 666 |
Eisenstein series | 240 | 48 | 192 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(156))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(156))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(156)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)