Defining parameters
Level: | \( N \) | = | \( 234 = 2 \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 15 \) | ||
Newform subspaces: | \( 32 \) | ||
Sturm bound: | \(9072\) | ||
Trace bound: | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(234))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3216 | 786 | 2430 |
Cusp forms | 2832 | 786 | 2046 |
Eisenstein series | 384 | 0 | 384 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(234))\)
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 the newforms together with their dimension.
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(234))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(234)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 2}\)