Defining parameters
Level: | \( N \) | = | \( 68 = 2^{2} \cdot 17 \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 5 \) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(864\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(68))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 328 | 180 | 148 |
Cusp forms | 248 | 152 | 96 |
Eisenstein series | 80 | 28 | 52 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(68))\)
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 \(S_{3}^{\mathrm{old}}(\Gamma_1(68))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(68)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 2}\)