Defining parameters
Level: | \( N \) | = | \( 668 = 2^{2} \cdot 167 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(55776\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(668))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14359 | 8300 | 6059 |
Cusp forms | 13530 | 7968 | 5562 |
Eisenstein series | 829 | 332 | 497 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(668))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(668)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 2}\)