Defining parameters
Level: | \( N \) | = | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 6 \) | ||
Newform subspaces: | \( 13 \) | ||
Sturm bound: | \(896\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(39))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 416 | 304 | 112 |
Cusp forms | 368 | 280 | 88 |
Eisenstein series | 48 | 24 | 24 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(39))\)
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 \(S_{8}^{\mathrm{old}}(\Gamma_1(39))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(39)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 2}\)