Defining parameters
Level: | \( N \) | = | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 20 \) | ||
Newform subspaces: | \( 70 \) | ||
Sturm bound: | \(16128\) | ||
Trace bound: | \(18\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(390))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 4416 | 909 | 3507 |
Cusp forms | 3649 | 909 | 2740 |
Eisenstein series | 767 | 0 | 767 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(390))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(390)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 2}\)