Defining parameters
Level: | \( N \) | = | \( 195 = 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 20 \) | ||
Newform subspaces: | \( 36 \) | ||
Sturm bound: | \(5376\) | ||
Trace bound: | \(6\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(195))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1536 | 979 | 557 |
Cusp forms | 1153 | 851 | 302 |
Eisenstein series | 383 | 128 | 255 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)
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 \(S_{2}^{\mathrm{old}}(\Gamma_1(195))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(195)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)