Defining parameters
Level: | \( N \) | = | \( 1275 = 3 \cdot 5^{2} \cdot 17 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 36 \) | ||
Sturm bound: | \(460800\) | ||
Trace bound: | \(14\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1275))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 174592 | 119236 | 55356 |
Cusp forms | 171008 | 118004 | 53004 |
Eisenstein series | 3584 | 1232 | 2352 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1275))\)
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.
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1275))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1275)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(51))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(255))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(425))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1275))\)\(^{\oplus 1}\)