Defining parameters
Level: | \( N \) | = | \( 1225 = 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 24 \) | ||
Sturm bound: | \(470400\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1225))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 178080 | 157010 | 21070 |
Cusp forms | 174720 | 155021 | 19699 |
Eisenstein series | 3360 | 1989 | 1371 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1225))\)
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 \(S_{4}^{\mathrm{old}}(\Gamma_1(1225))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(1225)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 2}\)