Defining parameters
Level: | \( N \) | = | \( 25 = 5^{2} \) |
Weight: | \( k \) | = | \( 36 \) |
Nonzero newspaces: | \( 4 \) | ||
Sturm bound: | \(1800\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{36}(\Gamma_1(25))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 889 | 819 | 70 |
Cusp forms | 861 | 798 | 63 |
Eisenstein series | 28 | 21 | 7 |
Trace form
Decomposition of \(S_{36}^{\mathrm{new}}(\Gamma_1(25))\)
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.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
25.36.a | \(\chi_{25}(1, \cdot)\) | 25.36.a.a | 3 | 1 |
25.36.a.b | 5 | |||
25.36.a.c | 6 | |||
25.36.a.d | 12 | |||
25.36.a.e | 12 | |||
25.36.a.f | 16 | |||
25.36.b | \(\chi_{25}(24, \cdot)\) | 25.36.b.a | 6 | 1 |
25.36.b.b | 10 | |||
25.36.b.c | 12 | |||
25.36.b.d | 24 | |||
25.36.d | \(\chi_{25}(6, \cdot)\) | n/a | 348 | 4 |
25.36.e | \(\chi_{25}(4, \cdot)\) | n/a | 344 | 4 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{36}^{\mathrm{old}}(\Gamma_1(25))\) into lower level spaces
\( S_{36}^{\mathrm{old}}(\Gamma_1(25)) \cong \) \(S_{36}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{36}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)