Defining parameters
Level: | \( N \) | = | \( 49 = 7^{2} \) |
Weight: | \( k \) | = | \( 22 \) |
Nonzero newspaces: | \( 4 \) | ||
Sturm bound: | \(4312\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{22}(\Gamma_1(49))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2088 | 2000 | 88 |
Cusp forms | 2028 | 1951 | 77 |
Eisenstein series | 60 | 49 | 11 |
Trace form
Decomposition of \(S_{22}^{\mathrm{new}}(\Gamma_1(49))\)
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 |
---|---|---|---|---|
49.22.a | \(\chi_{49}(1, \cdot)\) | 49.22.a.a | 1 | 1 |
49.22.a.b | 1 | |||
49.22.a.c | 5 | |||
49.22.a.d | 6 | |||
49.22.a.e | 10 | |||
49.22.a.f | 13 | |||
49.22.a.g | 13 | |||
49.22.a.h | 20 | |||
49.22.c | \(\chi_{49}(18, \cdot)\) | n/a | 136 | 2 |
49.22.e | \(\chi_{49}(8, \cdot)\) | n/a | 582 | 6 |
49.22.g | \(\chi_{49}(2, \cdot)\) | n/a | 1164 | 12 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{22}^{\mathrm{old}}(\Gamma_1(49))\) into lower level spaces
\( S_{22}^{\mathrm{old}}(\Gamma_1(49)) \cong \) \(S_{22}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{22}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)