Defining parameters
Level: | \( N \) | = | \( 121 = 11^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 20 \) | ||
Sturm bound: | \(4840\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(121))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1895 | 1856 | 39 |
Cusp forms | 1735 | 1715 | 20 |
Eisenstein series | 160 | 141 | 19 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(121))\)
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 |
---|---|---|---|---|
121.4.a | \(\chi_{121}(1, \cdot)\) | 121.4.a.a | 1 | 1 |
121.4.a.b | 2 | |||
121.4.a.c | 2 | |||
121.4.a.d | 2 | |||
121.4.a.e | 2 | |||
121.4.a.f | 4 | |||
121.4.a.g | 4 | |||
121.4.a.h | 6 | |||
121.4.c | \(\chi_{121}(3, \cdot)\) | 121.4.c.a | 4 | 4 |
121.4.c.b | 8 | |||
121.4.c.c | 8 | |||
121.4.c.d | 8 | |||
121.4.c.e | 8 | |||
121.4.c.f | 8 | |||
121.4.c.g | 8 | |||
121.4.c.h | 8 | |||
121.4.c.i | 8 | |||
121.4.c.j | 24 | |||
121.4.e | \(\chi_{121}(12, \cdot)\) | 121.4.e.a | 320 | 10 |
121.4.g | \(\chi_{121}(4, \cdot)\) | 121.4.g.a | 1280 | 40 |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(121))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(121)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)