Defining parameters
Level: | \( N \) | = | \( 1338 = 2 \cdot 3 \cdot 223 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(198912\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1338))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 50616 | 12433 | 38183 |
Cusp forms | 48841 | 12433 | 36408 |
Eisenstein series | 1775 | 0 | 1775 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1338))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
1338.2.a | \(\chi_{1338}(1, \cdot)\) | 1338.2.a.a | 1 | 1 |
1338.2.a.b | 2 | |||
1338.2.a.c | 3 | |||
1338.2.a.d | 3 | |||
1338.2.a.e | 3 | |||
1338.2.a.f | 3 | |||
1338.2.a.g | 4 | |||
1338.2.a.h | 5 | |||
1338.2.a.i | 6 | |||
1338.2.a.j | 7 | |||
1338.2.d | \(\chi_{1338}(1337, \cdot)\) | 1338.2.d.a | 76 | 1 |
1338.2.e | \(\chi_{1338}(931, \cdot)\) | 1338.2.e.a | 2 | 2 |
1338.2.e.b | 2 | |||
1338.2.e.c | 2 | |||
1338.2.e.d | 4 | |||
1338.2.e.e | 4 | |||
1338.2.e.f | 4 | |||
1338.2.e.g | 12 | |||
1338.2.e.h | 14 | |||
1338.2.e.i | 14 | |||
1338.2.e.j | 18 | |||
1338.2.f | \(\chi_{1338}(263, \cdot)\) | n/a | 148 | 2 |
1338.2.i | \(\chi_{1338}(7, \cdot)\) | n/a | 1296 | 36 |
1338.2.j | \(\chi_{1338}(59, \cdot)\) | n/a | 2736 | 36 |
1338.2.m | \(\chi_{1338}(19, \cdot)\) | n/a | 2736 | 72 |
1338.2.p | \(\chi_{1338}(5, \cdot)\) | n/a | 5328 | 72 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1338))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1338)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(223))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(446))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(669))\)\(^{\oplus 2}\)