Defining parameters
Level: | \( N \) | = | \( 2738 = 2 \cdot 37^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(936396\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2738))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 236079 | 77920 | 158159 |
Cusp forms | 232120 | 77920 | 154200 |
Eisenstein series | 3959 | 0 | 3959 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2738))\)
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 |
---|---|---|---|---|
2738.2.a | \(\chi_{2738}(1, \cdot)\) | 2738.2.a.a | 1 | 1 |
2738.2.a.b | 1 | |||
2738.2.a.c | 1 | |||
2738.2.a.d | 1 | |||
2738.2.a.e | 2 | |||
2738.2.a.f | 2 | |||
2738.2.a.g | 2 | |||
2738.2.a.h | 2 | |||
2738.2.a.i | 2 | |||
2738.2.a.j | 2 | |||
2738.2.a.k | 2 | |||
2738.2.a.l | 2 | |||
2738.2.a.m | 3 | |||
2738.2.a.n | 3 | |||
2738.2.a.o | 3 | |||
2738.2.a.p | 3 | |||
2738.2.a.q | 6 | |||
2738.2.a.r | 6 | |||
2738.2.a.s | 6 | |||
2738.2.a.t | 6 | |||
2738.2.a.u | 9 | |||
2738.2.a.v | 9 | |||
2738.2.a.w | 18 | |||
2738.2.a.x | 18 | |||
2738.2.b | \(\chi_{2738}(2737, \cdot)\) | n/a | 110 | 1 |
2738.2.c | \(\chi_{2738}(581, \cdot)\) | n/a | 218 | 2 |
2738.2.e | \(\chi_{2738}(1951, \cdot)\) | n/a | 220 | 2 |
2738.2.f | \(\chi_{2738}(737, \cdot)\) | n/a | 666 | 6 |
2738.2.h | \(\chi_{2738}(437, \cdot)\) | n/a | 672 | 6 |
2738.2.j | \(\chi_{2738}(75, \cdot)\) | n/a | 4284 | 36 |
2738.2.k | \(\chi_{2738}(73, \cdot)\) | n/a | 4248 | 36 |
2738.2.l | \(\chi_{2738}(47, \cdot)\) | n/a | 8568 | 72 |
2738.2.n | \(\chi_{2738}(11, \cdot)\) | n/a | 8496 | 72 |
2738.2.o | \(\chi_{2738}(7, \cdot)\) | n/a | 25272 | 216 |
2738.2.q | \(\chi_{2738}(3, \cdot)\) | n/a | 25056 | 216 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2738))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(2738)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1369))\)\(^{\oplus 2}\)