Defining parameters
Level: | \( N \) | = | \( 1369 = 37^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(312132\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1369))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 79023 | 78873 | 150 |
Cusp forms | 77044 | 76964 | 80 |
Eisenstein series | 1979 | 1909 | 70 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1369))\)
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 |
---|---|---|---|---|
1369.2.a | \(\chi_{1369}(1, \cdot)\) | 1369.2.a.a | 1 | 1 |
1369.2.a.b | 1 | |||
1369.2.a.c | 1 | |||
1369.2.a.d | 1 | |||
1369.2.a.e | 1 | |||
1369.2.a.f | 1 | |||
1369.2.a.g | 2 | |||
1369.2.a.h | 2 | |||
1369.2.a.i | 3 | |||
1369.2.a.j | 3 | |||
1369.2.a.k | 3 | |||
1369.2.a.l | 3 | |||
1369.2.a.m | 18 | |||
1369.2.a.n | 27 | |||
1369.2.a.o | 27 | |||
1369.2.b | \(\chi_{1369}(1368, \cdot)\) | 1369.2.b.a | 2 | 1 |
1369.2.b.b | 2 | |||
1369.2.b.c | 2 | |||
1369.2.b.d | 4 | |||
1369.2.b.e | 6 | |||
1369.2.b.f | 6 | |||
1369.2.b.g | 18 | |||
1369.2.b.h | 54 | |||
1369.2.c | \(\chi_{1369}(581, \cdot)\) | n/a | 190 | 2 |
1369.2.e | \(\chi_{1369}(582, \cdot)\) | n/a | 188 | 2 |
1369.2.f | \(\chi_{1369}(678, \cdot)\) | n/a | 564 | 6 |
1369.2.h | \(\chi_{1369}(300, \cdot)\) | n/a | 558 | 6 |
1369.2.j | \(\chi_{1369}(38, \cdot)\) | n/a | 4140 | 36 |
1369.2.k | \(\chi_{1369}(36, \cdot)\) | n/a | 4176 | 36 |
1369.2.l | \(\chi_{1369}(10, \cdot)\) | n/a | 8280 | 72 |
1369.2.n | \(\chi_{1369}(11, \cdot)\) | n/a | 8352 | 72 |
1369.2.o | \(\chi_{1369}(7, \cdot)\) | n/a | 25056 | 216 |
1369.2.q | \(\chi_{1369}(3, \cdot)\) | n/a | 25272 | 216 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1369))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1369)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1369))\)\(^{\oplus 1}\)