Defining parameters
Level: | \( N \) | = | \( 1682 = 2 \cdot 29^{2} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(353220\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1682))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 89509 | 29366 | 60143 |
Cusp forms | 87102 | 29366 | 57736 |
Eisenstein series | 2407 | 0 | 2407 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1682))\)
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 |
---|---|---|---|---|
1682.2.a | \(\chi_{1682}(1, \cdot)\) | 1682.2.a.a | 1 | 1 |
1682.2.a.b | 1 | |||
1682.2.a.c | 1 | |||
1682.2.a.d | 1 | |||
1682.2.a.e | 1 | |||
1682.2.a.f | 1 | |||
1682.2.a.g | 1 | |||
1682.2.a.h | 1 | |||
1682.2.a.i | 1 | |||
1682.2.a.j | 1 | |||
1682.2.a.k | 2 | |||
1682.2.a.l | 2 | |||
1682.2.a.m | 3 | |||
1682.2.a.n | 3 | |||
1682.2.a.o | 4 | |||
1682.2.a.p | 4 | |||
1682.2.a.q | 6 | |||
1682.2.a.r | 6 | |||
1682.2.a.s | 6 | |||
1682.2.a.t | 6 | |||
1682.2.a.u | 8 | |||
1682.2.a.v | 8 | |||
1682.2.b | \(\chi_{1682}(1681, \cdot)\) | 1682.2.b.a | 2 | 1 |
1682.2.b.b | 2 | |||
1682.2.b.c | 2 | |||
1682.2.b.d | 2 | |||
1682.2.b.e | 2 | |||
1682.2.b.f | 4 | |||
1682.2.b.g | 6 | |||
1682.2.b.h | 8 | |||
1682.2.b.i | 12 | |||
1682.2.b.j | 12 | |||
1682.2.b.k | 16 | |||
1682.2.d | \(\chi_{1682}(571, \cdot)\) | n/a | 402 | 6 |
1682.2.e | \(\chi_{1682}(63, \cdot)\) | n/a | 408 | 6 |
1682.2.g | \(\chi_{1682}(59, \cdot)\) | n/a | 2044 | 28 |
1682.2.h | \(\chi_{1682}(57, \cdot)\) | n/a | 2016 | 28 |
1682.2.j | \(\chi_{1682}(7, \cdot)\) | n/a | 12264 | 168 |
1682.2.k | \(\chi_{1682}(5, \cdot)\) | n/a | 12096 | 168 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1682))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(1682)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(841))\)\(^{\oplus 2}\)