Defining parameters
Level: | \( N \) | = | \( 2672 = 2^{4} \cdot 167 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(892416\) | ||
Trace bound: | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2672))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 225428 | 126229 | 99199 |
Cusp forms | 220781 | 124745 | 96036 |
Eisenstein series | 4647 | 1484 | 3163 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2672))\)
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 |
---|---|---|---|---|
2672.2.a | \(\chi_{2672}(1, \cdot)\) | 2672.2.a.a | 1 | 1 |
2672.2.a.b | 2 | |||
2672.2.a.c | 2 | |||
2672.2.a.d | 2 | |||
2672.2.a.e | 2 | |||
2672.2.a.f | 2 | |||
2672.2.a.g | 2 | |||
2672.2.a.h | 3 | |||
2672.2.a.i | 3 | |||
2672.2.a.j | 5 | |||
2672.2.a.k | 7 | |||
2672.2.a.l | 7 | |||
2672.2.a.m | 9 | |||
2672.2.a.n | 12 | |||
2672.2.a.o | 12 | |||
2672.2.a.p | 12 | |||
2672.2.b | \(\chi_{2672}(2671, \cdot)\) | 2672.2.b.a | 28 | 1 |
2672.2.b.b | 56 | |||
2672.2.c | \(\chi_{2672}(1337, \cdot)\) | None | 0 | 1 |
2672.2.h | \(\chi_{2672}(1335, \cdot)\) | None | 0 | 1 |
2672.2.j | \(\chi_{2672}(669, \cdot)\) | n/a | 664 | 2 |
2672.2.l | \(\chi_{2672}(667, \cdot)\) | n/a | 668 | 2 |
2672.2.m | \(\chi_{2672}(33, \cdot)\) | n/a | 6806 | 82 |
2672.2.n | \(\chi_{2672}(23, \cdot)\) | None | 0 | 82 |
2672.2.s | \(\chi_{2672}(9, \cdot)\) | None | 0 | 82 |
2672.2.t | \(\chi_{2672}(15, \cdot)\) | n/a | 6888 | 82 |
2672.2.u | \(\chi_{2672}(35, \cdot)\) | n/a | 54776 | 164 |
2672.2.w | \(\chi_{2672}(21, \cdot)\) | n/a | 54776 | 164 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2672))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(2672)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(167))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(668))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1336))\)\(^{\oplus 2}\)