Defining parameters
Level: | \( N \) | = | \( 670 = 2 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 39 \) | ||
Sturm bound: | \(53856\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(670))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13992 | 4115 | 9877 |
Cusp forms | 12937 | 4115 | 8822 |
Eisenstein series | 1055 | 0 | 1055 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(670))\)
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 |
---|---|---|---|---|
670.2.a | \(\chi_{670}(1, \cdot)\) | 670.2.a.a | 1 | 1 |
670.2.a.b | 1 | |||
670.2.a.c | 1 | |||
670.2.a.d | 1 | |||
670.2.a.e | 2 | |||
670.2.a.f | 2 | |||
670.2.a.g | 3 | |||
670.2.a.h | 3 | |||
670.2.a.i | 3 | |||
670.2.a.j | 4 | |||
670.2.c | \(\chi_{670}(269, \cdot)\) | 670.2.c.a | 10 | 1 |
670.2.c.b | 24 | |||
670.2.e | \(\chi_{670}(171, \cdot)\) | 670.2.e.a | 2 | 2 |
670.2.e.b | 2 | |||
670.2.e.c | 2 | |||
670.2.e.d | 2 | |||
670.2.e.e | 4 | |||
670.2.e.f | 4 | |||
670.2.e.g | 6 | |||
670.2.e.h | 6 | |||
670.2.e.i | 8 | |||
670.2.e.j | 12 | |||
670.2.f | \(\chi_{670}(133, \cdot)\) | 670.2.f.a | 68 | 2 |
670.2.h | \(\chi_{670}(29, \cdot)\) | 670.2.h.a | 4 | 2 |
670.2.h.b | 12 | |||
670.2.h.c | 52 | |||
670.2.k | \(\chi_{670}(81, \cdot)\) | 670.2.k.a | 40 | 10 |
670.2.k.b | 50 | |||
670.2.k.c | 50 | |||
670.2.k.d | 60 | |||
670.2.m | \(\chi_{670}(97, \cdot)\) | 670.2.m.a | 136 | 4 |
670.2.o | \(\chi_{670}(9, \cdot)\) | 670.2.o.a | 340 | 10 |
670.2.q | \(\chi_{670}(21, \cdot)\) | 670.2.q.a | 100 | 20 |
670.2.q.b | 120 | |||
670.2.q.c | 120 | |||
670.2.q.d | 140 | |||
670.2.s | \(\chi_{670}(3, \cdot)\) | 670.2.s.a | 680 | 20 |
670.2.v | \(\chi_{670}(19, \cdot)\) | 670.2.v.a | 680 | 20 |
670.2.w | \(\chi_{670}(7, \cdot)\) | 670.2.w.a | 1360 | 40 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(670))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(670)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(67))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(134))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(335))\)\(^{\oplus 2}\)