Defining parameters
Level: | \( N \) | = | \( 802 = 2 \cdot 401 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Newform subspaces: | \( 31 \) | ||
Sturm bound: | \(80400\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(802))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 20500 | 6699 | 13801 |
Cusp forms | 19701 | 6699 | 13002 |
Eisenstein series | 799 | 0 | 799 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(802))\)
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 |
---|---|---|---|---|
802.2.a | \(\chi_{802}(1, \cdot)\) | 802.2.a.a | 1 | 1 |
802.2.a.b | 1 | |||
802.2.a.c | 5 | |||
802.2.a.d | 7 | |||
802.2.a.e | 9 | |||
802.2.a.f | 10 | |||
802.2.b | \(\chi_{802}(801, \cdot)\) | 802.2.b.a | 2 | 1 |
802.2.b.b | 16 | |||
802.2.b.c | 16 | |||
802.2.c | \(\chi_{802}(381, \cdot)\) | 802.2.c.a | 4 | 2 |
802.2.c.b | 30 | |||
802.2.c.c | 34 | |||
802.2.d | \(\chi_{802}(39, \cdot)\) | 802.2.d.a | 64 | 4 |
802.2.d.b | 72 | |||
802.2.e | \(\chi_{802}(45, \cdot)\) | 802.2.e.a | 64 | 4 |
802.2.e.b | 68 | |||
802.2.f | \(\chi_{802}(29, \cdot)\) | 802.2.f.a | 4 | 4 |
802.2.f.b | 60 | |||
802.2.f.c | 72 | |||
802.2.h | \(\chi_{802}(179, \cdot)\) | 802.2.h.a | 136 | 8 |
802.2.h.b | 136 | |||
802.2.i | \(\chi_{802}(5, \cdot)\) | 802.2.i.a | 320 | 20 |
802.2.i.b | 360 | |||
802.2.j | \(\chi_{802}(35, \cdot)\) | 802.2.j.a | 256 | 16 |
802.2.j.b | 272 | |||
802.2.k | \(\chi_{802}(41, \cdot)\) | 802.2.k.a | 320 | 20 |
802.2.k.b | 360 | |||
802.2.m | \(\chi_{802}(49, \cdot)\) | 802.2.m.a | 680 | 40 |
802.2.m.b | 680 | |||
802.2.n | \(\chi_{802}(7, \cdot)\) | 802.2.n.a | 1280 | 80 |
802.2.n.b | 1360 |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(802))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(802)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(401))\)\(^{\oplus 2}\)