Defining parameters
Level: | \( N \) | = | \( 2075 = 5^{2} \cdot 83 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(688800\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2075))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 174496 | 160326 | 14170 |
Cusp forms | 169905 | 157006 | 12899 |
Eisenstein series | 4591 | 3320 | 1271 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2075))\)
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 |
---|---|---|---|---|
2075.2.a | \(\chi_{2075}(1, \cdot)\) | 2075.2.a.a | 1 | 1 |
2075.2.a.b | 1 | |||
2075.2.a.c | 1 | |||
2075.2.a.d | 1 | |||
2075.2.a.e | 2 | |||
2075.2.a.f | 6 | |||
2075.2.a.g | 6 | |||
2075.2.a.h | 7 | |||
2075.2.a.i | 8 | |||
2075.2.a.j | 8 | |||
2075.2.a.k | 11 | |||
2075.2.a.l | 19 | |||
2075.2.a.m | 19 | |||
2075.2.a.n | 20 | |||
2075.2.a.o | 20 | |||
2075.2.b | \(\chi_{2075}(499, \cdot)\) | n/a | 124 | 1 |
2075.2.e | \(\chi_{2075}(82, \cdot)\) | n/a | 248 | 2 |
2075.2.g | \(\chi_{2075}(416, \cdot)\) | n/a | 824 | 4 |
2075.2.j | \(\chi_{2075}(84, \cdot)\) | n/a | 816 | 4 |
2075.2.l | \(\chi_{2075}(248, \cdot)\) | n/a | 1664 | 8 |
2075.2.m | \(\chi_{2075}(26, \cdot)\) | n/a | 5200 | 40 |
2075.2.p | \(\chi_{2075}(49, \cdot)\) | n/a | 4960 | 40 |
2075.2.r | \(\chi_{2075}(18, \cdot)\) | n/a | 9920 | 80 |
2075.2.s | \(\chi_{2075}(11, \cdot)\) | n/a | 33280 | 160 |
2075.2.t | \(\chi_{2075}(4, \cdot)\) | n/a | 33280 | 160 |
2075.2.w | \(\chi_{2075}(2, \cdot)\) | n/a | 66560 | 320 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2075))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(2075)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(83))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(415))\)\(^{\oplus 2}\)