Defining parameters
Level: | \( N \) | = | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 10 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(47040\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(245))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 21408 | 18765 | 2643 |
Cusp forms | 20928 | 18475 | 2453 |
Eisenstein series | 480 | 290 | 190 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(245))\)
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 |
---|---|---|---|---|
245.10.a | \(\chi_{245}(1, \cdot)\) | 245.10.a.a | 1 | 1 |
245.10.a.b | 1 | |||
245.10.a.c | 2 | |||
245.10.a.d | 2 | |||
245.10.a.e | 4 | |||
245.10.a.f | 5 | |||
245.10.a.g | 6 | |||
245.10.a.h | 9 | |||
245.10.a.i | 9 | |||
245.10.a.j | 11 | |||
245.10.a.k | 11 | |||
245.10.a.l | 13 | |||
245.10.a.m | 13 | |||
245.10.a.n | 18 | |||
245.10.a.o | 18 | |||
245.10.b | \(\chi_{245}(99, \cdot)\) | n/a | 180 | 1 |
245.10.e | \(\chi_{245}(116, \cdot)\) | n/a | 240 | 2 |
245.10.f | \(\chi_{245}(48, \cdot)\) | n/a | 352 | 2 |
245.10.j | \(\chi_{245}(79, \cdot)\) | n/a | 352 | 2 |
245.10.k | \(\chi_{245}(36, \cdot)\) | n/a | 1008 | 6 |
245.10.l | \(\chi_{245}(68, \cdot)\) | n/a | 704 | 4 |
245.10.p | \(\chi_{245}(29, \cdot)\) | n/a | 1500 | 6 |
245.10.q | \(\chi_{245}(11, \cdot)\) | n/a | 2016 | 12 |
245.10.s | \(\chi_{245}(13, \cdot)\) | n/a | 3000 | 12 |
245.10.t | \(\chi_{245}(4, \cdot)\) | n/a | 3000 | 12 |
245.10.x | \(\chi_{245}(3, \cdot)\) | n/a | 6000 | 24 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(245))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(245)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 1}\)