Defining parameters
Level: | \( N \) | = | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(28224\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(245))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 12000 | 10489 | 1511 |
Cusp forms | 11520 | 10199 | 1321 |
Eisenstein series | 480 | 290 | 190 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(245))\)
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 |
---|---|---|---|---|
245.6.a | \(\chi_{245}(1, \cdot)\) | 245.6.a.a | 1 | 1 |
245.6.a.b | 1 | |||
245.6.a.c | 2 | |||
245.6.a.d | 3 | |||
245.6.a.e | 4 | |||
245.6.a.f | 5 | |||
245.6.a.g | 5 | |||
245.6.a.h | 6 | |||
245.6.a.i | 6 | |||
245.6.a.j | 8 | |||
245.6.a.k | 8 | |||
245.6.a.l | 10 | |||
245.6.a.m | 10 | |||
245.6.b | \(\chi_{245}(99, \cdot)\) | 245.6.b.a | 2 | 1 |
245.6.b.b | 2 | |||
245.6.b.c | 12 | |||
245.6.b.d | 14 | |||
245.6.b.e | 18 | |||
245.6.b.f | 18 | |||
245.6.b.g | 32 | |||
245.6.e | \(\chi_{245}(116, \cdot)\) | n/a | 132 | 2 |
245.6.f | \(\chi_{245}(48, \cdot)\) | n/a | 192 | 2 |
245.6.j | \(\chi_{245}(79, \cdot)\) | n/a | 192 | 2 |
245.6.k | \(\chi_{245}(36, \cdot)\) | n/a | 552 | 6 |
245.6.l | \(\chi_{245}(68, \cdot)\) | n/a | 384 | 4 |
245.6.p | \(\chi_{245}(29, \cdot)\) | n/a | 828 | 6 |
245.6.q | \(\chi_{245}(11, \cdot)\) | n/a | 1128 | 12 |
245.6.s | \(\chi_{245}(13, \cdot)\) | n/a | 1656 | 12 |
245.6.t | \(\chi_{245}(4, \cdot)\) | n/a | 1656 | 12 |
245.6.x | \(\chi_{245}(3, \cdot)\) | n/a | 3312 | 24 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(245))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(245)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)