Defining parameters
Level: | \( N \) | = | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | = | \( 6 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(174240\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(605))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 73240 | 65875 | 7365 |
Cusp forms | 71960 | 65033 | 6927 |
Eisenstein series | 1280 | 842 | 438 |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(605))\)
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 |
---|---|---|---|---|
605.6.a | \(\chi_{605}(1, \cdot)\) | 605.6.a.a | 1 | 1 |
605.6.a.b | 3 | |||
605.6.a.c | 4 | |||
605.6.a.d | 5 | |||
605.6.a.e | 6 | |||
605.6.a.f | 7 | |||
605.6.a.g | 7 | |||
605.6.a.h | 8 | |||
605.6.a.i | 9 | |||
605.6.a.j | 9 | |||
605.6.a.k | 10 | |||
605.6.a.l | 14 | |||
605.6.a.m | 18 | |||
605.6.a.n | 20 | |||
605.6.a.o | 20 | |||
605.6.a.p | 20 | |||
605.6.a.q | 20 | |||
605.6.b | \(\chi_{605}(364, \cdot)\) | n/a | 264 | 1 |
605.6.e | \(\chi_{605}(362, \cdot)\) | n/a | 524 | 2 |
605.6.g | \(\chi_{605}(81, \cdot)\) | n/a | 720 | 4 |
605.6.j | \(\chi_{605}(9, \cdot)\) | n/a | 1048 | 4 |
605.6.k | \(\chi_{605}(56, \cdot)\) | n/a | 2200 | 10 |
605.6.m | \(\chi_{605}(112, \cdot)\) | n/a | 2096 | 8 |
605.6.o | \(\chi_{605}(34, \cdot)\) | n/a | 3280 | 10 |
605.6.r | \(\chi_{605}(32, \cdot)\) | n/a | 6560 | 20 |
605.6.s | \(\chi_{605}(16, \cdot)\) | n/a | 8800 | 40 |
605.6.u | \(\chi_{605}(4, \cdot)\) | n/a | 13120 | 40 |
605.6.w | \(\chi_{605}(2, \cdot)\) | n/a | 26240 | 80 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(605))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_1(605)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)