Defining parameters
Level: | \( N \) | = | \( 539 = 7^{2} \cdot 11 \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(94080\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(539))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 35880 | 33726 | 2154 |
Cusp forms | 34680 | 32854 | 1826 |
Eisenstein series | 1200 | 872 | 328 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(539))\)
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 |
---|---|---|---|---|
539.4.a | \(\chi_{539}(1, \cdot)\) | 539.4.a.a | 1 | 1 |
539.4.a.b | 1 | |||
539.4.a.c | 1 | |||
539.4.a.d | 2 | |||
539.4.a.e | 2 | |||
539.4.a.f | 4 | |||
539.4.a.g | 4 | |||
539.4.a.h | 5 | |||
539.4.a.i | 6 | |||
539.4.a.j | 9 | |||
539.4.a.k | 9 | |||
539.4.a.l | 10 | |||
539.4.a.m | 10 | |||
539.4.a.n | 10 | |||
539.4.a.o | 10 | |||
539.4.a.p | 18 | |||
539.4.b | \(\chi_{539}(538, \cdot)\) | n/a | 116 | 1 |
539.4.e | \(\chi_{539}(67, \cdot)\) | n/a | 200 | 2 |
539.4.f | \(\chi_{539}(148, \cdot)\) | n/a | 472 | 4 |
539.4.i | \(\chi_{539}(362, \cdot)\) | n/a | 232 | 2 |
539.4.j | \(\chi_{539}(78, \cdot)\) | n/a | 840 | 6 |
539.4.m | \(\chi_{539}(195, \cdot)\) | n/a | 464 | 4 |
539.4.p | \(\chi_{539}(76, \cdot)\) | n/a | 996 | 6 |
539.4.q | \(\chi_{539}(214, \cdot)\) | n/a | 928 | 8 |
539.4.r | \(\chi_{539}(23, \cdot)\) | n/a | 1680 | 12 |
539.4.s | \(\chi_{539}(19, \cdot)\) | n/a | 928 | 8 |
539.4.v | \(\chi_{539}(15, \cdot)\) | n/a | 3984 | 24 |
539.4.w | \(\chi_{539}(10, \cdot)\) | n/a | 1992 | 12 |
539.4.z | \(\chi_{539}(6, \cdot)\) | n/a | 3984 | 24 |
539.4.bc | \(\chi_{539}(4, \cdot)\) | n/a | 7968 | 48 |
539.4.bf | \(\chi_{539}(17, \cdot)\) | n/a | 7968 | 48 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(539))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(539)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 2}\)