Defining parameters
Level: | \( N \) | = | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | = | \( 18 \) |
Nonzero newspaces: | \( 7 \) | ||
Sturm bound: | \(6912\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{18}(\Gamma_1(80))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 3320 | 1696 | 1624 |
Cusp forms | 3208 | 1670 | 1538 |
Eisenstein series | 112 | 26 | 86 |
Trace form
Decomposition of \(S_{18}^{\mathrm{new}}(\Gamma_1(80))\)
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 |
---|---|---|---|---|
80.18.a | \(\chi_{80}(1, \cdot)\) | 80.18.a.a | 1 | 1 |
80.18.a.b | 2 | |||
80.18.a.c | 2 | |||
80.18.a.d | 2 | |||
80.18.a.e | 2 | |||
80.18.a.f | 2 | |||
80.18.a.g | 3 | |||
80.18.a.h | 3 | |||
80.18.a.i | 4 | |||
80.18.a.j | 4 | |||
80.18.a.k | 4 | |||
80.18.a.l | 5 | |||
80.18.c | \(\chi_{80}(49, \cdot)\) | 80.18.c.a | 8 | 1 |
80.18.c.b | 8 | |||
80.18.c.c | 8 | |||
80.18.c.d | 26 | |||
80.18.d | \(\chi_{80}(41, \cdot)\) | None | 0 | 1 |
80.18.f | \(\chi_{80}(9, \cdot)\) | None | 0 | 1 |
80.18.j | \(\chi_{80}(43, \cdot)\) | n/a | 404 | 2 |
80.18.l | \(\chi_{80}(21, \cdot)\) | n/a | 272 | 2 |
80.18.n | \(\chi_{80}(47, \cdot)\) | n/a | 102 | 2 |
80.18.o | \(\chi_{80}(7, \cdot)\) | None | 0 | 2 |
80.18.q | \(\chi_{80}(29, \cdot)\) | n/a | 404 | 2 |
80.18.s | \(\chi_{80}(3, \cdot)\) | n/a | 404 | 2 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{18}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces
\( S_{18}^{\mathrm{old}}(\Gamma_1(80)) \cong \) \(S_{18}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 10}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 5}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 2}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{18}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 2}\)