Defining parameters
Level: | \( N \) | = | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | = | \( 8 \) |
Nonzero newspaces: | \( 4 \) | ||
Sturm bound: | \(55680\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(354))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24592 | 6088 | 18504 |
Cusp forms | 24128 | 6088 | 18040 |
Eisenstein series | 464 | 0 | 464 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(354))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
354.8.a | \(\chi_{354}(1, \cdot)\) | 354.8.a.a | 1 | 1 |
354.8.a.b | 5 | |||
354.8.a.c | 7 | |||
354.8.a.d | 8 | |||
354.8.a.e | 9 | |||
354.8.a.f | 9 | |||
354.8.a.g | 9 | |||
354.8.a.h | 10 | |||
354.8.a.i | 10 | |||
354.8.c | \(\chi_{354}(353, \cdot)\) | n/a | 140 | 1 |
354.8.e | \(\chi_{354}(7, \cdot)\) | n/a | 1960 | 28 |
354.8.g | \(\chi_{354}(11, \cdot)\) | n/a | 3920 | 28 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(354))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_1(354)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(59))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(118))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(177))\)\(^{\oplus 2}\)