Defining parameters
Level: | \( N \) | \(=\) | \( 350 = 2 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 350.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 15 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(350, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 432 | 64 | 368 |
Cusp forms | 408 | 64 | 344 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(350, [\chi])\) into newform subspaces
Decomposition of \(S_{8}^{\mathrm{old}}(350, [\chi])\) into lower level spaces
\( S_{8}^{\mathrm{old}}(350, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(50, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 2}\)