Defining parameters
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.i (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 7 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 25 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(980, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1056 | 80 | 976 |
Cusp forms | 960 | 80 | 880 |
Eisenstein series | 96 | 0 | 96 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(980, [\chi])\) into newform subspaces
Decomposition of \(S_{4}^{\mathrm{old}}(980, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(980, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(14, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(98, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(196, [\chi])\)\(^{\oplus 2}\)