Defining parameters
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 4 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 8 \) | ||
Sturm bound: | \(105\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(100, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 60 | 36 |
Cusp forms | 84 | 54 | 30 |
Eisenstein series | 12 | 6 | 6 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(100, [\chi])\) into newform subspaces
Decomposition of \(S_{7}^{\mathrm{old}}(100, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(4, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)