Defining parameters
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 20 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(105\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{7}(100, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 96 | 56 | 40 |
Cusp forms | 84 | 52 | 32 |
Eisenstein series | 12 | 4 | 8 |
Trace form
Decomposition of \(S_{7}^{\mathrm{new}}(100, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
100.7.d.a | $4$ | $23.005$ | \(\Q(i, \sqrt{15})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{2})q^{2}-4\beta _{2}q^{3}+(56-2\beta _{3})q^{4}+\cdots\) |
100.7.d.b | $24$ | $23.005$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
100.7.d.c | $24$ | $23.005$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{7}^{\mathrm{old}}(100, [\chi])\) into lower level spaces
\( S_{7}^{\mathrm{old}}(100, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 2}\)