Defining parameters
Level: | \( N \) | \(=\) | \( 100 = 2^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 100.l (of order \(20\) and degree \(8\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 100 \) |
Character field: | \(\Q(\zeta_{20})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(30\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(100, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 136 | 136 | 0 |
Cusp forms | 104 | 104 | 0 |
Eisenstein series | 32 | 32 | 0 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(100, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
100.2.l.a | $8$ | $0.799$ | \(\Q(\zeta_{20})\) | \(\Q(\sqrt{-1}) \) | \(2\) | \(0\) | \(4\) | \(0\) | \(q+(1-\zeta_{20}^{2}+\zeta_{20}^{3}+\zeta_{20}^{4}-\zeta_{20}^{6}+\cdots)q^{2}+\cdots\) |
100.2.l.b | $96$ | $0.799$ | None | \(-10\) | \(0\) | \(-20\) | \(0\) |