Defining parameters
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(120\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(575, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 66 | 34 | 32 |
Cusp forms | 54 | 34 | 20 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(575, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
575.2.b.a | $2$ | $4.591$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+2iq^{2}-2q^{4}+iq^{7}+3q^{9}+2q^{11}+\cdots\) |
575.2.b.b | $2$ | $4.591$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{2}+q^{4}-iq^{7}+3iq^{8}+3q^{9}+\cdots\) |
575.2.b.c | $4$ | $4.591$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{3}q^{3}+3\beta _{2}q^{4}+(1+\cdots)q^{6}+\cdots\) |
575.2.b.d | $4$ | $4.591$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\) |
575.2.b.e | $8$ | $4.591$ | 8.0.\(\cdots\).11 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{7}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\) |
575.2.b.f | $14$ | $4.591$ | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(-2+\beta _{2})q^{4}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(575, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(575, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(115, [\chi])\)\(^{\oplus 2}\)