Defining parameters
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.m (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 95 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(570, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 256 | 40 | 216 |
Cusp forms | 224 | 40 | 184 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(570, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
570.2.m.a | $20$ | $4.551$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(0\) | \(-4\) | \(-4\) | \(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots\) |
570.2.m.b | $20$ | $4.551$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(0\) | \(12\) | \(-4\) | \(q+\beta _{7}q^{2}-\beta _{10}q^{3}+\beta _{2}q^{4}+(1+\beta _{6}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(570, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(570, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(190, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)