Defining parameters
Level: | \( N \) | \(=\) | \( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 660.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 5 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(288\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(660, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 8 | 148 |
Cusp forms | 132 | 8 | 124 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(660, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
660.2.c.a | $2$ | $5.270$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+iq^{3}+(-1+2i)q^{5}+2iq^{7}-q^{9}+\cdots\) |
660.2.c.b | $2$ | $5.270$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+iq^{3}+(1-2i)q^{5}-q^{9}+q^{11}-4iq^{13}+\cdots\) |
660.2.c.c | $4$ | $5.270$ | \(\Q(i, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{2})q^{7}-q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(660, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(660, [\chi]) \cong \)