Defining parameters
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.n (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(168\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(585, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 184 | 74 | 110 |
Cusp forms | 152 | 66 | 86 |
Eisenstein series | 32 | 8 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(585, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
585.2.n.a | $2$ | $4.671$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(-2\) | \(8\) | \(q-iq^{2}+q^{4}+(-1-2i)q^{5}+4q^{7}+\cdots\) |
585.2.n.b | $2$ | $4.671$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(2\) | \(8\) | \(q+iq^{2}+q^{4}+(1+2i)q^{5}+4q^{7}+3iq^{8}+\cdots\) |
585.2.n.c | $2$ | $4.671$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(4\) | \(-4\) | \(q-iq^{2}+q^{4}+(2+i)q^{5}-2q^{7}-3iq^{8}+\cdots\) |
585.2.n.d | $4$ | $4.671$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(-12\) | \(q+2q^{4}-\zeta_{8}^{2}q^{5}-3q^{7}+(-2\zeta_{8}^{2}+\cdots)q^{11}+\cdots\) |
585.2.n.e | $8$ | $4.671$ | 8.0.619810816.2 | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q-\beta _{6}q^{2}+(-1-\beta _{4}+\beta _{5}+\beta _{7})q^{4}+\cdots\) |
585.2.n.f | $20$ | $4.671$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q-\beta _{1}q^{2}+(-2+\beta _{2})q^{4}-\beta _{18}q^{5}+\cdots\) |
585.2.n.g | $28$ | $4.671$ | None | \(0\) | \(0\) | \(-8\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(585, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \)