Defining parameters
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.y (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 80 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(960, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 416 | 48 | 368 |
Cusp forms | 352 | 48 | 304 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(960, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
960.2.y.a | $2$ | $7.666$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(-2\) | \(-2\) | \(-6\) | \(q-q^{3}+(-1-2i)q^{5}+(-3-3i)q^{7}+\cdots\) |
960.2.y.b | $2$ | $7.666$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(-2\) | \(2\) | \(q+q^{3}+(-1-2i)q^{5}+(1+i)q^{7}+q^{9}+\cdots\) |
960.2.y.c | $2$ | $7.666$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(2\) | \(2\) | \(-6\) | \(q+q^{3}+(1-2i)q^{5}+(-3-3i)q^{7}+\cdots\) |
960.2.y.d | $6$ | $7.666$ | 6.0.399424.1 | None | \(0\) | \(-6\) | \(6\) | \(2\) | \(q-q^{3}+(1+2\beta _{1})q^{5}-\beta _{5}q^{7}+q^{9}+\cdots\) |
960.2.y.e | $16$ | $7.666$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(-16\) | \(-4\) | \(4\) | \(q-q^{3}+(\beta _{5}+\beta _{7})q^{5}+(\beta _{3}-\beta _{5}-\beta _{6}+\cdots)q^{7}+\cdots\) |
960.2.y.f | $20$ | $7.666$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(20\) | \(0\) | \(4\) | \(q+q^{3}+\beta _{8}q^{5}+\beta _{1}q^{7}+q^{9}-\beta _{5}q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(960, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)