Defining parameters
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.k (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(15\) | ||
Distinguishing \(T_p\): | \(7\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(960, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 216 | 16 | 200 |
Cusp forms | 168 | 16 | 152 |
Eisenstein series | 48 | 0 | 48 |
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.k.a | $2$ | $7.666$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q-iq^{3}-iq^{5}-4q^{7}-q^{9}-4iq^{11}+\cdots\) |
960.2.k.b | $2$ | $7.666$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-iq^{3}-iq^{5}-q^{9}-6iq^{13}-q^{15}+\cdots\) |
960.2.k.c | $2$ | $7.666$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+iq^{3}-iq^{5}-q^{9}-6iq^{13}+q^{15}+\cdots\) |
960.2.k.d | $2$ | $7.666$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+iq^{3}-iq^{5}+4q^{7}-q^{9}+4iq^{11}+\cdots\) |
960.2.k.e | $4$ | $7.666$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q-\zeta_{12}q^{3}+\zeta_{12}q^{5}-2q^{7}-q^{9}+(2\zeta_{12}+\cdots)q^{11}+\cdots\) |
960.2.k.f | $4$ | $7.666$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+\zeta_{12}q^{3}+\zeta_{12}q^{5}+2q^{7}-q^{9}+(-2\zeta_{12}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(960, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)