Defining parameters
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.o (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 60 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(9\) | ||
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 | 216 | 52 | 164 |
Cusp forms | 168 | 44 | 124 |
Eisenstein series | 48 | 8 | 40 |
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.o.a | $4$ | $7.666$ | \(\Q(\sqrt{-3}, \sqrt{5})\) | \(\Q(\sqrt{-15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}-\beta _{1}q^{5}-3q^{9}+\beta _{3}q^{15}+\cdots\) |
960.2.o.b | $4$ | $7.666$ | \(\Q(\sqrt{2}, \sqrt{-5})\) | \(\Q(\sqrt{-5}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\) |
960.2.o.c | $4$ | $7.666$ | \(\Q(\sqrt{-2}, \sqrt{-5})\) | \(\Q(\sqrt{-5}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(2\beta _{1}-\beta _{2})q^{7}+(2+\cdots)q^{9}+\cdots\) |
960.2.o.d | $8$ | $7.666$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{2}q^{3}+\zeta_{24}q^{5}+(1-\zeta_{24}+\zeta_{24}^{4}+\cdots)q^{9}+\cdots\) |
960.2.o.e | $24$ | $7.666$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(960, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)