Properties

Label 960.2.h
Level $960$
Weight $2$
Character orbit 960.h
Rep. character $\chi_{960}(191,\cdot)$
Character field $\Q$
Dimension $32$
Newform subspaces $7$
Sturm bound $384$
Trace bound $9$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 960.h (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 12 \)
Character field: \(\Q\)
Newform subspaces: \( 7 \)
Sturm bound: \(384\)
Trace bound: \(9\)
Distinguishing \(T_p\): \(7\), \(11\), \(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(960, [\chi])\).

Total New Old
Modular forms 216 32 184
Cusp forms 168 32 136
Eisenstein series 48 0 48

Trace form

\( 32 q + O(q^{10}) \) \( 32 q - 16 q^{13} - 32 q^{25} + 16 q^{33} + 16 q^{37} - 32 q^{49} - 16 q^{57} + 32 q^{61} - 16 q^{85} - 48 q^{93} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.2.h.a 960.h 12.b $4$ $7.666$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\zeta_{8}^{2})q^{3}-\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
960.2.h.b 960.h 12.b $4$ $7.666$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{5}+\cdots\)
960.2.h.c 960.h 12.b $4$ $7.666$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}+\beta _{3})q^{7}+3\beta _{2}q^{9}+\cdots\)
960.2.h.d 960.h 12.b $4$ $7.666$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{3}q^{3}-\zeta_{12}q^{5}-2\zeta_{12}^{2}q^{7}+\cdots\)
960.2.h.e 960.h 12.b $4$ $7.666$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{8}^{2})q^{3}+\zeta_{8}q^{5}+(2\zeta_{8}+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
960.2.h.f 960.h 12.b $4$ $7.666$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
960.2.h.g 960.h 12.b $8$ $7.666$ 8.0.342102016.5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}-\beta _{1}q^{5}+(\beta _{3}+\beta _{4})q^{7}+\beta _{6}q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(192, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)