Properties

Label 960.4.f
Level $960$
Weight $4$
Character orbit 960.f
Rep. character $\chi_{960}(769,\cdot)$
Character field $\Q$
Dimension $72$
Newform subspaces $21$
Sturm bound $768$
Trace bound $11$

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Defining parameters

Level: \( N \) \(=\) \( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 960.f (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 21 \)
Sturm bound: \(768\)
Trace bound: \(11\)
Distinguishing \(T_p\): \(7\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(960, [\chi])\).

Total New Old
Modular forms 600 72 528
Cusp forms 552 72 480
Eisenstein series 48 0 48

Trace form

\( 72 q - 648 q^{9} + O(q^{10}) \) \( 72 q - 648 q^{9} - 88 q^{25} + 944 q^{41} - 3528 q^{49} + 912 q^{61} - 560 q^{65} - 528 q^{69} + 5832 q^{81} - 2352 q^{85} + 176 q^{89} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(960, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
960.4.f.a 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3iq^{3}+(-5+10i)q^{5}+4iq^{7}+\cdots\)
960.4.f.b 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3iq^{3}+(-5-10i)q^{5}+4iq^{7}+\cdots\)
960.4.f.c 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(-2+11i)q^{5}+2iq^{7}+\cdots\)
960.4.f.d 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(-2-11i)q^{5}+2iq^{7}+\cdots\)
960.4.f.e 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(2+11i)q^{5}+10iq^{7}-9q^{9}+\cdots\)
960.4.f.f 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(2-11i)q^{5}+10iq^{7}-9q^{9}+\cdots\)
960.4.f.g 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(10-5i)q^{5}+10iq^{7}-9q^{9}+\cdots\)
960.4.f.h 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3iq^{3}+(10-5i)q^{5}+18iq^{7}-9q^{9}+\cdots\)
960.4.f.i 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3iq^{3}+(10+5i)q^{5}+22iq^{7}-9q^{9}+\cdots\)
960.4.f.j 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3iq^{3}+(10-5i)q^{5}+22iq^{7}-9q^{9}+\cdots\)
960.4.f.k 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3iq^{3}+(10+5i)q^{5}+18iq^{7}-9q^{9}+\cdots\)
960.4.f.l 960.f 5.b $2$ $56.642$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(10+5i)q^{5}+10iq^{7}-9q^{9}+\cdots\)
960.4.f.m 960.f 5.b $4$ $56.642$ \(\Q(i, \sqrt{89})\) None \(0\) \(0\) \(-24\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}+(-6-\beta _{2})q^{5}-22\beta _{1}q^{7}+\cdots\)
960.4.f.n 960.f 5.b $4$ $56.642$ \(\Q(i, \sqrt{129})\) None \(0\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}+(-5+5\beta _{1}-\beta _{2})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.o 960.f 5.b $4$ $56.642$ \(\Q(i, \sqrt{129})\) None \(0\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}+(-5-6\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.p 960.f 5.b $4$ $56.642$ \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-1+\beta _{1}+2\beta _{2}-\beta _{3})q^{5}+\cdots\)
960.4.f.q 960.f 5.b $4$ $56.642$ \(\Q(i, \sqrt{41})\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-1-\beta _{2}-\beta _{3})q^{5}+(3\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.r 960.f 5.b $6$ $56.642$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\beta _{1}q^{3}+(-2+\beta _{1}-\beta _{2})q^{5}+(10\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.s 960.f 5.b $6$ $56.642$ 6.0.\(\cdots\).1 None \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3\beta _{1}q^{3}+(-2-\beta _{1}-\beta _{4})q^{5}+(10\beta _{1}+\cdots)q^{7}+\cdots\)
960.4.f.t 960.f 5.b $8$ $56.642$ 8.0.\(\cdots\).9 None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{1}q^{3}+(-2+\beta _{4})q^{5}+(4\beta _{1}-\beta _{5}+\cdots)q^{7}+\cdots\)
960.4.f.u 960.f 5.b $8$ $56.642$ 8.0.\(\cdots\).3 None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3\beta _{2}q^{3}+(1+\beta _{3})q^{5}+(2^{4}\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(960, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(960, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(10, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(20, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(60, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(240, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 2}\)