Properties

Label 968.2.i
Level $968$
Weight $2$
Character orbit 968.i
Rep. character $\chi_{968}(9,\cdot)$
Character field $\Q(\zeta_{5})$
Dimension $108$
Newform subspaces $20$
Sturm bound $264$
Trace bound $7$

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Defining parameters

Level: \( N \) \(=\) \( 968 = 2^{3} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 968.i (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 11 \)
Character field: \(\Q(\zeta_{5})\)
Newform subspaces: \( 20 \)
Sturm bound: \(264\)
Trace bound: \(7\)
Distinguishing \(T_p\): \(3\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(968, [\chi])\).

Total New Old
Modular forms 624 108 516
Cusp forms 432 108 324
Eisenstein series 192 0 192

Trace form

\( 108 q - 2 q^{3} - 4 q^{7} - 21 q^{9} + O(q^{10}) \) \( 108 q - 2 q^{3} - 4 q^{7} - 21 q^{9} - 2 q^{13} + 18 q^{15} + 8 q^{17} + 11 q^{19} + 8 q^{21} + 28 q^{23} - 3 q^{25} + 19 q^{27} - 6 q^{31} - 10 q^{35} - 16 q^{37} - 44 q^{39} - 20 q^{41} - 30 q^{43} - 76 q^{45} - 18 q^{47} - 45 q^{49} - 35 q^{51} + 36 q^{53} + 9 q^{57} + 29 q^{59} + 18 q^{61} + 8 q^{63} + 20 q^{65} + 82 q^{67} + 52 q^{69} + 36 q^{71} + 8 q^{73} - 3 q^{75} + 8 q^{79} - 68 q^{81} + 13 q^{83} - 36 q^{85} + 40 q^{87} - 46 q^{89} - 30 q^{91} - 6 q^{93} - 4 q^{95} + 7 q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(968, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
968.2.i.a 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 968.2.a.f \(0\) \(-4\) \(-5\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.b 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 968.2.a.f \(0\) \(-4\) \(-5\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.c 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 88.2.i.a \(0\) \(-2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.d 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 88.2.i.a \(0\) \(-2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.e 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 968.2.a.d \(0\) \(-1\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{5}-4\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.f 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 968.2.a.d \(0\) \(-1\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{5}+4\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.g 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 968.2.a.b \(0\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q-3\zeta_{10}q^{5}-4\zeta_{10}^{3}q^{7}+(3-3\zeta_{10}+\cdots)q^{9}+\cdots\)
968.2.i.h 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 968.2.a.b \(0\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q-3\zeta_{10}q^{5}+4\zeta_{10}^{3}q^{7}+(3-3\zeta_{10}+\cdots)q^{9}+\cdots\)
968.2.i.i 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 88.2.a.a \(0\) \(3\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-3\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.j 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 88.2.a.a \(0\) \(3\) \(3\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-3\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.k 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 88.2.i.a \(0\) \(3\) \(3\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
968.2.i.l 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 968.2.a.f \(0\) \(6\) \(5\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots\)
968.2.i.m 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None 968.2.a.f \(0\) \(6\) \(5\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots\)
968.2.i.n 968.i 11.c $8$ $7.730$ 8.0.324000000.3 None 968.2.a.k \(0\) \(-2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{2}+\beta _{7})q^{3}+(-\beta _{1}-2\beta _{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
968.2.i.o 968.i 11.c $8$ $7.730$ 8.0.324000000.3 None 968.2.a.k \(0\) \(-2\) \(4\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{2}+\beta _{7})q^{3}+(-\beta _{1}-2\beta _{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
968.2.i.p 968.i 11.c $8$ $7.730$ 8.0.682515625.5 None 88.2.i.b \(0\) \(-1\) \(-3\) \(-7\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{4}-\beta _{6})q^{3}+(\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
968.2.i.q 968.i 11.c $8$ $7.730$ 8.0.1305015625.1 None 88.2.a.b \(0\) \(-1\) \(-3\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{5}q^{3}+(-2-\beta _{1}+2\beta _{2}-2\beta _{3}+\cdots)q^{5}+\cdots\)
968.2.i.r 968.i 11.c $8$ $7.730$ 8.0.1305015625.1 None 88.2.a.b \(0\) \(-1\) \(-3\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{5}q^{3}+(-2-\beta _{1}+2\beta _{2}-2\beta _{3}+\cdots)q^{5}+\cdots\)
968.2.i.s 968.i 11.c $8$ $7.730$ 8.0.682515625.5 None 88.2.i.b \(0\) \(-1\) \(2\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{2}+\beta _{5})q^{3}+(1-\beta _{2}+\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\)
968.2.i.t 968.i 11.c $8$ $7.730$ 8.0.682515625.5 None 88.2.i.b \(0\) \(-1\) \(2\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\beta _{2}+\beta _{5})q^{3}+(1-\beta _{2}+\beta _{4}-\beta _{6}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(968, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(968, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(22, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(44, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(121, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(242, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(484, [\chi])\)\(^{\oplus 2}\)