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Properties

Label 931.2.f
Level $931$
Weight $2$
Character orbit 931.f
Rep. character $\chi_{931}(324,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $120$
Newform subspaces $18$
Sturm bound $186$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 931 = 7^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 931.f (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 18 \)
Sturm bound: \(186\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(2\), \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(931, [\chi])\).

Total New Old
Modular forms 204 120 84
Cusp forms 172 120 52
Eisenstein series 32 0 32

Trace form

\( 120 q + 4 q^{2} - 56 q^{4} + 3 q^{5} - 24 q^{8} - 56 q^{9} + O(q^{10}) \) \( 120 q + 4 q^{2} - 56 q^{4} + 3 q^{5} - 24 q^{8} - 56 q^{9} - 4 q^{10} + 15 q^{11} - 10 q^{12} - 8 q^{15} - 40 q^{16} + 10 q^{17} + 2 q^{18} + 4 q^{19} - 16 q^{22} - 2 q^{23} + 8 q^{24} - 73 q^{25} + 20 q^{26} + 36 q^{27} - 16 q^{29} + 8 q^{30} - 8 q^{31} + 58 q^{32} - 18 q^{33} - 40 q^{36} + 10 q^{37} + 6 q^{38} + 24 q^{39} + 16 q^{41} - 38 q^{43} + 68 q^{44} + 15 q^{45} + 32 q^{46} + 21 q^{47} + 72 q^{48} - 52 q^{50} + 10 q^{51} + 10 q^{52} - 30 q^{53} - 32 q^{54} - 16 q^{58} - 12 q^{59} + 12 q^{60} + 15 q^{61} - 56 q^{62} + 8 q^{64} - 48 q^{65} + 72 q^{66} + 36 q^{67} + 52 q^{69} + 4 q^{71} + 56 q^{72} + 21 q^{73} - 56 q^{74} + 26 q^{75} - 20 q^{76} + 36 q^{78} + 40 q^{79} - 10 q^{80} - 44 q^{81} - 60 q^{82} + 20 q^{83} + 62 q^{85} + 16 q^{86} - 20 q^{87} - 66 q^{88} - 50 q^{89} - 96 q^{90} + 204 q^{92} - 12 q^{93} + 42 q^{94} - q^{95} - 32 q^{96} + 32 q^{97} - 150 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(931, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
931.2.f.a 931.f 7.c $2$ $7.434$ \(\Q(\sqrt{-3}) \) None \(-2\) \(2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-2\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots\)
931.2.f.b 931.f 7.c $2$ $7.434$ \(\Q(\sqrt{-3}) \) None \(0\) \(-2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
931.2.f.c 931.f 7.c $2$ $7.434$ \(\Q(\sqrt{-3}) \) None \(0\) \(2\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
931.2.f.d 931.f 7.c $4$ $7.434$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(-3\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+2\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
931.2.f.e 931.f 7.c $4$ $7.434$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-2\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
931.2.f.f 931.f 7.c $4$ $7.434$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{3})q^{3}+2\beta _{1}q^{5}-2q^{6}+\cdots\)
931.2.f.g 931.f 7.c $4$ $7.434$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(1\) \(-3\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(1-\beta _{1}+2\beta _{2}-\beta _{3})q^{3}+\cdots\)
931.2.f.h 931.f 7.c $4$ $7.434$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(1\) \(3\) \(6\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1+\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots\)
931.2.f.i 931.f 7.c $4$ $7.434$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}-\beta _{3})q^{3}+\cdots\)
931.2.f.j 931.f 7.c $4$ $7.434$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(3\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{3})q^{2}+(\beta _{1}+\beta _{2}+\beta _{3})q^{3}+\cdots\)
931.2.f.k 931.f 7.c $4$ $7.434$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(3\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{1}+\beta _{3})q^{2}+(-\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
931.2.f.l 931.f 7.c $6$ $7.434$ 6.0.1415907.1 None \(-2\) \(-3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}+\beta _{5})q^{2}+(-1-\beta _{1}-\beta _{4})q^{3}+\cdots\)
931.2.f.m 931.f 7.c $6$ $7.434$ 6.0.1415907.1 None \(-2\) \(3\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{4}+\beta _{5})q^{2}+(1+\beta _{1}+\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
931.2.f.n 931.f 7.c $8$ $7.434$ 8.0.2672476416.4 None \(0\) \(-2\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{4}-\beta _{7})q^{3}+(\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
931.2.f.o 931.f 7.c $8$ $7.434$ 8.0.2672476416.4 None \(0\) \(2\) \(8\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{7})q^{3}+(\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
931.2.f.p 931.f 7.c $14$ $7.434$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{10}q^{2}-\beta _{7}q^{3}+(-1-\beta _{2}-\beta _{4}+\cdots)q^{4}+\cdots\)
931.2.f.q 931.f 7.c $20$ $7.434$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(-4\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-\beta _{11}+\beta _{18})q^{3}+(-\beta _{14}+\cdots)q^{4}+\cdots\)
931.2.f.r 931.f 7.c $20$ $7.434$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(2\) \(4\) \(16\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(\beta _{11}-\beta _{18})q^{3}+(-\beta _{14}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(931, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(931, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(49, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(133, [\chi])\)\(^{\oplus 2}\)