Properties

Label 31.2.c
Level $31$
Weight $2$
Character orbit 31.c
Rep. character $\chi_{31}(5,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $4$
Newform subspaces $1$
Sturm bound $5$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 31.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(31, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} - 6 q^{6} - 2 q^{7} - 12 q^{8} + O(q^{10}) \) \( 4 q - 4 q^{2} + 2 q^{3} + 4 q^{4} - 2 q^{5} - 6 q^{6} - 2 q^{7} - 12 q^{8} + 2 q^{10} + 2 q^{11} + 10 q^{12} + 2 q^{13} + 6 q^{14} - 4 q^{15} + 12 q^{16} + 6 q^{17} + 8 q^{18} - 6 q^{19} - 2 q^{20} + 6 q^{21} - 14 q^{22} - 16 q^{23} - 10 q^{24} + 8 q^{25} + 6 q^{26} - 4 q^{27} - 10 q^{28} - 16 q^{29} + 12 q^{30} - 20 q^{31} + 12 q^{32} + 28 q^{33} + 2 q^{34} + 4 q^{35} - 16 q^{36} - 2 q^{37} + 2 q^{38} - 12 q^{39} + 6 q^{40} - 2 q^{41} - 14 q^{42} + 2 q^{43} + 26 q^{44} + 16 q^{46} + 16 q^{47} + 6 q^{48} + 8 q^{49} - 8 q^{50} + 2 q^{51} - 14 q^{52} - 6 q^{53} - 4 q^{54} + 2 q^{55} + 10 q^{56} + 2 q^{57} + 6 q^{59} - 20 q^{60} + 20 q^{62} + 16 q^{63} - 28 q^{64} + 2 q^{65} - 60 q^{66} + 2 q^{67} - 10 q^{68} - 8 q^{69} - 12 q^{70} + 14 q^{71} + 8 q^{72} - 2 q^{73} + 2 q^{74} - 8 q^{75} + 2 q^{76} - 28 q^{77} + 20 q^{78} + 22 q^{79} - 6 q^{80} + 2 q^{81} + 26 q^{82} + 6 q^{83} + 22 q^{84} - 12 q^{85} + 26 q^{86} - 18 q^{88} - 16 q^{89} + 8 q^{90} + 12 q^{91} - 16 q^{92} - 22 q^{93} + 16 q^{94} + 12 q^{95} + 2 q^{96} + 32 q^{97} + 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(31, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
31.2.c.a 31.c 31.c $4$ $0.248$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)