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Properties

Label 31.2.d
Level $31$
Weight $2$
Character orbit 31.d
Rep. character $\chi_{31}(2,\cdot)$
Character field $\Q(\zeta_{5})$
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.d (of order \(5\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{5})\)
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 12 12 0
Cusp forms 4 4 0
Eisenstein series 8 8 0

Trace form

\( 4 q - 3 q^{2} + q^{3} + 3 q^{4} - 6 q^{5} - 2 q^{6} - 3 q^{7} - 5 q^{8} + 2 q^{9} + O(q^{10}) \) \( 4 q - 3 q^{2} + q^{3} + 3 q^{4} - 6 q^{5} - 2 q^{6} - 3 q^{7} - 5 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{11} + 2 q^{12} + 6 q^{13} + 6 q^{14} + q^{15} + 9 q^{16} - 3 q^{17} + 6 q^{18} - 5 q^{19} - 7 q^{20} + 3 q^{21} - 6 q^{22} + 11 q^{23} + 5 q^{24} - 6 q^{25} - 12 q^{26} - 5 q^{27} - 6 q^{28} + 5 q^{29} - 2 q^{30} - 11 q^{31} - 18 q^{32} - 8 q^{33} + 11 q^{34} + 12 q^{35} + 4 q^{36} - 8 q^{37} + 10 q^{38} + 9 q^{39} + 10 q^{40} + 8 q^{41} - 6 q^{42} + q^{43} + 6 q^{44} - 8 q^{45} - 7 q^{46} + 7 q^{47} + 6 q^{48} - 2 q^{49} + 12 q^{50} + 3 q^{51} - 3 q^{52} + 21 q^{53} + 10 q^{54} - 2 q^{55} - 20 q^{57} - 15 q^{58} + 5 q^{59} - 3 q^{60} + 8 q^{61} - 8 q^{62} - 24 q^{63} - 7 q^{64} - 9 q^{65} + 6 q^{66} - 8 q^{67} - 6 q^{68} - 11 q^{69} - 9 q^{70} - 7 q^{71} - 10 q^{72} + 21 q^{73} + 11 q^{74} - 9 q^{75} + 15 q^{76} + 24 q^{77} - 3 q^{78} - 6 q^{80} - q^{81} + 4 q^{82} - 14 q^{83} - 9 q^{84} + 2 q^{85} - 7 q^{86} + 30 q^{87} + 20 q^{88} + 5 q^{89} - 4 q^{90} + 18 q^{91} + 22 q^{92} - 4 q^{93} - 14 q^{94} - 5 q^{95} - 2 q^{96} - 3 q^{97} + 4 q^{98} + 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.d.a 31.d 31.d $4$ $0.248$ \(\Q(\zeta_{10})\) None \(-3\) \(1\) \(-6\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\zeta_{10}^{2})q^{2}+(1-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{3}+\cdots\)