Properties

Label 31.2.c
Level 31
Weight 2
Character orbit c
Rep. character \(\chi_{31}(5,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newforms 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: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(31, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
31.2.c.a \(4\) \(0.248\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-4\) \(2\) \(-2\) \(-2\) \(q+(-1+\beta _{3})q^{2}+(1+\beta _{1}+\beta _{2})q^{3}+\cdots\)