Properties

Label 31.2.g
Level 31
Weight 2
Character orbit g
Rep. character \(\chi_{31}(7,\cdot)\)
Character field \(\Q(\zeta_{15})\)
Dimension 16
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 31 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 31.g (of order \(15\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 31 \)
Character field: \(\Q(\zeta_{15})\)
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 32 32 0
Cusp forms 16 16 0
Eisenstein series 16 16 0

Trace form

\(16q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 14q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 17q^{8} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(16q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut -\mathstrut 14q^{4} \) \(\mathstrut -\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 17q^{8} \) \(\mathstrut -\mathstrut 10q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 7q^{11} \) \(\mathstrut +\mathstrut 5q^{12} \) \(\mathstrut -\mathstrut 7q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 14q^{15} \) \(\mathstrut -\mathstrut 2q^{16} \) \(\mathstrut -\mathstrut 6q^{17} \) \(\mathstrut -\mathstrut 3q^{18} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 37q^{20} \) \(\mathstrut +\mathstrut 9q^{21} \) \(\mathstrut +\mathstrut 9q^{22} \) \(\mathstrut +\mathstrut q^{23} \) \(\mathstrut -\mathstrut 20q^{24} \) \(\mathstrut -\mathstrut 13q^{25} \) \(\mathstrut +\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 14q^{29} \) \(\mathstrut -\mathstrut 22q^{30} \) \(\mathstrut +\mathstrut 15q^{31} \) \(\mathstrut -\mathstrut 42q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut -\mathstrut 32q^{34} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut +\mathstrut q^{36} \) \(\mathstrut -\mathstrut 8q^{37} \) \(\mathstrut +\mathstrut 8q^{38} \) \(\mathstrut -\mathstrut 3q^{39} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut -\mathstrut 8q^{41} \) \(\mathstrut +\mathstrut 69q^{42} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 39q^{44} \) \(\mathstrut +\mathstrut 65q^{45} \) \(\mathstrut +\mathstrut 34q^{46} \) \(\mathstrut +\mathstrut 14q^{47} \) \(\mathstrut +\mathstrut 34q^{48} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 3q^{50} \) \(\mathstrut -\mathstrut 42q^{51} \) \(\mathstrut +\mathstrut 29q^{52} \) \(\mathstrut +\mathstrut 6q^{53} \) \(\mathstrut -\mathstrut 46q^{54} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut -\mathstrut 30q^{56} \) \(\mathstrut -\mathstrut 17q^{57} \) \(\mathstrut -\mathstrut 15q^{58} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 75q^{60} \) \(\mathstrut -\mathstrut 60q^{61} \) \(\mathstrut -\mathstrut 25q^{62} \) \(\mathstrut -\mathstrut 46q^{63} \) \(\mathstrut +\mathstrut 23q^{64} \) \(\mathstrut -\mathstrut 12q^{65} \) \(\mathstrut -\mathstrut 30q^{66} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut +\mathstrut 30q^{68} \) \(\mathstrut +\mathstrut 38q^{69} \) \(\mathstrut +\mathstrut 12q^{70} \) \(\mathstrut -\mathstrut 14q^{71} \) \(\mathstrut +\mathstrut 37q^{72} \) \(\mathstrut +\mathstrut 2q^{73} \) \(\mathstrut +\mathstrut 13q^{74} \) \(\mathstrut +\mathstrut 13q^{75} \) \(\mathstrut -\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut -\mathstrut 15q^{78} \) \(\mathstrut +\mathstrut 18q^{79} \) \(\mathstrut +\mathstrut 36q^{80} \) \(\mathstrut +\mathstrut 23q^{81} \) \(\mathstrut +\mathstrut 14q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 8q^{84} \) \(\mathstrut +\mathstrut 37q^{85} \) \(\mathstrut -\mathstrut 26q^{86} \) \(\mathstrut +\mathstrut 15q^{87} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 64q^{92} \) \(\mathstrut +\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 44q^{94} \) \(\mathstrut -\mathstrut 22q^{95} \) \(\mathstrut +\mathstrut 8q^{96} \) \(\mathstrut +\mathstrut 3q^{97} \) \(\mathstrut -\mathstrut 10q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.g.a \(16\) \(0.248\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-6\) \(-12\) \(-3\) \(2\) \(q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots\)