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Properties

Label 31.3.f
Level $31$
Weight $3$
Character orbit 31.f
Rep. character $\chi_{31}(15,\cdot)$
Character field $\Q(\zeta_{10})$
Dimension $20$
Newform subspaces $1$
Sturm bound $8$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 31 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 31.f (of order \(10\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 31 \)
Character field: \(\Q(\zeta_{10})\)
Newform subspaces: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(31, [\chi])\).

Total New Old
Modular forms 28 28 0
Cusp forms 20 20 0
Eisenstein series 8 8 0

Trace form

\( 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + O(q^{10}) \) \( 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + 12 q^{10} - 10 q^{11} + 90 q^{12} + 10 q^{13} - 85 q^{15} - 103 q^{16} + 35 q^{17} + 6 q^{18} + 47 q^{19} - 125 q^{20} - 125 q^{21} + 150 q^{22} + 75 q^{23} + 195 q^{24} + 82 q^{25} + 25 q^{27} + 88 q^{28} + 5 q^{29} + 73 q^{31} + 226 q^{32} - 206 q^{33} - 265 q^{34} - 50 q^{35} - 520 q^{36} + 8 q^{38} + 91 q^{39} - 466 q^{40} - 98 q^{41} + 245 q^{43} + 380 q^{44} - 162 q^{45} - 445 q^{46} - 187 q^{47} + 570 q^{48} + 328 q^{49} - 44 q^{50} + 185 q^{51} - 15 q^{52} + 25 q^{53} + 920 q^{54} + 190 q^{55} + 64 q^{56} - 85 q^{58} - 173 q^{59} + 275 q^{60} - 40 q^{62} + 252 q^{63} - 469 q^{64} - 345 q^{65} - 564 q^{66} + 76 q^{67} - 197 q^{69} - 11 q^{70} - 467 q^{71} - 982 q^{72} - 15 q^{73} + 45 q^{74} - 175 q^{75} + 55 q^{76} - 320 q^{77} - 91 q^{78} + 500 q^{79} + 1030 q^{80} + 117 q^{81} + 178 q^{82} - 50 q^{83} + 65 q^{84} + 20 q^{85} + 1125 q^{86} - 366 q^{87} + 55 q^{89} + 444 q^{90} + 300 q^{91} + 502 q^{93} + 62 q^{94} - 559 q^{95} - 10 q^{96} - 405 q^{97} - 1000 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(31, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
31.3.f.a 31.f 31.f $20$ $0.845$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None 31.3.f.a \(-3\) \(-5\) \(-14\) \(-1\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{10}q^{2}-\beta _{13}q^{3}+(3\beta _{11}+\beta _{19})q^{4}+\cdots\)