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Properties

Label 617.2.d
Level $617$
Weight $2$
Character orbit 617.d
Rep. character $\chi_{617}(142,\cdot)$
Character field $\Q(\zeta_{7})$
Dimension $300$
Newform subspaces $1$
Sturm bound $103$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 617 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 617.d (of order \(7\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 617 \)
Character field: \(\Q(\zeta_{7})\)
Newform subspaces: \( 1 \)
Sturm bound: \(103\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(617, [\chi])\).

Total New Old
Modular forms 312 312 0
Cusp forms 300 300 0
Eisenstein series 12 12 0

Trace form

\( 300 q - q^{2} - q^{3} - 47 q^{4} - 18 q^{5} - 9 q^{6} - q^{7} + 3 q^{8} - 43 q^{9} + O(q^{10}) \) \( 300 q - q^{2} - q^{3} - 47 q^{4} - 18 q^{5} - 9 q^{6} - q^{7} + 3 q^{8} - 43 q^{9} + 16 q^{10} - 5 q^{11} - 54 q^{12} - 5 q^{13} + 14 q^{14} - 2 q^{15} - 39 q^{16} - 13 q^{18} - 16 q^{19} - 14 q^{20} + 13 q^{21} - 63 q^{22} - 25 q^{23} + 25 q^{24} - 88 q^{25} - 2 q^{26} + 14 q^{27} + 5 q^{28} - 102 q^{29} - 63 q^{30} - 16 q^{31} + 11 q^{32} + 12 q^{33} + 13 q^{34} + 37 q^{35} - 33 q^{36} - 34 q^{37} - 5 q^{39} + 41 q^{40} - 18 q^{41} - 38 q^{42} + 25 q^{43} + 85 q^{44} - 11 q^{45} - 126 q^{46} + 21 q^{47} + 147 q^{48} - 31 q^{49} + 5 q^{50} + 20 q^{51} + 57 q^{52} - q^{53} + 97 q^{54} - 10 q^{55} + 24 q^{56} - 34 q^{57} - 18 q^{58} - 47 q^{59} + 75 q^{60} + 41 q^{61} + 61 q^{62} + 44 q^{63} - 67 q^{64} - 88 q^{65} - 83 q^{66} + 53 q^{67} - q^{68} - 68 q^{69} + 2 q^{70} - 30 q^{71} - 83 q^{72} + 68 q^{73} + 4 q^{74} - 120 q^{75} + 73 q^{76} + 99 q^{77} - 25 q^{78} + 5 q^{79} - 59 q^{80} + 31 q^{81} + 74 q^{82} + 45 q^{83} - 95 q^{84} - q^{85} - 26 q^{86} + 78 q^{87} + 60 q^{88} - 42 q^{90} + 47 q^{91} - 73 q^{92} - 57 q^{93} + 45 q^{94} + 26 q^{95} + 19 q^{96} - 3 q^{97} + 144 q^{98} + 138 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(617, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
617.2.d.a 617.d 617.d $300$ $4.927$ None 617.2.d.a \(-1\) \(-1\) \(-18\) \(-1\) $\mathrm{SU}(2)[C_{7}]$