Properties

Label 637.2.bj
Level $637$
Weight $2$
Character orbit 637.bj
Rep. character $\chi_{637}(9,\cdot)$
Character field $\Q(\zeta_{21})$
Dimension $756$
Newform subspaces $1$
Sturm bound $130$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.bj (of order \(21\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{21})\)
Newform subspaces: \( 1 \)
Sturm bound: \(130\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(637, [\chi])\).

Total New Old
Modular forms 804 804 0
Cusp forms 756 756 0
Eisenstein series 48 48 0

Trace form

\( 756 q - 8 q^{2} + q^{3} + 52 q^{4} - 26 q^{5} - q^{6} - 11 q^{7} - 16 q^{8} - 121 q^{9} + O(q^{10}) \) \( 756 q - 8 q^{2} + q^{3} + 52 q^{4} - 26 q^{5} - q^{6} - 11 q^{7} - 16 q^{8} - 121 q^{9} - 5 q^{10} - q^{11} - 30 q^{12} - 10 q^{13} - 30 q^{14} - 8 q^{15} + 40 q^{16} - 14 q^{17} - 15 q^{18} - 14 q^{19} - 9 q^{20} - 34 q^{21} - 5 q^{22} - 8 q^{23} + 37 q^{24} + 27 q^{25} - 2 q^{27} + 85 q^{28} - 3 q^{29} + 2 q^{30} - 27 q^{31} - 10 q^{32} + 7 q^{33} + 10 q^{35} + 42 q^{36} - 111 q^{37} - 54 q^{38} + 35 q^{39} - 32 q^{40} + 4 q^{41} - 39 q^{42} - 5 q^{43} + 26 q^{44} - 17 q^{45} - 27 q^{46} - 89 q^{47} + 94 q^{48} + 13 q^{49} + 35 q^{50} - 66 q^{51} + 4 q^{52} - 64 q^{53} - 19 q^{54} + 17 q^{55} + 24 q^{56} - 73 q^{57} - 13 q^{58} + 4 q^{59} - 49 q^{60} + 58 q^{61} - 9 q^{62} + 117 q^{63} - 156 q^{64} - 34 q^{65} + 33 q^{66} - 14 q^{67} + 148 q^{68} - 114 q^{69} - 44 q^{70} - 224 q^{71} + 103 q^{72} - 32 q^{73} + 4 q^{74} + 26 q^{75} - 109 q^{76} - 75 q^{77} - q^{78} - 28 q^{79} - 22 q^{80} - 121 q^{81} + 94 q^{82} - 23 q^{83} - 15 q^{84} - 62 q^{85} - 78 q^{86} - 100 q^{87} + 41 q^{88} + 65 q^{89} + 309 q^{90} + 177 q^{91} + 24 q^{92} - 234 q^{93} - 52 q^{94} - 93 q^{95} + 386 q^{96} + 58 q^{97} + 196 q^{98} - 4 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(637, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
637.2.bj.a 637.bj 637.aj $756$ $5.086$ None \(-8\) \(1\) \(-26\) \(-11\) $\mathrm{SU}(2)[C_{21}]$