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Properties

Label 637.2.bt
Level $637$
Weight $2$
Character orbit 637.bt
Rep. character $\chi_{637}(36,\cdot)$
Character field $\Q(\zeta_{42})$
Dimension $768$
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.bt (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{42})\)
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 816 816 0
Cusp forms 768 768 0
Eisenstein series 48 48 0

Trace form

\( 768 q - 15 q^{2} - 3 q^{3} - 69 q^{4} - 15 q^{6} - 21 q^{7} + 57 q^{9} + O(q^{10}) \) \( 768 q - 15 q^{2} - 3 q^{3} - 69 q^{4} - 15 q^{6} - 21 q^{7} + 57 q^{9} - 13 q^{10} - 27 q^{11} - 16 q^{12} - 8 q^{13} - 20 q^{14} - 33 q^{15} + 47 q^{16} - 9 q^{17} - 30 q^{19} - 15 q^{20} - 13 q^{22} - 5 q^{23} - 21 q^{24} + 100 q^{25} + 50 q^{26} - 24 q^{27} + 105 q^{28} - 9 q^{29} - 14 q^{30} - 39 q^{32} + 9 q^{33} - 27 q^{35} - 49 q^{36} - 30 q^{37} - 56 q^{38} - 14 q^{39} - 132 q^{40} - 33 q^{41} - 53 q^{42} + 9 q^{43} - 120 q^{45} + 15 q^{46} - 88 q^{48} - 27 q^{49} - 378 q^{50} - 16 q^{51} + 50 q^{52} - 62 q^{53} + 6 q^{54} - 22 q^{55} - 107 q^{56} - 15 q^{58} - 63 q^{59} + 2 q^{61} - 15 q^{62} - 117 q^{63} + 228 q^{64} - 62 q^{65} - 116 q^{66} - 54 q^{67} - 168 q^{68} + 49 q^{69} + 15 q^{71} - 39 q^{72} - 19 q^{74} - 87 q^{75} + 9 q^{76} - 78 q^{77} + 16 q^{78} - 8 q^{79} + 60 q^{80} + 61 q^{81} + 136 q^{82} - 39 q^{84} - 165 q^{85} - 49 q^{87} - 47 q^{88} + 120 q^{89} + 468 q^{90} - 42 q^{91} - 236 q^{92} + 108 q^{93} - 6 q^{94} + 84 q^{95} + 180 q^{97} - 147 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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.bt.a 637.bt 637.at $768$ $5.086$ None \(-15\) \(-3\) \(0\) \(-21\) $\mathrm{SU}(2)[C_{42}]$