Properties

Label 637.2.bg
Level $637$
Weight $2$
Character orbit 637.bg
Rep. character $\chi_{637}(64,\cdot)$
Character field $\Q(\zeta_{14})$
Dimension $372$
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.bg (of order \(14\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 637 \)
Character field: \(\Q(\zeta_{14})\)
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 396 396 0
Cusp forms 372 372 0
Eisenstein series 24 24 0

Trace form

\( 372 q - 14 q^{3} + 46 q^{4} - 64 q^{9} + O(q^{10}) \) \( 372 q - 14 q^{3} + 46 q^{4} - 64 q^{9} - 14 q^{10} + 6 q^{12} - 15 q^{13} - 10 q^{14} - 78 q^{16} - 6 q^{17} - 38 q^{22} - 10 q^{23} + 36 q^{25} - 5 q^{26} - 2 q^{27} - 6 q^{29} - 52 q^{30} - 36 q^{35} + 50 q^{36} + 32 q^{38} - 51 q^{39} + 6 q^{40} - 94 q^{42} + 22 q^{43} + 160 q^{48} + 20 q^{49} + 10 q^{51} - 85 q^{52} + 68 q^{53} - 68 q^{55} - 40 q^{56} + 98 q^{61} + 12 q^{62} - 38 q^{64} + 17 q^{65} - 112 q^{66} + 120 q^{68} + 158 q^{69} - 62 q^{74} - 16 q^{75} + 12 q^{77} + 35 q^{78} - 68 q^{79} + 28 q^{81} - 28 q^{82} - 86 q^{87} + 44 q^{88} - 198 q^{90} + 9 q^{91} - 52 q^{92} - 48 q^{94} + 120 q^{95} + O(q^{100}) \)

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.bg.a 637.bg 637.ag $372$ $5.086$ None \(0\) \(-14\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$