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Properties

Label 637.2.bs
Level $637$
Weight $2$
Character orbit 637.bs
Rep. character $\chi_{637}(25,\cdot)$
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.bs (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

\( 768 q - 24 q^{3} - 90 q^{4} + 36 q^{9} + O(q^{10}) \) \( 768 q - 24 q^{3} - 90 q^{4} + 36 q^{9} - 22 q^{10} - 46 q^{12} - 2 q^{13} - 2 q^{14} + 26 q^{16} - 36 q^{17} + 8 q^{22} - 26 q^{23} - 86 q^{25} - 22 q^{26} - 60 q^{27} - 24 q^{29} - 44 q^{30} + 80 q^{36} - 62 q^{38} - 29 q^{39} - 24 q^{40} + 40 q^{42} - 24 q^{43} + 20 q^{48} - 12 q^{49} + 8 q^{51} - 28 q^{52} - 92 q^{53} - 10 q^{55} - 230 q^{56} - 58 q^{61} - 72 q^{62} + 156 q^{64} - 2 q^{65} + 40 q^{66} - 180 q^{68} - 140 q^{69} + 2 q^{74} - 78 q^{75} + 6 q^{77} - 86 q^{78} - 20 q^{79} + 148 q^{81} + 268 q^{82} - 184 q^{87} - 50 q^{88} - 414 q^{90} + 22 q^{92} + 390 q^{94} + 132 q^{95} + O(q^{100}) \)

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.bs.a 637.bs 637.as $768$ $5.086$ None \(0\) \(-24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{42}]$