Properties

Label 37.2.b
Level $37$
Weight $2$
Character orbit 37.b
Rep. character $\chi_{37}(36,\cdot)$
Character field $\Q$
Dimension $2$
Newform subspaces $1$
Sturm bound $6$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 37.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(37, [\chi])\).

Total New Old
Modular forms 4 4 0
Cusp forms 2 2 0
Eisenstein series 2 2 0

Trace form

\( 2 q - 2 q^{3} - 4 q^{4} + 6 q^{7} - 4 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{3} - 4 q^{4} + 6 q^{7} - 4 q^{9} + 8 q^{10} - 6 q^{11} + 4 q^{12} - 8 q^{16} - 6 q^{21} + 2 q^{25} + 24 q^{26} + 10 q^{27} - 12 q^{28} - 8 q^{30} + 6 q^{33} - 8 q^{34} + 8 q^{36} - 2 q^{37} - 24 q^{38} - 6 q^{41} + 12 q^{44} - 16 q^{46} + 6 q^{47} + 8 q^{48} + 4 q^{49} + 18 q^{53} + 16 q^{58} - 12 q^{63} + 16 q^{64} - 24 q^{65} - 24 q^{67} + 24 q^{70} - 6 q^{71} + 18 q^{73} - 24 q^{74} - 2 q^{75} - 18 q^{77} - 24 q^{78} + 2 q^{81} + 18 q^{83} + 12 q^{84} + 8 q^{85} + 24 q^{86} - 16 q^{90} + 24 q^{95} + 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(37, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
37.2.b.a 37.b 37.b $2$ $0.295$ \(\Q(\sqrt{-1}) \) None 37.2.b.a \(0\) \(-2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-q^{3}-2q^{4}-2iq^{5}-2iq^{6}+\cdots\)