Properties

Label 37.2.c
Level $37$
Weight $2$
Character orbit 37.c
Rep. character $\chi_{37}(10,\cdot)$
Character field $\Q(\zeta_{3})$
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.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{3})\)
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 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\( 2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9} + O(q^{10}) \) \( 2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{13} + 4 q^{14} + q^{16} - 3 q^{17} + 3 q^{18} + 6 q^{19} + q^{20} + 2 q^{22} - 8 q^{23} + 4 q^{25} - 4 q^{26} + 2 q^{28} + 18 q^{29} - 20 q^{31} - 5 q^{32} - 3 q^{34} - 2 q^{35} + 6 q^{36} - 11 q^{37} - 12 q^{38} + 3 q^{40} + 9 q^{41} + 4 q^{43} - 2 q^{44} - 6 q^{45} + 4 q^{46} + 12 q^{47} + 3 q^{49} + 4 q^{50} - 2 q^{52} + 2 q^{53} + 2 q^{55} + 6 q^{56} - 9 q^{58} + 4 q^{59} - q^{61} + 10 q^{62} - 12 q^{63} + 14 q^{64} + 2 q^{65} + 10 q^{67} - 6 q^{68} - 2 q^{70} - 6 q^{71} - 9 q^{72} - 20 q^{73} + 10 q^{74} - 6 q^{76} + 4 q^{77} - 10 q^{79} - 2 q^{80} - 9 q^{81} - 18 q^{82} + 12 q^{83} + 6 q^{85} - 2 q^{86} + 12 q^{88} - 7 q^{89} + 3 q^{90} + 4 q^{91} - 4 q^{92} - 6 q^{94} + 6 q^{95} + 14 q^{97} + 3 q^{98} - 6 q^{99} + O(q^{100}) \)

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.c.a 37.c 37.c $2$ $0.295$ \(\Q(\sqrt{-3}) \) None 37.2.c.a \(-1\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)