Properties

Label 37.2.e
Level $37$
Weight $2$
Character orbit 37.e
Rep. character $\chi_{37}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $4$
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.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 37 \)
Character field: \(\Q(\zeta_{6})\)
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 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4 q + 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{9} + O(q^{10}) \) \( 4 q + 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{9} - 8 q^{10} - 12 q^{11} + 2 q^{12} + 12 q^{13} + 6 q^{15} + 2 q^{16} + 6 q^{17} + 12 q^{18} - 6 q^{19} + 6 q^{20} + 12 q^{21} + 6 q^{22} - 18 q^{24} + 4 q^{25} - 16 q^{27} + 2 q^{30} - 12 q^{33} - 4 q^{34} - 24 q^{35} + 4 q^{36} + 2 q^{37} - 12 q^{38} + 12 q^{39} + 12 q^{40} - 6 q^{41} - 12 q^{42} + 6 q^{44} - 2 q^{46} + 12 q^{47} + 4 q^{48} - 10 q^{49} + 24 q^{50} - 12 q^{52} + 12 q^{53} + 6 q^{55} + 36 q^{56} + 12 q^{57} - 4 q^{58} - 12 q^{59} - 6 q^{61} + 6 q^{62} + 48 q^{63} - 28 q^{64} - 12 q^{65} + 18 q^{67} - 12 q^{70} - 12 q^{71} - 36 q^{72} - 40 q^{75} + 6 q^{76} + 12 q^{77} - 12 q^{78} - 18 q^{79} - 2 q^{81} + 6 q^{83} - 24 q^{84} + 4 q^{85} + 6 q^{87} + 18 q^{89} - 8 q^{90} + 6 q^{92} - 36 q^{93} + 18 q^{94} + 18 q^{95} + 30 q^{96} + 18 q^{99} + O(q^{100}) \)

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
37.2.e.a 37.e 37.e $4$ $0.295$ \(\Q(\zeta_{12})\) None \(0\) \(2\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)