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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
37.2.c.a \(2\) \(0.295\) \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)