Properties

Label 37.2.e
Level 37
Weight 2
Character orbit e
Rep. character \(\chi_{37}(11,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 4
Newforms 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: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(37, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
37.2.e.a \(4\) \(0.295\) \(\Q(\zeta_{12})\) None \(0\) \(2\) \(-6\) \(0\) \(q+\zeta_{12}q^{2}+(-\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{3}+\cdots\)