Properties

Label 36.2.h
Level 36
Weight 2
Character orbit h
Rep. character \(\chi_{36}(11,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 8
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 36.h (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 36 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(36, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8q - 3q^{2} - q^{4} - 6q^{5} - 3q^{6} - 6q^{9} + O(q^{10}) \) \( 8q - 3q^{2} - q^{4} - 6q^{5} - 3q^{6} - 6q^{9} - 8q^{10} + 6q^{12} - 2q^{13} + 12q^{14} - q^{16} + 18q^{18} + 18q^{20} - 6q^{21} + 3q^{22} + 3q^{24} - 6q^{25} - 12q^{28} + 6q^{29} - 18q^{30} - 33q^{32} + 24q^{33} + 7q^{34} - 33q^{36} - 8q^{37} - 27q^{38} + 10q^{40} + 24q^{41} - 18q^{42} + 6q^{45} + 12q^{46} + 21q^{48} - 10q^{49} + 21q^{50} + 16q^{52} + 39q^{54} + 18q^{56} + 6q^{57} + 4q^{58} + 6q^{60} - 2q^{61} + 26q^{64} - 30q^{65} - 24q^{66} - 15q^{68} - 30q^{69} - 6q^{70} - 21q^{72} + 4q^{73} - 30q^{74} - 3q^{76} - 30q^{77} - 12q^{78} - 30q^{81} + 10q^{82} + 30q^{84} + 8q^{85} + 21q^{86} - 21q^{88} + 6q^{90} + 24q^{92} + 30q^{93} - 18q^{94} + 12q^{96} + 4q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(36, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
36.2.h.a \(8\) \(0.287\) 8.0.170772624.1 None \(-3\) \(0\) \(-6\) \(0\) \(q+(1-\beta _{1}+\beta _{4}+\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)