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Properties

Label 36.2.h
Level $36$
Weight $2$
Character orbit 36.h
Rep. character $\chi_{36}(11,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $8$
Newform subspaces $1$
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: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
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

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(36, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
36.2.h.a 36.h 36.h $8$ $0.287$ 8.0.170772624.1 None \(-3\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{1}+\beta _{4}+\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots\)