Properties

Label 45.2.e
Level $45$
Weight $2$
Character orbit 45.e
Rep. character $\chi_{45}(16,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $2$
Sturm bound $12$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 45.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(12\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(45, [\chi])\).

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

Trace form

\( 8q - 2q^{2} - 2q^{3} - 4q^{4} - 2q^{5} - 4q^{6} - 2q^{7} - 4q^{9} + O(q^{10}) \) \( 8q - 2q^{2} - 2q^{3} - 4q^{4} - 2q^{5} - 4q^{6} - 2q^{7} - 4q^{9} + 4q^{11} + 14q^{12} - 2q^{13} + 12q^{14} - 2q^{15} - 4q^{16} + 4q^{17} - 20q^{18} - 8q^{19} - 6q^{20} + 6q^{22} - 6q^{23} + 24q^{24} - 4q^{25} - 8q^{26} - 2q^{27} + 16q^{28} + 8q^{29} + 14q^{30} - 8q^{31} - 22q^{32} + 20q^{33} + 16q^{35} + 16q^{36} + 4q^{37} + 10q^{38} - 20q^{39} - 6q^{40} + 8q^{41} - 42q^{42} - 2q^{43} - 40q^{44} + 8q^{45} - 20q^{47} - 10q^{48} - 2q^{50} - 16q^{51} + 10q^{52} - 8q^{53} - 4q^{54} + 22q^{57} + 18q^{58} + 16q^{59} - 22q^{60} - 8q^{61} + 84q^{62} + 24q^{63} - 16q^{64} - 6q^{65} - 8q^{66} - 8q^{67} + 26q^{68} + 48q^{69} + 6q^{70} - 16q^{71} + 6q^{72} - 8q^{73} + 20q^{74} - 2q^{75} + 4q^{76} - 6q^{77} + 2q^{78} + 4q^{79} + 12q^{80} - 28q^{81} - 48q^{82} + 6q^{83} - 36q^{84} + 6q^{85} - 20q^{86} - 26q^{87} + 18q^{88} - 48q^{89} - 2q^{90} + 32q^{91} - 36q^{92} - 42q^{93} + 24q^{94} - 12q^{95} + 28q^{96} + 16q^{97} - 76q^{98} + 16q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(45, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
45.2.e.a \(2\) \(0.359\) \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(1\) \(3\) \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
45.2.e.b \(6\) \(0.359\) 6.0.954288.1 None \(-1\) \(1\) \(-3\) \(-5\) \(q+(-\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5})q^{2}+\beta _{4}q^{3}+\cdots\)