Properties

Label 36.2.e
Level 36
Weight 2
Character orbit e
Rep. character \(\chi_{36}(13,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 2
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.e (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
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 18 2 16
Cusp forms 6 2 4
Eisenstein series 12 0 12

Trace form

\( 2q - 3q^{5} + q^{7} - 6q^{9} + O(q^{10}) \) \( 2q - 3q^{5} + q^{7} - 6q^{9} - 3q^{11} + q^{13} + 9q^{15} + 12q^{17} - 8q^{19} + 3q^{21} + 3q^{23} - 4q^{25} - 3q^{29} - 5q^{31} - 9q^{33} - 6q^{35} + 4q^{37} - 3q^{39} - 3q^{41} + q^{43} + 9q^{45} + 9q^{47} + 6q^{49} - 12q^{53} + 18q^{55} + 3q^{59} + 13q^{61} - 3q^{63} + 3q^{65} + 7q^{67} - 9q^{69} - 24q^{71} - 20q^{73} - 12q^{75} + 3q^{77} - 11q^{79} + 18q^{81} + 9q^{83} - 18q^{85} - 9q^{87} + 12q^{89} + 2q^{91} + 15q^{93} + 12q^{95} - 11q^{97} + 9q^{99} + O(q^{100}) \)

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.e.a \(2\) \(0.287\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(-3\) \(1\) \(q+(1-2\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+\zeta_{6}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(36, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(36, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 2}\)