Properties

Label 13.2.e
Level 13
Weight 2
Character orbit e
Rep. character \(\chi_{13}(4,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 2
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 13.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(13, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\( 2q - 3q^{2} - 2q^{3} + q^{4} + 6q^{6} - q^{9} + O(q^{10}) \) \( 2q - 3q^{2} - 2q^{3} + q^{4} + 6q^{6} - q^{9} - 3q^{10} - 4q^{12} - 5q^{13} + 6q^{15} + 5q^{16} + 3q^{17} - 6q^{19} + 3q^{20} + 6q^{23} - 6q^{24} + 4q^{25} + 3q^{26} - 8q^{27} - 3q^{29} - 6q^{30} - 9q^{32} + q^{36} + 15q^{37} + 12q^{38} + 14q^{39} + 6q^{40} - 9q^{41} - 8q^{43} - 3q^{45} - 18q^{46} + 10q^{48} - 7q^{49} - 6q^{50} - 12q^{51} + 2q^{52} - 6q^{53} + 12q^{54} + 9q^{58} + 12q^{59} - q^{61} + 6q^{62} - 2q^{64} - 9q^{65} + 6q^{67} - 3q^{68} + 12q^{69} + 6q^{71} + 3q^{72} - 15q^{74} - 4q^{75} - 6q^{76} - 24q^{78} + 8q^{79} - 15q^{80} + 11q^{81} + 9q^{82} + 9q^{85} - 6q^{87} - 12q^{89} + 6q^{90} + 12q^{92} - 12q^{93} - 6q^{94} + 6q^{95} + 12q^{97} + 21q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(13, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
13.2.e.a \(2\) \(0.104\) \(\Q(\sqrt{-3}) \) None \(-3\) \(-2\) \(0\) \(0\) \(q+(-1-\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)