Properties

Label 13.5.d
Level 13
Weight 5
Character orbit d
Rep. character \(\chi_{13}(5,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 6
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 13.d (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(5\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(13, [\chi])\).

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\( 6q - 2q^{2} - 4q^{3} - 14q^{5} + 32q^{6} + 48q^{7} - 96q^{8} - 58q^{9} + O(q^{10}) \) \( 6q - 2q^{2} - 4q^{3} - 14q^{5} + 32q^{6} + 48q^{7} - 96q^{8} - 58q^{9} - 32q^{11} - 244q^{14} + 404q^{15} + 1044q^{16} - 802q^{18} + 732q^{19} + 428q^{20} - 2128q^{21} - 1632q^{22} - 24q^{24} + 910q^{26} + 236q^{27} + 1884q^{28} + 4184q^{29} - 3468q^{31} + 2092q^{32} + 2324q^{33} - 5304q^{34} - 4204q^{35} - 1758q^{37} + 1196q^{39} - 708q^{40} + 4750q^{41} + 9532q^{42} - 3956q^{44} + 830q^{45} + 516q^{46} - 6872q^{47} - 9436q^{48} - 322q^{50} + 3900q^{52} + 2108q^{53} - 184q^{54} + 6408q^{55} - 5800q^{57} + 6516q^{58} + 4372q^{59} + 1324q^{60} + 5988q^{61} - 652q^{63} - 5018q^{65} - 4592q^{66} + 72q^{67} - 10572q^{68} + 7368q^{70} - 14672q^{71} - 7980q^{72} + 5874q^{73} + 1544q^{74} + 3576q^{76} + 5720q^{78} + 2616q^{79} - 12080q^{80} - 19450q^{81} + 19264q^{83} + 6296q^{84} + 4164q^{85} + 29376q^{86} + 35584q^{87} - 986q^{89} - 30888q^{91} + 5304q^{92} - 9520q^{93} - 36156q^{94} + 20720q^{96} - 23154q^{97} - 41426q^{98} + 17492q^{99} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(13, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
13.5.d.a \(6\) \(1.344\) 6.0.\(\cdots\).1 None \(-2\) \(-4\) \(-14\) \(48\) \(q-\beta _{1}q^{2}+(-1+\beta _{4})q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)