Properties

Label 13.5.f
Level 13
Weight 5
Character orbit f
Rep. character \(\chi_{13}(2,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 16
Newforms 1
Sturm bound 5
Trace bound 0

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 13.f (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q(\zeta_{12})\)
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 24 24 0
Cusp forms 16 16 0
Eisenstein series 8 8 0

Trace form

\( 16q - 4q^{2} - 2q^{3} - 6q^{4} + 8q^{5} - 38q^{6} + 56q^{7} + 90q^{8} - 164q^{9} + O(q^{10}) \) \( 16q - 4q^{2} - 2q^{3} - 6q^{4} + 8q^{5} - 38q^{6} + 56q^{7} + 90q^{8} - 164q^{9} - 486q^{10} - 100q^{11} + 294q^{13} + 808q^{14} + 346q^{15} + 230q^{16} + 984q^{17} + 2434q^{18} - 1498q^{19} - 3962q^{20} - 1076q^{21} - 1524q^{22} - 1014q^{23} - 2142q^{24} + 614q^{26} + 3352q^{27} + 5764q^{28} + 814q^{29} + 9162q^{30} + 4060q^{31} - 4996q^{32} - 5636q^{33} - 2502q^{34} - 4892q^{35} - 15750q^{36} - 1790q^{37} + 6982q^{39} + 18816q^{40} + 4280q^{41} - 1204q^{42} - 1368q^{43} + 10736q^{44} - 6806q^{45} - 15246q^{46} + 1484q^{47} - 3002q^{48} - 11820q^{49} - 13574q^{50} + 1432q^{52} + 7204q^{53} + 13240q^{54} + 6936q^{55} + 8124q^{56} + 12736q^{57} + 3030q^{58} - 2380q^{59} - 6472q^{60} - 162q^{61} + 19614q^{62} + 12004q^{63} - 5248q^{65} - 23872q^{66} - 14854q^{67} - 6444q^{68} + 2412q^{69} - 34524q^{70} - 8050q^{71} + 15420q^{72} - 15448q^{73} - 2882q^{74} + 8280q^{75} + 10622q^{76} - 11672q^{78} - 17064q^{79} + 2564q^{80} + 2128q^{81} - 5346q^{82} + 12788q^{83} + 25948q^{84} + 35382q^{85} + 67260q^{86} + 29342q^{87} + 40836q^{88} + 20492q^{89} + 8996q^{91} - 49884q^{92} - 78920q^{93} - 30606q^{94} - 98574q^{95} - 94664q^{96} + 50944q^{97} + 61484q^{98} - 21632q^{99} + O(q^{100}) \)

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.f.a \(16\) \(1.344\) \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(-4\) \(-2\) \(8\) \(56\) \(q-\beta _{12}q^{2}+(-1-\beta _{8}+\beta _{9}+\beta _{12}+\cdots)q^{3}+\cdots\)