Properties

Label 13.3.d
Level 13
Weight 3
Character orbit d
Rep. character \(\chi_{13}(5,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 1
Sturm bound 3
Trace bound 0

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Defining parameters

Level: \( N \) = \( 13 \)
Weight: \( k \) = \( 3 \)
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: \(3\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(13, [\chi])\).

Total New Old
Modular forms 8 8 0
Cusp forms 4 4 0
Eisenstein series 4 4 0

Trace form

\( 4q - 4q^{2} - 4q^{3} + 8q^{5} - 16q^{6} - 12q^{7} + 36q^{8} + 8q^{9} + O(q^{10}) \) \( 4q - 4q^{2} - 4q^{3} + 8q^{5} - 16q^{6} - 12q^{7} + 36q^{8} + 8q^{9} - 4q^{11} + 8q^{13} + 4q^{14} - 28q^{15} - 84q^{16} + 32q^{18} + 16q^{20} + 32q^{21} + 88q^{22} + 24q^{24} - 88q^{26} - 52q^{27} + 4q^{28} + 40q^{29} + 40q^{31} + 20q^{32} - 76q^{33} - 108q^{34} - 68q^{35} + 40q^{37} + 92q^{39} + 84q^{40} + 32q^{41} + 76q^{42} - 172q^{44} + 56q^{45} + 132q^{46} - 4q^{47} - 76q^{48} - 128q^{50} + 80q^{52} - 80q^{53} + 152q^{54} + 64q^{55} - 40q^{57} - 140q^{58} + 56q^{59} - 116q^{60} - 296q^{61} - 64q^{63} + 56q^{65} + 112q^{66} - 84q^{67} + 444q^{68} - 32q^{70} + 284q^{71} - 48q^{72} + 100q^{74} + 80q^{76} - 232q^{78} + 64q^{79} - 88q^{80} - 220q^{81} - 52q^{83} - 184q^{84} - 144q^{85} - 24q^{86} + 160q^{87} + 200q^{89} + 156q^{91} - 456q^{92} + 80q^{93} - 452q^{94} + 320q^{96} - 68q^{97} + 224q^{98} + 152q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(13, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
13.3.d.a \(4\) \(0.354\) \(\Q(i, \sqrt{10})\) None \(-4\) \(-4\) \(8\) \(-12\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+(-1-\beta _{1}+\beta _{3})q^{3}+\cdots\)