Properties

Label 15.4.e
Level 15
Weight 4
Character orbit e
Rep. character \(\chi_{15}(2,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 8
Newforms 1
Sturm bound 8
Trace bound 0

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 15.e (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 15 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(8\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(15, [\chi])\).

Total New Old
Modular forms 16 16 0
Cusp forms 8 8 0
Eisenstein series 8 8 0

Trace form

\( 8q - 6q^{3} - 12q^{6} - 16q^{7} + O(q^{10}) \) \( 8q - 6q^{3} - 12q^{6} - 16q^{7} - 100q^{10} + 132q^{12} + 68q^{13} + 90q^{15} + 284q^{16} - 240q^{18} - 492q^{21} - 500q^{22} - 220q^{25} + 702q^{27} + 508q^{28} + 660q^{30} + 616q^{31} - 240q^{33} - 804q^{36} - 1156q^{37} - 600q^{40} + 540q^{42} + 548q^{43} + 180q^{45} + 736q^{46} - 1116q^{48} - 852q^{51} + 224q^{52} + 460q^{55} + 684q^{57} + 60q^{58} + 540q^{60} + 16q^{61} + 1428q^{63} + 2040q^{66} + 404q^{67} - 2220q^{70} - 1800q^{72} - 2512q^{73} - 2910q^{75} - 1488q^{76} - 360q^{78} + 288q^{81} + 2800q^{82} + 4940q^{85} - 1680q^{87} + 2460q^{88} + 600q^{90} - 1304q^{91} + 3408q^{93} + 4164q^{96} + 1904q^{97} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(15, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.4.e.a \(8\) \(0.885\) 8.0.\(\cdots\).8 None \(0\) \(-6\) \(0\) \(-16\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)