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

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

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 \(0\) \(-6\) \(0\) \(-16\) \(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{5})q^{3}+(\beta _{2}+\cdots)q^{4}+\cdots\)