Properties

Label 15.3.f
Level 15
Weight 3
Character orbit f
Rep. character \(\chi_{15}(7,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 4
Newforms 1
Sturm bound 6
Trace bound 0

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 15.f (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 5 \)
Character field: \(\Q(i)\)
Newforms: \( 1 \)
Sturm bound: \(6\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(15, [\chi])\).

Total New Old
Modular forms 12 4 8
Cusp forms 4 4 0
Eisenstein series 8 0 8

Trace form

\(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(4q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut -\mathstrut 4q^{5} \) \(\mathstrut -\mathstrut 12q^{6} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 16q^{11} \) \(\mathstrut +\mathstrut 24q^{12} \) \(\mathstrut -\mathstrut 32q^{13} \) \(\mathstrut +\mathstrut 24q^{15} \) \(\mathstrut -\mathstrut 20q^{16} \) \(\mathstrut -\mathstrut 40q^{17} \) \(\mathstrut -\mathstrut 12q^{18} \) \(\mathstrut -\mathstrut 36q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut +\mathstrut 56q^{23} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut +\mathstrut 88q^{26} \) \(\mathstrut +\mathstrut 44q^{28} \) \(\mathstrut -\mathstrut 24q^{30} \) \(\mathstrut -\mathstrut 16q^{31} \) \(\mathstrut -\mathstrut 76q^{32} \) \(\mathstrut -\mathstrut 36q^{33} \) \(\mathstrut -\mathstrut 40q^{35} \) \(\mathstrut +\mathstrut 12q^{36} \) \(\mathstrut +\mathstrut 64q^{37} \) \(\mathstrut -\mathstrut 96q^{38} \) \(\mathstrut +\mathstrut 48q^{40} \) \(\mathstrut -\mathstrut 56q^{41} \) \(\mathstrut +\mathstrut 12q^{42} \) \(\mathstrut -\mathstrut 8q^{43} \) \(\mathstrut +\mathstrut 36q^{45} \) \(\mathstrut -\mathstrut 136q^{46} \) \(\mathstrut +\mathstrut 128q^{47} \) \(\mathstrut +\mathstrut 48q^{48} \) \(\mathstrut +\mathstrut 164q^{50} \) \(\mathstrut +\mathstrut 72q^{51} \) \(\mathstrut -\mathstrut 80q^{52} \) \(\mathstrut +\mathstrut 56q^{53} \) \(\mathstrut -\mathstrut 124q^{55} \) \(\mathstrut -\mathstrut 72q^{57} \) \(\mathstrut -\mathstrut 12q^{58} \) \(\mathstrut -\mathstrut 84q^{60} \) \(\mathstrut +\mathstrut 200q^{61} \) \(\mathstrut +\mathstrut 88q^{62} \) \(\mathstrut +\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 112q^{65} \) \(\mathstrut +\mathstrut 24q^{66} \) \(\mathstrut -\mathstrut 200q^{67} \) \(\mathstrut -\mathstrut 104q^{68} \) \(\mathstrut -\mathstrut 60q^{70} \) \(\mathstrut -\mathstrut 272q^{71} \) \(\mathstrut -\mathstrut 36q^{72} \) \(\mathstrut +\mathstrut 76q^{73} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut +\mathstrut 312q^{76} \) \(\mathstrut +\mathstrut 88q^{77} \) \(\mathstrut +\mathstrut 120q^{78} \) \(\mathstrut +\mathstrut 164q^{80} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 128q^{82} \) \(\mathstrut -\mathstrut 16q^{83} \) \(\mathstrut +\mathstrut 232q^{85} \) \(\mathstrut -\mathstrut 224q^{86} \) \(\mathstrut -\mathstrut 84q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut -\mathstrut 96q^{90} \) \(\mathstrut -\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 104q^{92} \) \(\mathstrut -\mathstrut 72q^{93} \) \(\mathstrut +\mathstrut 144q^{95} \) \(\mathstrut -\mathstrut 84q^{96} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut -\mathstrut 188q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(15, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.3.f.a \(4\) \(0.409\) \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(-4\) \(4\) \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)