Properties

Label 15.3.f
Level $15$
Weight $3$
Character orbit 15.f
Rep. character $\chi_{15}(7,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $1$
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: \(\Q(i)\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{3}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

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