Properties

Label 15.3.c
Level 15
Weight 3
Character orbit c
Rep. character \(\chi_{15}(11,\cdot)\)
Character field \(\Q\)
Dimension 2
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.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
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 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\(2q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 2q^{4} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut -\mathstrut 12q^{7} \) \(\mathstrut -\mathstrut 2q^{9} \) \(\mathstrut +\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 4q^{12} \) \(\mathstrut +\mathstrut 32q^{13} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut -\mathstrut 38q^{16} \) \(\mathstrut -\mathstrut 40q^{18} \) \(\mathstrut -\mathstrut 4q^{19} \) \(\mathstrut +\mathstrut 24q^{21} \) \(\mathstrut +\mathstrut 20q^{22} \) \(\mathstrut +\mathstrut 30q^{24} \) \(\mathstrut -\mathstrut 10q^{25} \) \(\mathstrut +\mathstrut 44q^{27} \) \(\mathstrut +\mathstrut 12q^{28} \) \(\mathstrut -\mathstrut 20q^{30} \) \(\mathstrut -\mathstrut 36q^{31} \) \(\mathstrut -\mathstrut 20q^{33} \) \(\mathstrut +\mathstrut 20q^{34} \) \(\mathstrut +\mathstrut 2q^{36} \) \(\mathstrut -\mathstrut 32q^{37} \) \(\mathstrut -\mathstrut 64q^{39} \) \(\mathstrut +\mathstrut 30q^{40} \) \(\mathstrut -\mathstrut 60q^{42} \) \(\mathstrut +\mathstrut 32q^{43} \) \(\mathstrut +\mathstrut 40q^{45} \) \(\mathstrut +\mathstrut 60q^{46} \) \(\mathstrut +\mathstrut 76q^{48} \) \(\mathstrut -\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 20q^{51} \) \(\mathstrut -\mathstrut 32q^{52} \) \(\mathstrut +\mathstrut 70q^{54} \) \(\mathstrut -\mathstrut 20q^{55} \) \(\mathstrut +\mathstrut 8q^{57} \) \(\mathstrut -\mathstrut 140q^{58} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 164q^{61} \) \(\mathstrut +\mathstrut 12q^{63} \) \(\mathstrut -\mathstrut 82q^{64} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut +\mathstrut 48q^{67} \) \(\mathstrut -\mathstrut 60q^{69} \) \(\mathstrut -\mathstrut 60q^{70} \) \(\mathstrut -\mathstrut 120q^{72} \) \(\mathstrut -\mathstrut 148q^{73} \) \(\mathstrut +\mathstrut 20q^{75} \) \(\mathstrut +\mathstrut 4q^{76} \) \(\mathstrut +\mathstrut 160q^{78} \) \(\mathstrut +\mathstrut 276q^{79} \) \(\mathstrut -\mathstrut 158q^{81} \) \(\mathstrut +\mathstrut 280q^{82} \) \(\mathstrut -\mathstrut 24q^{84} \) \(\mathstrut -\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 140q^{87} \) \(\mathstrut +\mathstrut 60q^{88} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut -\mathstrut 192q^{91} \) \(\mathstrut +\mathstrut 72q^{93} \) \(\mathstrut -\mathstrut 220q^{94} \) \(\mathstrut -\mathstrut 70q^{96} \) \(\mathstrut -\mathstrut 332q^{97} \) \(\mathstrut +\mathstrut 80q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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.c.a \(2\) \(0.409\) \(\Q(\sqrt{-5}) \) None \(0\) \(-4\) \(0\) \(-12\) \(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots\)