Properties

Label 15.5.c
Level 15
Weight 5
Character orbit c
Rep. character \(\chi_{15}(11,\cdot)\)
Character field \(\Q\)
Dimension 6
Newforms 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) = \( 15 = 3 \cdot 5 \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 15.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 3 \)
Character field: \(\Q\)
Newforms: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(15, [\chi])\).

Total New Old
Modular forms 10 6 4
Cusp forms 6 6 0
Eisenstein series 4 0 4

Trace form

\(6q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 50q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 76q^{7} \) \(\mathstrut +\mathstrut 118q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 50q^{4} \) \(\mathstrut -\mathstrut 2q^{6} \) \(\mathstrut +\mathstrut 76q^{7} \) \(\mathstrut +\mathstrut 118q^{9} \) \(\mathstrut +\mathstrut 50q^{10} \) \(\mathstrut -\mathstrut 452q^{12} \) \(\mathstrut -\mathstrut 424q^{13} \) \(\mathstrut +\mathstrut 50q^{15} \) \(\mathstrut +\mathstrut 802q^{16} \) \(\mathstrut +\mathstrut 1160q^{18} \) \(\mathstrut -\mathstrut 244q^{19} \) \(\mathstrut -\mathstrut 876q^{21} \) \(\mathstrut +\mathstrut 340q^{22} \) \(\mathstrut -\mathstrut 786q^{24} \) \(\mathstrut -\mathstrut 750q^{25} \) \(\mathstrut -\mathstrut 352q^{27} \) \(\mathstrut -\mathstrut 3764q^{28} \) \(\mathstrut +\mathstrut 2200q^{30} \) \(\mathstrut +\mathstrut 3772q^{31} \) \(\mathstrut +\mathstrut 4420q^{33} \) \(\mathstrut +\mathstrut 3124q^{34} \) \(\mathstrut -\mathstrut 7606q^{36} \) \(\mathstrut +\mathstrut 1896q^{37} \) \(\mathstrut -\mathstrut 1336q^{39} \) \(\mathstrut -\mathstrut 4650q^{40} \) \(\mathstrut -\mathstrut 1980q^{42} \) \(\mathstrut -\mathstrut 7384q^{43} \) \(\mathstrut +\mathstrut 1900q^{45} \) \(\mathstrut +\mathstrut 8196q^{46} \) \(\mathstrut +\mathstrut 14668q^{48} \) \(\mathstrut -\mathstrut 1318q^{49} \) \(\mathstrut -\mathstrut 8492q^{51} \) \(\mathstrut +\mathstrut 8976q^{52} \) \(\mathstrut -\mathstrut 278q^{54} \) \(\mathstrut -\mathstrut 1300q^{55} \) \(\mathstrut -\mathstrut 11584q^{57} \) \(\mathstrut -\mathstrut 23740q^{58} \) \(\mathstrut +\mathstrut 5050q^{60} \) \(\mathstrut +\mathstrut 6452q^{61} \) \(\mathstrut +\mathstrut 14796q^{63} \) \(\mathstrut +\mathstrut 3174q^{64} \) \(\mathstrut -\mathstrut 12760q^{66} \) \(\mathstrut +\mathstrut 13816q^{67} \) \(\mathstrut +\mathstrut 5472q^{69} \) \(\mathstrut -\mathstrut 2100q^{70} \) \(\mathstrut -\mathstrut 2040q^{72} \) \(\mathstrut +\mathstrut 596q^{73} \) \(\mathstrut -\mathstrut 1000q^{75} \) \(\mathstrut +\mathstrut 21348q^{76} \) \(\mathstrut -\mathstrut 1400q^{78} \) \(\mathstrut -\mathstrut 16124q^{79} \) \(\mathstrut +\mathstrut 5086q^{81} \) \(\mathstrut -\mathstrut 31240q^{82} \) \(\mathstrut -\mathstrut 14736q^{84} \) \(\mathstrut -\mathstrut 3100q^{85} \) \(\mathstrut -\mathstrut 4900q^{87} \) \(\mathstrut +\mathstrut 15660q^{88} \) \(\mathstrut +\mathstrut 7550q^{90} \) \(\mathstrut -\mathstrut 11632q^{91} \) \(\mathstrut -\mathstrut 8184q^{93} \) \(\mathstrut +\mathstrut 34924q^{94} \) \(\mathstrut +\mathstrut 14354q^{96} \) \(\mathstrut +\mathstrut 9756q^{97} \) \(\mathstrut +\mathstrut 9680q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(15, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
15.5.c.a \(6\) \(1.551\) \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(8\) \(0\) \(76\) \(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)