Properties

Label 15.5.c
Level $15$
Weight $5$
Character orbit 15.c
Rep. character $\chi_{15}(11,\cdot)$
Character field $\Q$
Dimension $6$
Newform subspaces $1$
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: \(\Q\)
Newform subspaces: \( 1 \)
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

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

Decomposition of \(S_{5}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.5.c.a 15.c 3.b $6$ $1.551$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(8\) \(0\) \(76\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1-\beta _{2})q^{3}+(-8+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)