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Properties

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

Trace form

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

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.3.c.a 15.c 3.b $2$ $0.409$ \(\Q(\sqrt{-5}) \) None \(0\) \(-4\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-2-\beta )q^{3}-q^{4}-\beta q^{5}+\cdots\)