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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

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

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.f.a 15.f 5.c $4$ $0.409$ \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{2}+\beta _{3}q^{3}+(-2\beta _{1}+\cdots)q^{4}+\cdots\)