Properties

Label 15.9.d
Level $15$
Weight $9$
Character orbit 15.d
Rep. character $\chi_{15}(14,\cdot)$
Character field $\Q$
Dimension $14$
Newform subspaces $3$
Sturm bound $18$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 15.d (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 15 \)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(18\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(15, [\chi])\).

Total New Old
Modular forms 18 18 0
Cusp forms 14 14 0
Eisenstein series 4 4 0

Trace form

\( 14 q + 1770 q^{4} - 258 q^{6} - 9702 q^{9} + O(q^{10}) \) \( 14 q + 1770 q^{4} - 258 q^{6} - 9702 q^{9} - 14030 q^{10} + 5730 q^{15} + 267538 q^{16} - 131804 q^{19} - 604044 q^{21} + 559194 q^{24} - 1254970 q^{25} + 3563460 q^{30} + 3384148 q^{31} - 1943356 q^{34} - 9878814 q^{36} + 3780864 q^{39} - 8085790 q^{40} + 9523980 q^{45} + 18711884 q^{46} + 5307302 q^{49} + 510132 q^{51} - 35212698 q^{54} - 16903440 q^{55} + 13241970 q^{60} - 63308972 q^{61} + 85683554 q^{64} + 111065040 q^{66} - 80973888 q^{69} + 3903480 q^{70} + 15031440 q^{75} - 246110748 q^{76} + 281168116 q^{79} + 184574214 q^{81} - 528357816 q^{84} - 143488940 q^{85} + 358023330 q^{90} - 100211328 q^{91} + 817264124 q^{94} + 289774386 q^{96} - 640360080 q^{99} + O(q^{100}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
15.9.d.a 15.d 15.d $1$ $6.111$ \(\Q\) \(\Q(\sqrt{-15}) \) 15.9.d.a \(-17\) \(-81\) \(-625\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots\)
15.9.d.b 15.d 15.d $1$ $6.111$ \(\Q\) \(\Q(\sqrt{-15}) \) 15.9.d.a \(17\) \(81\) \(625\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots\)
15.9.d.c 15.d 15.d $12$ $6.111$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 15.9.d.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots\)