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 $2$

Related objects

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