Space of modular forms of level 15, weight 9, and Character 15.d

• 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: $2$

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 - 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

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

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.9.d.a	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	✓			15.9.d.a	$2$	$0$	\(-17\)	\(-81\)	\(-625\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-17q^{2}-3^{4}q^{3}+33q^{4}-5^{4}q^{5}+\cdots\)
15.9.d.b	$15$	$9$	15.d	15.d	$2$	$1$	$1$	$6.111$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	✓			15.9.d.a	$2$	$0$	\(17\)	\(81\)	\(625\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+17q^{2}+3^{4}q^{3}+33q^{4}+5^{4}q^{5}+\cdots\)
15.9.d.c	$15$	$9$	15.d	15.d	$2$	$12$	$12$	$6.111$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓	✓		15.9.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{13}\cdot 3^{18}\cdot 5^{7}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(142-\beta _{1}+\cdots)q^{4}+\cdots\)