Space of modular forms of level 15, weight 5, and Character 15.d

• Label: 15.5.d
• Level: $15$
• Weight: $5$
• Character orbit: 15.d
• Rep. character: $\chi_{15}(14,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $10$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(10\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(15, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

Trace form

\( 6 q + 42 q^{4} - 66 q^{6} + 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(15, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.5.d.a	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-7\)	\(9\)	\(25\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-7q^{2}+9q^{3}+33q^{4}+5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.b	$15$	$5$	15.d	15.d	$2$	$1$	$1$	$1.551$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(7\)	\(-9\)	\(-25\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+7q^{2}-9q^{3}+33q^{4}-5^{2}q^{5}-63q^{6}+\cdots\)
15.5.d.c	$15$	$5$	15.d	15.d	$2$	$4$	$4$	$1.551$	\(\Q(\sqrt{10}, \sqrt{-26})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{2})q^{3}-6q^{4}+(2\beta _{2}+\cdots)q^{5}+\cdots\)