Space of modular forms of level 15, weight 3, and Character 15.d

• Label: 15.3.d
• Level: $15$
• Weight: $3$
• Character orbit: 15.d
• Rep. character: $\chi_{15}(14,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $6$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	15.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(6\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(15, [\chi])\).

	Total	New	Old
Modular forms	6	6	0
Cusp forms	2	2	0
Eisenstein series	4	4	0

Trace form

\( 2 q - 6 q^{4} - 6 q^{6} + 18 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(15, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.3.d.a	$15$	$3$	15.d	15.d	$2$	$1$	$1$	$0.409$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(-1\)	\(3\)	\(-5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q-q^{2}+3q^{3}-3q^{4}-5q^{5}-3q^{6}+\cdots\)
15.3.d.b	$15$	$3$	15.d	15.d	$2$	$1$	$1$	$0.409$	\(\Q\)	\(\Q(\sqrt{-15}) \)	✓	$2$	$0$	\(1\)	\(-3\)	\(5\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+q^{2}-3q^{3}-3q^{4}+5q^{5}-3q^{6}+\cdots\)