Space of modular forms of level 15, weight 6, and Character 15.e

• Label: 15.6.e
• Level: $15$
• Weight: $6$
• Character orbit: 15.e
• Rep. character: $\chi_{15}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 15 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(15, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	16	16	0
Eisenstein series	8	8	0

Trace form

\( 16 q - 84 q^{6} - 80 q^{7} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(15, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.6.e.a	$15$	$6$	15.e	15.e	$4$	$16$	$8$	$2.406$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-80\)	$2^{9}\cdot 3^{10}\cdot 5^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{7}q^{2}-\beta _{4}q^{3}+(-13\beta _{3}-\beta _{6})q^{4}+\cdots\)