Space of modular forms of level 15, weight 8, and Character 15.e

• Label: 15.8.e
• Level: $15$
• Weight: $8$
• Character orbit: 15.e
• Rep. character: $\chi_{15}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(15, [\chi])\).

	Total	New	Old
Modular forms	32	32	0
Cusp forms	24	24	0
Eisenstein series	8	8	0

Trace form

\( 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(15, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
15.8.e.a	$15$	$8$	15.e	15.e	$4$	$24$	$12$	$4.686$		None		$4$	$0$	\(0\)	\(24\)	\(0\)	\(1344\)		$\mathrm{SU}(2)[C_{4}]$