Space of modular forms of level 17, weight 4, and Character 17.c

• Label: 17.4.c
• Level: $17$
• Weight: $4$
• Character orbit: 17.c
• Rep. character: $\chi_{17}(4,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	17.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(6\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(17, [\chi])\).

	Total	New	Old
Modular forms	12	12	0
Cusp forms	8	8	0
Eisenstein series	4	4	0

Trace form

\( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(17, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
17.4.c.a	$17$	$4$	17.c	17.c	$4$	$8$	$4$	$1.003$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(2\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(\beta _{1}-\beta _{3})q^{2}+\beta _{4}q^{3}+(-5-\beta _{2}+\cdots)q^{4}+\cdots\)