Space of modular forms of level 17, weight 10, and Character 17.d

• Label: 17.10.d
• Level: $17$
• Weight: $10$
• Character orbit: 17.d
• Rep. character: $\chi_{17}(2,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $52$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.d (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(17, [\chi])\).

	Total	New	Old
Modular forms	60	60	0
Cusp forms	52	52	0
Eisenstein series	8	8	0

Trace form

\( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(17, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
17.10.d.a	$17$	$10$	17.d	17.d	$8$	$52$	$13$	$8.756$		None		$2$	$0$	\(-4\)	\(-4\)	\(-1140\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$