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

• Label: 17.10.b
• Level: $17$
• Weight: $10$
• Character orbit: 17.b
• Rep. character: $\chi_{17}(16,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	17.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q\)
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	14	14	0
Cusp forms	12	12	0
Eisenstein series	2	2	0

Trace form

\( 12 q + 30 q^{2} + 1874 q^{4} + 23550 q^{8} - 9184 q^{9} + O(q^{10}) \)

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.b.a	$17$	$10$	17.b	17.b	$2$	$12$	$12$	$8.756$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(30\)	\(0\)	\(0\)	\(0\)	$2^{17}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(2+\beta _{2})q^{2}+\beta _{1}q^{3}+(154+4\beta _{2}+\cdots)q^{4}+\cdots\)