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

• Label: 17.10.c
• Level: $17$
• Weight: $10$
• Character orbit: 17.c
• Rep. character: $\chi_{17}(4,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 17 \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(15\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	28	28	0
Cusp forms	24	24	0
Eisenstein series	4	4	0

Trace form

\( 24 q + 144 q^{3} - 5124 q^{4} - 1710 q^{5} - 8174 q^{6} + 3810 q^{7} + O(q^{10}) \)

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.c.a	$17$	$10$	17.c	17.c	$4$	$24$	$12$	$8.756$		None		$2$	$0$	\(0\)	\(144\)	\(-1710\)	\(3810\)		$\mathrm{SU}(2)[C_{4}]$