Space of modular forms of level 11, weight 10, and Character 11.c

• Label: 11.10.c
• Level: $11$
• Weight: $10$
• Character orbit: 11.c
• Rep. character: $\chi_{11}(3,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $10$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(10\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(11, [\chi])\).

	Total	New	Old
Modular forms	40	40	0
Cusp forms	32	32	0
Eisenstein series	8	8	0

Trace form

\( 32 q - 21 q^{2} + 69 q^{3} - 1625 q^{4} + 225 q^{5} + 8173 q^{6} - 10675 q^{7} + 22863 q^{8} - 93587 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(11, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.10.c.a	$11$	$10$	11.c	11.c	$5$	$32$	$8$	$5.665$		None		$2$	$0$	\(-21\)	\(69\)	\(225\)	\(-10675\)		$\mathrm{SU}(2)[C_{5}]$