Space of modular forms of level 11, weight 5, and Character 11.b

• Label: 11.5.b
• Level: $11$
• Weight: $5$
• Character orbit: 11.b
• Rep. character: $\chi_{11}(10,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $5$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	11.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(5\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(11, [\chi])\).

	Total	New	Old
Modular forms	5	5	0
Cusp forms	3	3	0
Eisenstein series	2	2	0

Trace form

\( 3 q + q^{3} - 12 q^{4} + 13 q^{5} - 176 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(11, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.5.b.a	$11$	$5$	11.b	11.b	$2$	$1$	$1$	$1.137$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(7\)	\(-49\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+7q^{3}+2^{4}q^{4}-7^{2}q^{5}-2^{5}q^{9}+11^{2}q^{11}+\cdots\)
11.5.b.b	$11$	$5$	11.b	11.b	$2$	$2$	$2$	$1.137$	\(\Q(\sqrt{-30}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(62\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-3q^{3}-14q^{4}+31q^{5}-3\beta q^{6}+\cdots\)