Space of modular forms of level 11, weight 15, and Character 11.b

• Label: 11.15.b
• Level: $11$
• Weight: $15$
• Character orbit: 11.b
• Rep. character: $\chi_{11}(10,\cdot)$
• Character field: $\Q$
• Dimension: $13$
• Newform subspaces: $2$
• Sturm bound: $15$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 15 \)
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:			\(15\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{15}(11, [\chi])\).

	Total	New	Old
Modular forms	15	15	0
Cusp forms	13	13	0
Eisenstein series	2	2	0

Trace form

\( 13 q - 3317 q^{3} - 114140 q^{4} - 34881 q^{5} + 14743036 q^{9} + O(q^{10}) \)

Decomposition of \(S_{15}^{\mathrm{new}}(11, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
11.15.b.a	$11$	$15$	11.b	11.b	$2$	$1$	$1$	$13.676$	\(\Q\)	\(\Q(\sqrt{-11}) \)	✓	$2$	$0$	\(0\)	\(2515\)	\(100799\)	\(0\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2515q^{3}+2^{14}q^{4}+100799q^{5}+\cdots\)
11.15.b.b	$11$	$15$	11.b	11.b	$2$	$12$	$12$	$13.676$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$2$	$0$	\(0\)	\(-5832\)	\(-135680\)	\(0\)	$2^{22}\cdot 3^{6}\cdot 11^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-486+\beta _{3})q^{3}+(-10877+\cdots)q^{4}+\cdots\)