Space of modular forms of level 43, weight 11, and Character 43.h

• Label: 43.11.h
• Level: $43$
• Weight: $11$
• Character orbit: 43.h
• Rep. character: $\chi_{43}(3,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $432$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	43.h (of order \(42\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q(\zeta_{42})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(43, [\chi])\).

	Total	New	Old
Modular forms	456	456	0
Cusp forms	432	432	0
Eisenstein series	24	24	0

Trace form

\( 432 q - 14 q^{2} + 232 q^{3} + 38108 q^{4} - 11 q^{5} - 8518 q^{6} - 31398 q^{7} + 78834 q^{8} - 362010 q^{9} + O(q^{10}) \)

Decomposition of \(S_{11}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.11.h.a	$43$	$11$	43.h	43.h	$42$	$432$	$36$	$27.320$		None		$2$	$0$	\(-14\)	\(232\)	\(-11\)	\(-31398\)		$\mathrm{SU}(2)[C_{42}]$