Space of modular forms of level 43, weight 7, and Character 43.h

• Label: 43.7.h
• Level: $43$
• Weight: $7$
• Character orbit: 43.h
• Rep. character: $\chi_{43}(3,\cdot)$
• Character field: $\Q(\zeta_{42})$
• Dimension: $252$
• Newform subspaces: $1$
• Sturm bound: $25$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(25\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(43, [\chi])\).

	Total	New	Old
Modular forms	276	276	0
Cusp forms	252	252	0
Eisenstein series	24	24	0

Trace form

\( 252 q - 14 q^{2} - 11 q^{3} + 1180 q^{4} - 11 q^{5} - 118 q^{6} + 126 q^{7} - 2254 q^{8} - 8178 q^{9} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.7.h.a	$43$	$7$	43.h	43.h	$42$	$252$	$21$	$9.892$		None		$2$	$0$	\(-14\)	\(-11\)	\(-11\)	\(126\)		$\mathrm{SU}(2)[C_{42}]$