Space of modular forms of level 43, weight 8, and Character 43.e

• Label: 43.8.e
• Level: $43$
• Weight: $8$
• Character orbit: 43.e
• Rep. character: $\chi_{43}(4,\cdot)$
• Character field: $\Q(\zeta_{7})$
• Dimension: $144$
• Newform subspaces: $1$
• Sturm bound: $29$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.e (of order \(7\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 43 \)
Character field:			\(\Q(\zeta_{7})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(29\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(43, [\chi])\).

	Total	New	Old
Modular forms	156	156	0
Cusp forms	144	144	0
Eisenstein series	12	12	0

Trace form

\( 144 q + q^{2} - 33 q^{3} - 1531 q^{4} - 253 q^{5} + 484 q^{6} + 3440 q^{7} - 6339 q^{8} - 7461 q^{9} + O(q^{10}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(43, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
43.8.e.a	$43$	$8$	43.e	43.e	$7$	$144$	$24$	$13.433$		None		$2$	$0$	\(1\)	\(-33\)	\(-253\)	\(3440\)		$\mathrm{SU}(2)[C_{7}]$