Space of modular forms of level 241, weight 2, and Character 241.h

• Label: 241.2.h
• Level: $241$
• Weight: $2$
• Character orbit: 241.h
• Rep. character: $\chi_{241}(36,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	241.h (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 241 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(241, [\chi])\).

	Total	New	Old
Modular forms	80	80	0
Cusp forms	72	72	0
Eisenstein series	8	8	0

Trace form

\( 72 q - 7 q^{3} + 52 q^{4} - 9 q^{5} - 3 q^{6} - 5 q^{7} - 5 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(241, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
241.2.h.a	$241$	$2$	241.h	241.h	$10$	$72$	$18$	$1.924$		None		$2$	$0$	\(0\)	\(-7\)	\(-9\)	\(-5\)		$\mathrm{SU}(2)[C_{10}]$