Space of modular forms of level 67, weight 5, and Character 67.h

• Label: 67.5.h
• Level: $67$
• Weight: $5$
• Character orbit: 67.h
• Rep. character: $\chi_{67}(2,\cdot)$
• Character field: $\Q(\zeta_{66})$
• Dimension: $440$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 67 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	67.h (of order \(66\) and degree \(20\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 67 \)
Character field:			\(\Q(\zeta_{66})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(67, [\chi])\).

	Total	New	Old
Modular forms	480	480	0
Cusp forms	440	440	0
Eisenstein series	40	40	0

Trace form

\( 440 q - 19 q^{2} - 22 q^{3} - 191 q^{4} - 22 q^{5} - 53 q^{6} - 16 q^{7} - 517 q^{8} + 840 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(67, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
67.5.h.a	$67$	$5$	67.h	67.h	$66$	$440$	$22$	$6.926$		None		✓	✓	✓	67.5.h.a	$2$	$0$	\(-19\)	\(-22\)	\(-22\)	\(-16\)		$\mathrm{SU}(2)[C_{66}]$