Space of modular forms of level 76, weight 5, and Character 76.j

• Label: 76.5.j
• Level: $76$
• Weight: $5$
• Character orbit: 76.j
• Rep. character: $\chi_{76}(13,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $42$
• Newform subspaces: $1$
• Sturm bound: $50$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	76.j (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(50\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(76, [\chi])\).

	Total	New	Old
Modular forms	258	42	216
Cusp forms	222	42	180
Eisenstein series	36	0	36

Trace form

\( 42 q + 12 q^{3} - 45 q^{7} - 84 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(76, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
76.5.j.a	$76$	$5$	76.j	19.f	$18$	$42$	$7$	$7.856$		None		$2$	$0$	\(0\)	\(12\)	\(0\)	\(-45\)		$\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{5}^{\mathrm{old}}(76, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(76, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)