Space of modular forms of level 55, weight 4, and Character 55.g

• Label: 55.4.g
• Level: $55$
• Weight: $4$
• Character orbit: 55.g
• Rep. character: $\chi_{55}(16,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $48$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	55.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(55, [\chi])\).

	Total	New	Old
Modular forms	80	48	32
Cusp forms	64	48	16
Eisenstein series	16	0	16

Trace form

\( 48 q + 8 q^{2} - 4 q^{3} - 68 q^{4} + 60 q^{6} + 28 q^{7} - 68 q^{8} - 96 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(55, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
55.4.g.a	$55$	$4$	55.g	11.c	$5$	$24$	$6$	$3.245$		None		✓			55.4.g.a	$2$	$0$	\(2\)	\(-8\)	\(30\)	\(-53\)		$\mathrm{SU}(2)[C_{5}]$
55.4.g.b	$55$	$4$	55.g	11.c	$5$	$24$	$6$	$3.245$		None		✓			55.4.g.b	$2$	$0$	\(6\)	\(4\)	\(-30\)	\(81\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{4}^{\mathrm{old}}(55, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(55, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)