Space of modular forms of level 55, weight 2, and Character 55.l

• Label: 55.2.l
• Level: $55$
• Weight: $2$
• Character orbit: 55.l
• Rep. character: $\chi_{55}(2,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $32$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	55.l (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(55, [\chi])\).

	Total	New	Old
Modular forms	64	64	0
Cusp forms	32	32	0
Eisenstein series	32	32	0

Trace form

32 * q - 10 * q^2 - 4 * q^3 - 2 * q^5 - 20 * q^6 - 10 * q^8 - 24 * q^11 + 12 * q^12 - 10 * q^13 + 14 * q^15 - 8 * q^16 - 10 * q^18 + 16 * q^20 + 10 * q^22 - 24 * q^23 + 16 * q^25 + 20 * q^26 - 16 * q^27 + 50 * q^28 + 30 * q^30 - 28 * q^31 + 66 * q^33 - 10 * q^35 + 24 * q^36 - 8 * q^37 + 10 * q^38 - 50 * q^40 + 40 * q^41 - 10 * q^42 - 28 * q^45 + 60 * q^46 - 28 * q^47 - 54 * q^48 - 50 * q^50 + 20 * q^51 - 50 * q^52 - 24 * q^53 - 64 * q^55 - 80 * q^56 + 30 * q^57 - 50 * q^58 + 34 * q^60 - 60 * q^61 + 100 * q^62 - 30 * q^63 - 100 * q^66 - 8 * q^67 - 30 * q^68 + 30 * q^70 + 24 * q^71 + 80 * q^72 + 50 * q^73 + 34 * q^75 + 70 * q^77 + 60 * q^78 + 98 * q^80 - 12 * q^81 - 10 * q^82 + 90 * q^83 + 30 * q^85 + 100 * q^86 + 170 * q^88 - 20 * q^90 + 20 * q^91 - 68 * q^92 - 8 * q^93 - 40 * q^95 - 8 * q^97

Decomposition of \(S_{2}^{\mathrm{new}}(55, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
55.2.l.a	$55$	$2$	55.l	55.l	$20$	$32$	$4$	$0.439$		None		✓	✓	✓	55.2.l.a	$4$	$0$	\(-10\)	\(-4\)	\(-2\)	\(0\)		$\mathrm{SU}(2)[C_{20}]$