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

• Label: 55.2.g
• Level: $55$
• Weight: $2$
• Character orbit: 55.g
• Rep. character: $\chi_{55}(16,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $12$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(12\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	32	16	16
Cusp forms	16	16	0
Eisenstein series	16	0	16

Trace form

16 * q - 6 * q^2 - 4 * q^3 - 8 * q^4 + 6 * q^6 - 4 * q^7 + 2 * q^8 - 10 * q^9 + 8 * q^10 - 2 * q^11 - 12 * q^12 + 2 * q^13 + 6 * q^15 - 16 * q^16 - 12 * q^17 + 14 * q^18 + 14 * q^19 - 4 * q^20 - 32 * q^21 + 26 * q^22 - 8 * q^23 + 38 * q^24 - 4 * q^25 - 4 * q^26 + 20 * q^27 - 2 * q^28 + 10 * q^29 - 20 * q^30 - 4 * q^31 + 28 * q^32 - 14 * q^33 - 16 * q^34 - 12 * q^35 + 6 * q^36 + 28 * q^37 - 6 * q^38 + 30 * q^39 - 6 * q^40 + 4 * q^41 + 38 * q^42 + 4 * q^43 - 40 * q^44 - 38 * q^46 + 4 * q^47 - 14 * q^48 - 14 * q^49 - 6 * q^50 + 14 * q^51 - 54 * q^52 + 16 * q^53 - 24 * q^54 + 12 * q^55 + 52 * q^56 - 50 * q^57 + 6 * q^58 - 46 * q^59 + 26 * q^60 + 4 * q^61 - 68 * q^62 + 26 * q^63 - 20 * q^64 + 16 * q^65 + 26 * q^66 - 40 * q^67 + 46 * q^68 - 22 * q^69 + 32 * q^70 + 20 * q^71 - 64 * q^72 - 10 * q^73 + 68 * q^74 + 6 * q^75 + 16 * q^76 + 6 * q^77 - 4 * q^78 + 54 * q^79 + 16 * q^80 + 8 * q^81 + 30 * q^82 + 2 * q^83 + 24 * q^84 - 16 * q^85 - 34 * q^86 + 68 * q^87 - 14 * q^88 - 16 * q^89 - 26 * q^90 + 32 * q^91 + 92 * q^92 - 48 * q^93 + 50 * q^94 - 16 * q^95 + 6 * q^96 + 36 * q^97 - 68 * q^98 - 16 * q^99

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.g.a	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.159390625.1	None		✓			55.2.g.a	$2$	$0$	\(-4\)	\(1\)	\(-2\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q+(-\beta _{1}-\beta _{2}+\beta _{4})q^{2}+\beta _{1}q^{3}+(-2+\cdots)q^{4}+\cdots\)
55.2.g.b	$55$	$2$	55.g	11.c	$5$	$8$	$2$	$0.439$	8.0.13140625.1	None		✓			55.2.g.b	$2$	$0$	\(-2\)	\(-5\)	\(2\)	\(-1\)	$1$	$\mathrm{SU}(2)[C_{5}]$	\(q-\beta _{6}q^{2}+(-1+\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)