Space of modular forms of level 55, weight 3, and Character 55.c

• Label: 55.3.c
• Level: $55$
• Weight: $3$
• Character orbit: 55.c
• Rep. character: $\chi_{55}(21,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $18$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	55.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 11 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(18\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(55, [\chi])\).

	Total	New	Old
Modular forms	14	8	6
Cusp forms	10	8	2
Eisenstein series	4	0	4

Trace form

8 * q + 8 * q^3 - 28 * q^4 - 4 * q^9 + 8 * q^11 - 48 * q^12 + 20 * q^15 + 88 * q^16 - 20 * q^20 + 80 * q^22 + 8 * q^23 + 40 * q^25 - 100 * q^26 - 16 * q^27 + 36 * q^31 - 152 * q^33 + 80 * q^34 - 216 * q^36 - 88 * q^37 - 160 * q^38 + 280 * q^42 + 12 * q^44 - 8 * q^47 + 488 * q^48 + 172 * q^49 - 152 * q^53 - 20 * q^55 - 80 * q^56 + 160 * q^58 - 16 * q^59 - 300 * q^60 - 588 * q^64 + 180 * q^66 - 88 * q^67 + 8 * q^69 + 60 * q^70 + 276 * q^71 + 40 * q^75 + 160 * q^77 + 160 * q^78 + 320 * q^80 - 320 * q^81 - 520 * q^82 + 420 * q^86 - 520 * q^88 + 444 * q^89 - 40 * q^91 - 368 * q^92 - 104 * q^93 + 312 * q^97 - 184 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(55, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
55.3.c.a	$55$	$3$	55.c	11.b	$2$	$8$	$8$	$1.499$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓	✓	55.3.c.a	$2$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(1+\beta _{3})q^{3}+(-4+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(55, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(55, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(11, [\chi])\)\(^{\oplus 2}\)