Space of modular forms of level 55, weight 6, and Character 55.b

• Label: 55.6.b
• Level: $55$
• Weight: $6$
• Character orbit: 55.b
• Rep. character: $\chi_{55}(34,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $36$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	55.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(36\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(55, [\chi])\).

	Total	New	Old
Modular forms	32	24	8
Cusp forms	28	24	4
Eisenstein series	4	0	4

Trace form

\( 24 q - 372 q^{4} + 127 q^{5} - 260 q^{6} - 1178 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(55, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
55.6.b.a	$55$	$6$	55.b	5.b	$2$	$10$	$10$	$8.821$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(35\)	\(0\)	$2^{2}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(\beta _{1}-\beta _{6})q^{3}+(-12+\beta _{2}+\cdots)q^{4}+\cdots\)
55.6.b.b	$55$	$6$	55.b	5.b	$2$	$14$	$14$	$8.821$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(92\)	\(0\)	$2^{5}\cdot 3^{2}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{5}q^{3}+(-18+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{6}^{\mathrm{old}}(55, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(55, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)