Space of modular forms of level 110, weight 3, and Character 110.c

• Label: 110.3.c
• Level: $110$
• Weight: $3$
• Character orbit: 110.c
• Rep. character: $\chi_{110}(109,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $54$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	110.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(54\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(110, [\chi])\).

	Total	New	Old
Modular forms	40	12	28
Cusp forms	32	12	20
Eisenstein series	8	0	8

Trace form

\( 12 q + 24 q^{4} + 10 q^{5} - 48 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(110, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
110.3.c.a	$110$	$3$	110.c	55.d	$2$	$4$	$4$	$2.997$	\(\Q(\sqrt{2}, \sqrt{-13})\)	None		$4$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+5q^{5}+2\beta _{3}q^{6}+\cdots\)
110.3.c.b	$110$	$3$	110.c	55.d	$2$	$8$	$8$	$2.997$	8.0.\(\cdots\).7	None		$4$	$0$	\(0\)	\(0\)	\(-10\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{3}+2q^{4}+(-1+\beta _{5}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(110, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(110, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)