Space of modular forms of level 1110, weight 2, and Character 1110.ba

• Label: 1110.2.ba
• Level: $1110$
• Weight: $2$
• Character orbit: 1110.ba
• Rep. character: $\chi_{1110}(529,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $456$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.ba (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(456\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1110, [\chi])\).

	Total	New	Old
Modular forms	472	72	400
Cusp forms	440	72	368
Eisenstein series	32	0	32

Trace form

\( 72 q - 36 q^{4} + 6 q^{5} + 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1110, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1110.2.ba.a	$1110$	$2$	1110.ba	185.l	$6$	$36$	$18$	$8.863$		None		$2$	$0$	\(-18\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1110.2.ba.b	$1110$	$2$	1110.ba	185.l	$6$	$36$	$18$	$8.863$		None		$2$	$0$	\(18\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1110, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)