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

• Label: 1110.2.e
• Level: $1110$
• Weight: $2$
• Character orbit: 1110.e
• Rep. character: $\chi_{1110}(739,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $4$
• 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.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 185 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(456\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(7\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	236	36	200
Cusp forms	220	36	184
Eisenstein series	16	0	16

Trace form

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

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.e.a	$1110$	$2$	1110.e	185.d	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}-iq^{3}+q^{4}+(2-i)q^{5}+iq^{6}+\cdots\)
1110.2.e.b	$1110$	$2$	1110.e	185.d	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}-iq^{3}+q^{4}+(-2+i)q^{5}-iq^{6}+\cdots\)
1110.2.e.c	$1110$	$2$	1110.e	185.d	$2$	$16$	$16$	$8.863$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-16\)	\(0\)	\(-2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{2}+\beta _{7}q^{3}+q^{4}-\beta _{11}q^{5}-\beta _{7}q^{6}+\cdots\)
1110.2.e.d	$1110$	$2$	1110.e	185.d	$2$	$16$	$16$	$8.863$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(16\)	\(0\)	\(2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{2}+\beta _{7}q^{3}+q^{4}+\beta _{11}q^{5}+\beta _{7}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \)