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

• Label: 1110.2.h
• Level: $1110$
• Weight: $2$
• Character orbit: 1110.h
• Rep. character: $\chi_{1110}(961,\cdot)$
• Character field: $\Q$
• Dimension: $28$
• Newform subspaces: $7$
• Sturm bound: $456$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(456\)
Trace bound:			\(7\)
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	28	208
Cusp forms	220	28	192
Eisenstein series	16	0	16

Trace form

\( 28 q + 4 q^{3} - 28 q^{4} - 8 q^{7} + 28 q^{9} + O(q^{10}) \)

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.h.a	$1110$	$2$	1110.h	37.b	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}-q^{7}+\cdots\)
1110.2.h.b	$1110$	$2$	1110.h	37.b	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-q^{3}-q^{4}+iq^{5}-iq^{6}+2q^{7}+\cdots\)
1110.2.h.c	$1110$	$2$	1110.h	37.b	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{3}-q^{4}+iq^{5}+iq^{6}+q^{7}+\cdots\)
1110.2.h.d	$1110$	$2$	1110.h	37.b	$2$	$4$	$4$	$8.863$	\(\Q(i, \sqrt{73})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}-q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
1110.2.h.e	$1110$	$2$	1110.h	37.b	$2$	$4$	$4$	$8.863$	\(\Q(i, \sqrt{33})\)	None		$2$	$0$	\(0\)	\(-4\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots\)
1110.2.h.f	$1110$	$2$	1110.h	37.b	$2$	$6$	$6$	$8.863$	6.0.279290944.1	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-6\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}+\beta _{2}q^{6}+\cdots\)
1110.2.h.g	$1110$	$2$	1110.h	37.b	$2$	$8$	$8$	$8.863$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(8\)	\(0\)	\(-4\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{2}q^{2}+q^{3}-q^{4}+\beta _{2}q^{5}-\beta _{2}q^{6}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1110, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(370, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(555, [\chi])\)\(^{\oplus 2}\)