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

• Label: 1110.2.d
• Level: $1110$
• Weight: $2$
• Character orbit: 1110.d
• Rep. character: $\chi_{1110}(889,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $10$
• Sturm bound: $456$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(456\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(7\), \(11\)

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

\( 36 q - 36 q^{4} + 8 q^{5} - 4 q^{6} - 36 q^{9} + O(q^{10}) \)

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.d.a	$1110$	$2$	1110.d	5.b	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
1110.2.d.b	$1110$	$2$	1110.d	5.b	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+(-1+2i)q^{5}+\cdots\)
1110.2.d.c	$1110$	$2$	1110.d	5.b	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}-iq^{3}-q^{4}+(1-2i)q^{5}+q^{6}+\cdots\)
1110.2.d.d	$1110$	$2$	1110.d	5.b	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}-q^{6}+\cdots\)
1110.2.d.e	$1110$	$2$	1110.d	5.b	$2$	$2$	$2$	$8.863$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}+q^{6}+\cdots\)
1110.2.d.f	$1110$	$2$	1110.d	5.b	$2$	$4$	$4$	$8.863$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{2}q^{5}-q^{6}+\cdots\)
1110.2.d.g	$1110$	$2$	1110.d	5.b	$2$	$4$	$4$	$8.863$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{2}q^{3}-q^{4}+(-\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
1110.2.d.h	$1110$	$2$	1110.d	5.b	$2$	$4$	$4$	$8.863$	\(\Q(i, \sqrt{6})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{2}-\beta _{2}q^{3}-q^{4}+(1+\beta _{2}+\beta _{3})q^{5}+\cdots\)
1110.2.d.i	$1110$	$2$	1110.d	5.b	$2$	$6$	$6$	$8.863$	6.0.5161984.1	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{2}-\beta _{4}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
1110.2.d.j	$1110$	$2$	1110.d	5.b	$2$	$8$	$8$	$8.863$	8.0.\(\cdots\).2	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{2}-\beta _{3}q^{3}-q^{4}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)

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

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