Space of modular forms of level 1116, weight 2, and Character 1116.g

• Label: 1116.2.g
• Level: $1116$
• Weight: $2$
• Character orbit: 1116.g
• Rep. character: $\chi_{1116}(991,\cdot)$
• Character field: $\Q$
• Dimension: $78$
• Newform subspaces: $10$
• Sturm bound: $384$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 1116 = 2^{2} \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1116.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 124 \)
Character field:			\(\Q\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(384\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1116, [\chi])\).

	Total	New	Old
Modular forms	200	82	118
Cusp forms	184	78	106
Eisenstein series	16	4	12

Trace form

\( 78 q + 2 q^{2} + 2 q^{4} + 4 q^{5} - 7 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1116, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1116.2.g.a	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	\(\Q(i, \sqrt{30})\)	None		✓	1116.2.g.a	$4$	$0$	\(-4\)	\(0\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+q^{5}-3\beta _{1}q^{7}+\cdots\)
1116.2.g.b	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	\(\Q(\sqrt{6}, \sqrt{-7})\)	None			124.2.d.b	$4$	$0$	\(-2\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-2-\beta _{1})q^{4}+2q^{5}+(2+\cdots)q^{8}+\cdots\)
1116.2.g.c	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	\(\Q(\sqrt{-2}, \sqrt{31})\)	\(\Q(\sqrt{-93}) \)		✓	1116.2.g.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}-2q^{4}-2\beta _{1}q^{8}+4q^{16}+\cdots\)
1116.2.g.d	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	\(\Q(i, \sqrt{6})\)	None			124.2.d.a	$4$	$0$	\(4\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}-q^{5}-3\beta _{1}q^{7}+\cdots\)
1116.2.g.e	$1116$	$2$	1116.g	124.d	$2$	$4$	$4$	$8.911$	\(\Q(i, \sqrt{30})\)	None		✓	1116.2.g.a	$4$	$0$	\(4\)	\(0\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1-\beta _{1})q^{2}-2\beta _{1}q^{4}-q^{5}+3\beta _{1}q^{7}+\cdots\)
1116.2.g.f	$1116$	$2$	1116.g	124.d	$2$	$6$	$6$	$8.911$	6.0.21717639.1	\(\Q(\sqrt{-31}) \)			124.2.d.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{2}-\beta _{5})q^{5}+\cdots\)
1116.2.g.g	$1116$	$2$	1116.g	124.d	$2$	$8$	$8$	$8.911$	8.0.49787136.1	None		✓	1116.2.g.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{5}+\beta _{7})q^{2}+(1-\beta _{3})q^{4}+(\beta _{5}+2\beta _{7})q^{5}+\cdots\)
1116.2.g.h	$1116$	$2$	1116.g	124.d	$2$	$12$	$12$	$8.911$	12.0.\(\cdots\).1	\(\Q(\sqrt{-31}) \)		✓	1116.2.g.h	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{U}(1)[D_{2}]$	\(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{8}-\beta _{11})q^{5}+\cdots\)
1116.2.g.i	$1116$	$2$	1116.g	124.d	$2$	$16$	$16$	$8.911$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			372.2.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{6}q^{5}+\beta _{4}q^{7}+\cdots\)
1116.2.g.j	$1116$	$2$	1116.g	124.d	$2$	$16$	$16$	$8.911$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None			372.2.g.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{7}q^{2}+\beta _{5}q^{4}-\beta _{6}q^{5}+\beta _{3}q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1116, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1116, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(124, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(372, [\chi])\)\(^{\oplus 2}\)