Space of modular forms of level 1120, weight 2, and Character 1120.g

• Label: 1120.2.g
• Level: $1120$
• Weight: $2$
• Character orbit: 1120.g
• Rep. character: $\chi_{1120}(449,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $4$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(3\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1120, [\chi])\).

	Total	New	Old
Modular forms	208	36	172
Cusp forms	176	36	140
Eisenstein series	32	0	32

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(1120, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1120.2.g.a	$1120$	$2$	1120.g	5.b	$2$	$4$	$4$	$8.943$	\(\Q(i, \sqrt{5})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{1}q^{7}+2q^{9}+\beta _{3}q^{11}+\cdots\)
1120.2.g.b	$1120$	$2$	1120.g	5.b	$2$	$10$	$10$	$8.943$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}+\beta _{4}q^{5}+\beta _{5}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
1120.2.g.c	$1120$	$2$	1120.g	5.b	$2$	$10$	$10$	$8.943$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{3}-\beta _{6}q^{5}+\beta _{5}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)
1120.2.g.d	$1120$	$2$	1120.g	5.b	$2$	$12$	$12$	$8.943$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{3}-\beta _{11}q^{5}+\beta _{5}q^{7}+(-1-\beta _{3}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1120, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)