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

• Label: 1120.2.k
• Level: $1120$
• Weight: $2$
• Character orbit: 1120.k
• Rep. character: $\chi_{1120}(671,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	208	32	176
Cusp forms	176	32	144
Eisenstein series	32	0	32

Trace form

\( 32 q + 32 q^{9} + 8 q^{21} - 32 q^{25} + 16 q^{29} + 32 q^{37} - 8 q^{49} + 32 q^{53} + 32 q^{57} + 16 q^{65} - 16 q^{77} + 80 q^{81} - 96 q^{93}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1120.2.k.a	$1120$	$2$	1120.k	28.d	$2$	$16$	$16$	$8.943$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1120.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{9}q^{3}+\beta _{4}q^{5}-\beta _{14}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
1120.2.k.b	$1120$	$2$	1120.k	28.d	$2$	$16$	$16$	$8.943$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓			1120.2.k.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{11}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{9}q^{3}+\beta _{4}q^{5}+\beta _{14}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)