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

• Label: 1120.2.bw
• Level: $1120$
• Weight: $2$
• Character orbit: 1120.bw
• Rep. character: $\chi_{1120}(289,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bw (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 35 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 8 \)
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	416	96	320
Cusp forms	352	96	256
Eisenstein series	64	0	64

Trace form

\( 96 q + 48 q^{9} + O(q^{10}) \)

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.bw.a	$1120$	$2$	1120.bw	35.j	$6$	$4$	$2$	$8.943$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(2\zeta_{12}-\zeta_{12}^{2}-2\zeta_{12}^{3})q^{5}+\cdots\)
1120.2.bw.b	$1120$	$2$	1120.bw	35.j	$6$	$4$	$2$	$8.943$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\zeta_{12}q^{3}+(-2\zeta_{12}-\zeta_{12}^{2}+2\zeta_{12}^{3})q^{5}+\cdots\)
1120.2.bw.c	$1120$	$2$	1120.bw	35.j	$6$	$8$	$4$	$8.943$	8.0.12960000.1	\(\Q(\sqrt{-5}) \)		$4$	$0$	\(0\)	\(-6\)	\(0\)	\(6\)	$2^{4}$	$\mathrm{U}(1)[D_{6}]$	\(q+(-1+\beta _{1}-\beta _{3}-\beta _{4}+\beta _{6})q^{3}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
1120.2.bw.d	$1120$	$2$	1120.bw	35.j	$6$	$8$	$4$	$8.943$	8.0.303595776.1	None		$8$	$0$	\(0\)	\(0\)	\(6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{5}q^{3}+(2-\beta _{2}+2\beta _{4}+\beta _{6})q^{5}+\cdots\)
1120.2.bw.e	$1120$	$2$	1120.bw	35.j	$6$	$8$	$4$	$8.943$	8.0.49787136.1	None		$8$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2\beta _{3}+\beta _{4})q^{5}+(-\beta _{5}+\beta _{7})q^{7}+\cdots\)
1120.2.bw.f	$1120$	$2$	1120.bw	35.j	$6$	$8$	$4$	$8.943$	8.0.12960000.1	\(\Q(\sqrt{-5}) \)		$4$	$0$	\(0\)	\(6\)	\(0\)	\(-6\)	$2^{4}$	$\mathrm{U}(1)[D_{6}]$	\(q+(\beta _{3}+\beta _{4}-\beta _{5})q^{3}+(-\beta _{1}+\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
1120.2.bw.g	$1120$	$2$	1120.bw	35.j	$6$	$16$	$8$	$8.943$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{2}-\beta _{13})q^{3}+(-1-\beta _{4}+\beta _{9}+\cdots)q^{5}+\cdots\)
1120.2.bw.h	$1120$	$2$	1120.bw	35.j	$6$	$40$	$20$	$8.943$		None		$8$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)