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

• Label: 1120.2.bz
• Level: $1120$
• Weight: $2$
• Character orbit: 1120.bz
• Rep. character: $\chi_{1120}(271,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $6$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1120.bz (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 56 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	416	64	352
Cusp forms	352	64	288
Eisenstein series	64	0	64

Trace form

\( 64 q + 32 q^{9} + O(q^{10}) \)

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.bz.a	$1120$	$2$	1120.bz	56.m	$6$	$4$	$2$	$8.943$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(6\)	\(-2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{12}^{2})q^{3}+(-1+\zeta_{12}^{2})q^{5}+\cdots\)
1120.2.bz.b	$1120$	$2$	1120.bz	56.m	$6$	$4$	$2$	$8.943$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(6\)	\(-2\)	\(10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{5}+\cdots\)
1120.2.bz.c	$1120$	$2$	1120.bz	56.m	$6$	$4$	$2$	$8.943$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None		$2$	$0$	\(0\)	\(6\)	\(2\)	\(-10\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2+\beta _{1}-\beta _{2}-\beta _{3})q^{3}+(1-\beta _{2})q^{5}+\cdots\)
1120.2.bz.d	$1120$	$2$	1120.bz	56.m	$6$	$4$	$2$	$8.943$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(0\)	\(6\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{12}^{2})q^{3}+(1-\zeta_{12}^{2})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)
1120.2.bz.e	$1120$	$2$	1120.bz	56.m	$6$	$24$	$12$	$8.943$		None		$2$	$0$	\(0\)	\(-12\)	\(-12\)	\(-10\)		$\mathrm{SU}(2)[C_{6}]$
1120.2.bz.f	$1120$	$2$	1120.bz	56.m	$6$	$24$	$12$	$8.943$		None		$2$	$0$	\(0\)	\(-12\)	\(12\)	\(10\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1120, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(280, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 2}\)