Space of modular forms of level 1920, weight 2, and Character 1920.k

• Label: 1920.2.k
• Level: $1920$
• Weight: $2$
• Character orbit: 1920.k
• Rep. character: $\chi_{1920}(961,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $12$
• Sturm bound: $768$
• Trace bound: $23$

Defining parameters

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(768\)
Trace bound:			\(23\)
Distinguishing \(T_p\):			\(7\), \(11\), \(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1920, [\chi])\).

	Total	New	Old
Modular forms	416	32	384
Cusp forms	352	32	320
Eisenstein series	64	0	64

Trace form

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

Decomposition of \(S_{2}^{\mathrm{new}}(1920, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1920.2.k.a	$1920$	$2$	1920.k	8.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}-2q^{7}-q^{9}-2iq^{11}+\cdots\)
1920.2.k.b	$1920$	$2$	1920.k	8.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}-2q^{7}-q^{9}-2iq^{11}+\cdots\)
1920.2.k.c	$1920$	$2$	1920.k	8.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{5}-2q^{7}-q^{9}+2iq^{11}+\cdots\)
1920.2.k.d	$1920$	$2$	1920.k	8.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}-iq^{5}-2q^{7}-q^{9}+6iq^{11}+\cdots\)
1920.2.k.e	$1920$	$2$	1920.k	8.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}-iq^{5}+2q^{7}-q^{9}-6iq^{11}+\cdots\)
1920.2.k.f	$1920$	$2$	1920.k	8.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+iq^{5}+2q^{7}-q^{9}-2iq^{11}+\cdots\)
1920.2.k.g	$1920$	$2$	1920.k	8.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{5}+2q^{7}-q^{9}+2iq^{11}+\cdots\)
1920.2.k.h	$1920$	$2$	1920.k	8.b	$2$	$2$	$2$	$15.331$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-iq^{3}+iq^{5}+2q^{7}-q^{9}+2iq^{11}+\cdots\)
1920.2.k.i	$1920$	$2$	1920.k	8.b	$2$	$4$	$4$	$15.331$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}+\zeta_{8}q^{5}+(-2+\zeta_{8}^{3})q^{7}+\cdots\)
1920.2.k.j	$1920$	$2$	1920.k	8.b	$2$	$4$	$4$	$15.331$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+\zeta_{8}q^{5}-2q^{7}-q^{9}+(2\zeta_{8}+\cdots)q^{11}+\cdots\)
1920.2.k.k	$1920$	$2$	1920.k	8.b	$2$	$4$	$4$	$15.331$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{8}q^{3}+\zeta_{8}q^{5}+2q^{7}-q^{9}+(-2\zeta_{8}+\cdots)q^{11}+\cdots\)
1920.2.k.l	$1920$	$2$	1920.k	8.b	$2$	$4$	$4$	$15.331$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}q^{3}+\zeta_{8}q^{5}+(2+\zeta_{8}^{3})q^{7}-q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1920, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1920, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(80, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)