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

• Label: 1920.2.d
• Level: $1920$
• Weight: $2$
• Character orbit: 1920.d
• Rep. character: $\chi_{1920}(1729,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $8$
• Sturm bound: $768$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1920 = 2^{7} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1920.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 40 \)
Character field:			\(\Q\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(768\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\), \(13\), \(31\), \(43\)

Dimensions

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

	Total	New	Old
Modular forms	416	48	368
Cusp forms	352	48	304
Eisenstein series	64	0	64

Trace form

\( 48 q + 48 q^{9} + 16 q^{25} - 32 q^{41} - 48 q^{49} + 32 q^{65} + 48 q^{81} + 96 q^{89}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1920.2.d.a	$1920$	$2$	1920.d	40.f	$2$	$4$	$4$	$15.331$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			1920.2.d.a	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{1}q^{5}+q^{9}+(-\beta _{1}-\beta _{2})q^{13}+\cdots\)
1920.2.d.b	$1920$	$2$	1920.d	40.f	$2$	$4$	$4$	$15.331$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None		✓			1920.2.d.a	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{1}q^{5}+q^{9}+(\beta _{1}+\beta _{2})q^{13}+\cdots\)
1920.2.d.c	$1920$	$2$	1920.d	40.f	$2$	$6$	$6$	$15.331$	6.0.350464.1	None		✓			1920.2.d.c	$2$	$0$	\(0\)	\(-6\)	\(-2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{3}q^{5}-\beta _{5}q^{7}+q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
1920.2.d.d	$1920$	$2$	1920.d	40.f	$2$	$6$	$6$	$15.331$	6.0.350464.1	None		✓			1920.2.d.c	$2$	$0$	\(0\)	\(-6\)	\(2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{4}q^{5}-\beta _{5}q^{7}+q^{9}+(\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
1920.2.d.e	$1920$	$2$	1920.d	40.f	$2$	$6$	$6$	$15.331$	6.0.350464.1	None		✓			1920.2.d.c	$2$	$0$	\(0\)	\(6\)	\(-2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{4}q^{5}-\beta _{5}q^{7}+q^{9}+(-\beta _{3}+\cdots)q^{11}+\cdots\)
1920.2.d.f	$1920$	$2$	1920.d	40.f	$2$	$6$	$6$	$15.331$	6.0.350464.1	None		✓			1920.2.d.c	$2$	$0$	\(0\)	\(6\)	\(2\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{3}q^{5}-\beta _{5}q^{7}+q^{9}+(\beta _{3}-\beta _{4}+\cdots)q^{11}+\cdots\)
1920.2.d.g	$1920$	$2$	1920.d	40.f	$2$	$8$	$8$	$15.331$	8.0.3288334336.1	None		✓			1920.2.d.g	$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}-\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}+\beta _{7}q^{11}+\cdots\)
1920.2.d.h	$1920$	$2$	1920.d	40.f	$2$	$8$	$8$	$15.331$	8.0.3288334336.1	None		✓			1920.2.d.g	$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta _{4}q^{5}+\beta _{1}q^{7}+q^{9}-\beta _{7}q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1920, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(160, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(320, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(480, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(640, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(960, [\chi])\)\(^{\oplus 2}\)