Space of modular forms of level 1984, weight 2, and Character 1984.b

• Label: 1984.2.b
• Level: $1984$
• Weight: $2$
• Character orbit: 1984.b
• Rep. character: $\chi_{1984}(991,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $512$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1984 = 2^{6} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1984.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 248 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(512\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1984, [\chi])\).

	Total	New	Old
Modular forms	268	64	204
Cusp forms	244	64	180
Eisenstein series	24	0	24

Trace form

\( 64 q - 64 q^{9} - 64 q^{25} - 96 q^{49} + 64 q^{81} - 64 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1984, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1984.2.b.a	$1984$	$2$	1984.b	248.b	$2$	$8$	$8$	$15.842$	8.0.3317760000.4	None		✓			1984.2.b.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{3}+\beta _{2}q^{5}+\beta _{1}q^{7}+q^{9}+2\beta _{5}q^{11}+\cdots\)
1984.2.b.b	$1984$	$2$	1984.b	248.b	$2$	$16$	$16$	$15.842$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	\(\Q(\sqrt{-62}) \)		✓			1984.2.b.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{22}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{5}q^{3}-\beta _{3}q^{7}+(-3+\beta _{8})q^{9}-\beta _{2}q^{11}+\cdots\)
1984.2.b.c	$1984$	$2$	1984.b	248.b	$2$	$40$	$40$	$15.842$		None		✓	✓		1984.2.b.c	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1984, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1984, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(248, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(992, [\chi])\)\(^{\oplus 2}\)