Space of modular forms of level 1976, weight 1, and Character 1976.o

• Label: 1976.1.o
• Level: $1976$
• Weight: $1$
• Character orbit: 1976.o
• Rep. character: $\chi_{1976}(493,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $7$
• Sturm bound: $280$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 1976 = 2^{3} \cdot 13 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1976.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1976 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(280\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1976, [\chi])\).

	Total	New	Old
Modular forms	26	26	0
Cusp forms	22	22	0
Eisenstein series	4	4	0

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	22	0	0	0

Trace form

\( 22 q + 8 q^{4} + 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1976, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1976.1.o.a	$1976$	$1$	1976.o	1976.o	$2$	$2$	$2$	$0.986$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-38}) \), \(\Q(\sqrt{-247}) \)	\(\Q(\sqrt{26}) \)		✓	1976.1.o.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-q^{4}+iq^{8}-q^{9}+iq^{13}+\cdots\)
1976.1.o.b	$1976$	$1$	1976.o	1976.o	$2$	$3$	$3$	$0.986$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-494}) \)	None	✓	✓	1976.1.o.b	$2$	$0$	\(-3\)	\(-1\)	\(1\)	\(0\)	$1$		\(q-q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
1976.1.o.c	$1976$	$1$	1976.o	1976.o	$2$	$3$	$3$	$0.986$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-494}) \)	None	✓	✓	1976.1.o.b	$2$	$0$	\(-3\)	\(1\)	\(-1\)	\(0\)	$1$		\(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
1976.1.o.d	$1976$	$1$	1976.o	1976.o	$2$	$3$	$3$	$0.986$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-494}) \)	None	✓	✓	1976.1.o.b	$2$	$0$	\(3\)	\(-1\)	\(-1\)	\(0\)	$1$		\(q+q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
1976.1.o.e	$1976$	$1$	1976.o	1976.o	$2$	$3$	$3$	$0.986$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-494}) \)	None	✓	✓	1976.1.o.b	$2$	$0$	\(3\)	\(1\)	\(1\)	\(0\)	$1$		\(q+q^{2}+\beta _{1}q^{3}+q^{4}-\beta _{2}q^{5}+\beta _{1}q^{6}+\cdots\)
1976.1.o.f	$1976$	$1$	1976.o	1976.o	$2$	$4$	$4$	$0.986$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-38}) \)	None		✓	1976.1.o.f	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}+\zeta_{12}^{5})q^{3}-q^{4}+\cdots\)
1976.1.o.g	$1976$	$1$	1976.o	1976.o	$2$	$4$	$4$	$0.986$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-247}) \)	None		✓	1976.1.o.g	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{8}-q^{9}+\cdots\)