Newform orbit 2783.2.a.c

• Label: 2783.2.a.c
• Level: $2783$
• Weight: $2$
• Character orbit: 2783.a
• Self dual: yes
• Analytic conductor: $22.222$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2783 = 11^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2783.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(22.2223668825\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{5}) \)
Defining polynomial:	\( x^{2} - x - 1 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{5})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q + \beta q^{2} + (2 \beta - 1) q^{3} + (\beta - 1) q^{4} - 2 \beta q^{5} + (\beta + 2) q^{6} + (2 \beta - 2) q^{7} + ( - 2 \beta + 1) q^{8} + 2 q^{9} +O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 2 q^{5} + 5 q^{6} - 2 q^{7} + 4 q^{9}+O(q^{10}) \)

Embeddings

For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.

For more information on an embedded modular form you can click on its label.

Label  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

1.1

−0.618034
1.61803

−0.618034

−2.23607

−1.61803

1.23607

1.38197

−3.23607

2.23607

2.00000

−0.763932

1.2

1.61803

2.23607

0.618034

−3.23607

3.61803

1.23607

−2.23607

2.00000

−5.23607

Atkin-Lehner signs

\( p \)	Sign
\(11\)	\(-1\)
\(23\)	\(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	2783.2.a.c		2
11.b	odd	2	1		23.2.a.a	✓	2
33.d	even	2	1		207.2.a.d		2
44.c	even	2	1		368.2.a.h		2
55.d	odd	2	1		575.2.a.f		2
55.e	even	4	2		575.2.b.d		4
77.b	even	2	1		1127.2.a.c		2
88.b	odd	2	1		1472.2.a.t		2
88.g	even	2	1		1472.2.a.s		2
132.d	odd	2	1		3312.2.a.ba		2
143.d	odd	2	1		3887.2.a.i		2
165.d	even	2	1		5175.2.a.be		2
187.b	odd	2	1		6647.2.a.b		2
209.d	even	2	1		8303.2.a.e		2
220.g	even	2	1		9200.2.a.bt		2
253.b	even	2	1		529.2.a.a		2
253.k	odd	22	10		529.2.c.o		20
253.l	even	22	10		529.2.c.n		20
759.h	odd	2	1		4761.2.a.w		2
1012.b	odd	2	1		8464.2.a.bb		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.2.a.a	✓	2	11.b	odd	2	1
207.2.a.d		2	33.d	even	2	1
368.2.a.h		2	44.c	even	2	1
529.2.a.a		2	253.b	even	2	1
529.2.c.n		20	253.l	even	22	10
529.2.c.o		20	253.k	odd	22	10
575.2.a.f		2	55.d	odd	2	1
575.2.b.d		4	55.e	even	4	2
1127.2.a.c		2	77.b	even	2	1
1472.2.a.s		2	88.g	even	2	1
1472.2.a.t		2	88.b	odd	2	1
2783.2.a.c		2	1.a	even	1	1	trivial
3312.2.a.ba		2	132.d	odd	2	1
3887.2.a.i		2	143.d	odd	2	1
4761.2.a.w		2	759.h	odd	2	1
5175.2.a.be		2	165.d	even	2	1
6647.2.a.b		2	187.b	odd	2	1
8303.2.a.e		2	209.d	even	2	1
8464.2.a.bb		2	1012.b	odd	2	1
9200.2.a.bt		2	220.g	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{2} - T_{2} - 1 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2783))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} - T - 1 \)
$3$	\( T^{2} - 5 \)
$5$	\( T^{2} + 2T - 4 \)
$7$	\( T^{2} + 2T - 4 \)
$11$	\( T^{2} \)