Newform orbit 4851.2.a.y

• Label: 4851.2.a.y
• Level: $4851$
• Weight: $2$
• Character orbit: 4851.a
• Self dual: yes
• Analytic conductor: $38.735$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4851 = 3^{2} \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4851.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(38.7354300205\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{5}) \)
Defining polynomial:	\( x^{2} - x - 1 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 2 \)
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

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

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

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

1.61803
−0.618034

−2.23607

0

3.00000

−2.00000

0

0

−2.23607

0

4.47214

1.2

2.23607

0

3.00000

−2.00000

0

0

2.23607

0

−4.47214

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\(-1\)
\(7\)	\(-1\)
\(11\)	\(-1\)

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	4851.2.a.y		2
3.b	odd	2	1		539.2.a.f		2
7.b	odd	2	1		693.2.a.h		2
12.b	even	2	1		8624.2.a.ce		2
21.c	even	2	1		77.2.a.d	✓	2
21.g	even	6	2		539.2.e.i		4
21.h	odd	6	2		539.2.e.j		4
33.d	even	2	1		5929.2.a.m		2
77.b	even	2	1		7623.2.a.bl		2
84.h	odd	2	1		1232.2.a.m		2
105.g	even	2	1		1925.2.a.r		2
105.k	odd	4	2		1925.2.b.h		4
168.e	odd	2	1		4928.2.a.bv		2
168.i	even	2	1		4928.2.a.bm		2
231.h	odd	2	1		847.2.a.f		2
231.r	odd	10	2		847.2.f.b		4
231.r	odd	10	2		847.2.f.m		4
231.u	even	10	2		847.2.f.a		4
231.u	even	10	2		847.2.f.n		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
77.2.a.d	✓	2	21.c	even	2	1
539.2.a.f		2	3.b	odd	2	1
539.2.e.i		4	21.g	even	6	2
539.2.e.j		4	21.h	odd	6	2
693.2.a.h		2	7.b	odd	2	1
847.2.a.f		2	231.h	odd	2	1
847.2.f.a		4	231.u	even	10	2
847.2.f.b		4	231.r	odd	10	2
847.2.f.m		4	231.r	odd	10	2
847.2.f.n		4	231.u	even	10	2
1232.2.a.m		2	84.h	odd	2	1
1925.2.a.r		2	105.g	even	2	1
1925.2.b.h		4	105.k	odd	4	2
4851.2.a.y		2	1.a	even	1	1	trivial
4928.2.a.bm		2	168.i	even	2	1
4928.2.a.bv		2	168.e	odd	2	1
5929.2.a.m		2	33.d	even	2	1
7623.2.a.bl		2	77.b	even	2	1
8624.2.a.ce		2	12.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4851))\):

\( T_{2}^{2} - 5 \)

\( T_{5} + 2 \)

\( T_{13}^{2} + 2T_{13} - 4 \)

\( T_{17}^{2} + 2T_{17} - 4 \)

Hecke characteristic polynomials

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