Newform orbit 7865.2.a.h

• Label: 7865.2.a.h
• Level: $7865$
• Weight: $2$
• Character orbit: 7865.a
• Self dual: yes
• Analytic conductor: $62.802$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 7865 = 5 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7865.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(62.8023411897\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{3}) \)
Defining polynomial:	\( x^{2} - 3 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 65)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{3}\). We also show the integral \(q\)-expansion of the trace form.

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

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

−1.73205
1.73205

−1.73205

−0.732051

1.00000

−1.00000

1.26795

−2.00000

1.73205

−2.46410

1.73205

1.2

1.73205

2.73205

1.00000

−1.00000

4.73205

−2.00000

−1.73205

4.46410

−1.73205

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\(1\)
\(11\)	\(-1\)
\(13\)	\(1\)

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	7865.2.a.h		2
11.b	odd	2	1		65.2.a.c	✓	2
33.d	even	2	1		585.2.a.k		2
44.c	even	2	1		1040.2.a.h		2
55.d	odd	2	1		325.2.a.g		2
55.e	even	4	2		325.2.b.e		4
77.b	even	2	1		3185.2.a.k		2
88.b	odd	2	1		4160.2.a.y		2
88.g	even	2	1		4160.2.a.bj		2
132.d	odd	2	1		9360.2.a.cm		2
143.d	odd	2	1		845.2.a.d		2
143.g	even	4	2		845.2.c.e		4
143.i	odd	6	2		845.2.e.f		4
143.k	odd	6	2		845.2.e.e		4
143.o	even	12	2		845.2.m.a		4
143.o	even	12	2		845.2.m.c		4
165.d	even	2	1		2925.2.a.z		2
165.l	odd	4	2		2925.2.c.v		4
220.g	even	2	1		5200.2.a.ca		2
429.e	even	2	1		7605.2.a.be		2
715.c	odd	2	1		4225.2.a.w		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
65.2.a.c	✓	2	11.b	odd	2	1
325.2.a.g		2	55.d	odd	2	1
325.2.b.e		4	55.e	even	4	2
585.2.a.k		2	33.d	even	2	1
845.2.a.d		2	143.d	odd	2	1
845.2.c.e		4	143.g	even	4	2
845.2.e.e		4	143.k	odd	6	2
845.2.e.f		4	143.i	odd	6	2
845.2.m.a		4	143.o	even	12	2
845.2.m.c		4	143.o	even	12	2
1040.2.a.h		2	44.c	even	2	1
2925.2.a.z		2	165.d	even	2	1
2925.2.c.v		4	165.l	odd	4	2
3185.2.a.k		2	77.b	even	2	1
4160.2.a.y		2	88.b	odd	2	1
4160.2.a.bj		2	88.g	even	2	1
4225.2.a.w		2	715.c	odd	2	1
5200.2.a.ca		2	220.g	even	2	1
7605.2.a.be		2	429.e	even	2	1
7865.2.a.h		2	1.a	even	1	1	trivial
9360.2.a.cm		2	132.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(7865))\):

\( T_{2}^{2} - 3 \)

\( T_{3}^{2} - 2T_{3} - 2 \)

Hecke characteristic polynomials

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