Newform orbit 9200.2.a.bt

• Label: 9200.2.a.bt
• Level: $9200$
• Weight: $2$
• Character orbit: 9200.a
• Self dual: yes
• Analytic conductor: $73.462$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 9200 = 2^{4} \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9200.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(73.4623698596\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{5}) \)
Defining polynomial:	\( x^{2} - x - 1 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 2 \)
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 \(\beta = \sqrt{5}\). We also show the integral \(q\)-expansion of the trace form.

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

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

1.61803
−0.618034

0

−2.23607

0

0

0

3.23607

0

2.00000

0

1.2

0

2.23607

0

0

0

−1.23607

0

2.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(-1\)
\(5\)	\(1\)
\(23\)	\(-1\)

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	9200.2.a.bt		2
4.b	odd	2	1		575.2.a.f		2
5.b	even	2	1		368.2.a.h		2
12.b	even	2	1		5175.2.a.be		2
15.d	odd	2	1		3312.2.a.ba		2
20.d	odd	2	1		23.2.a.a	✓	2
20.e	even	4	2		575.2.b.d		4
40.e	odd	2	1		1472.2.a.t		2
40.f	even	2	1		1472.2.a.s		2
60.h	even	2	1		207.2.a.d		2
115.c	odd	2	1		8464.2.a.bb		2
140.c	even	2	1		1127.2.a.c		2
220.g	even	2	1		2783.2.a.c		2
260.g	odd	2	1		3887.2.a.i		2
340.d	odd	2	1		6647.2.a.b		2
380.d	even	2	1		8303.2.a.e		2
460.g	even	2	1		529.2.a.a		2
460.n	odd	22	10		529.2.c.o		20
460.o	even	22	10		529.2.c.n		20
1380.b	odd	2	1		4761.2.a.w		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
23.2.a.a	✓	2	20.d	odd	2	1
207.2.a.d		2	60.h	even	2	1
368.2.a.h		2	5.b	even	2	1
529.2.a.a		2	460.g	even	2	1
529.2.c.n		20	460.o	even	22	10
529.2.c.o		20	460.n	odd	22	10
575.2.a.f		2	4.b	odd	2	1
575.2.b.d		4	20.e	even	4	2
1127.2.a.c		2	140.c	even	2	1
1472.2.a.s		2	40.f	even	2	1
1472.2.a.t		2	40.e	odd	2	1
2783.2.a.c		2	220.g	even	2	1
3312.2.a.ba		2	15.d	odd	2	1
3887.2.a.i		2	260.g	odd	2	1
4761.2.a.w		2	1380.b	odd	2	1
5175.2.a.be		2	12.b	even	2	1
6647.2.a.b		2	340.d	odd	2	1
8303.2.a.e		2	380.d	even	2	1
8464.2.a.bb		2	115.c	odd	2	1
9200.2.a.bt		2	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(9200))\):

\( T_{3}^{2} - 5 \)

\( T_{7}^{2} - 2T_{7} - 4 \)

\( T_{11}^{2} - 6T_{11} + 4 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} - 5 \)
$5$	\( T^{2} \)
$7$	\( T^{2} - 2T - 4 \)
$11$	\( T^{2} - 6T + 4 \)