Newform orbit 9025.2.a.b

• Label: 9025.2.a.b
• Level: $9025$
• Weight: $2$
• Character orbit: 9025.a
• Self dual: yes
• Analytic conductor: $72.065$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(72.0649878242\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

\( q - 2 q^{2} + 2 q^{4} + 4 q^{7} - 3 q^{9}+O(q^{10}) \)

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

−2.00000

0

2.00000

0

0

4.00000

0

−3.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\(-1\)
\(19\)	\(1\)

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	9025.2.a.b		1
5.b	even	2	1		9025.2.a.i		1
5.c	odd	4	2		1805.2.b.b		2
19.b	odd	2	1		9025.2.a.j		1
19.c	even	3	2		475.2.e.c		2
95.d	odd	2	1		9025.2.a.a		1
95.g	even	4	2		1805.2.b.a		2
95.i	even	6	2		475.2.e.a		2
95.m	odd	12	4		95.2.i.a	✓	4
285.v	even	12	4		855.2.be.a		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.2.i.a	✓	4	95.m	odd	12	4
475.2.e.a		2	95.i	even	6	2
475.2.e.c		2	19.c	even	3	2
855.2.be.a		4	285.v	even	12	4
1805.2.b.a		2	95.g	even	4	2
1805.2.b.b		2	5.c	odd	4	2
9025.2.a.a		1	95.d	odd	2	1
9025.2.a.b		1	1.a	even	1	1	trivial
9025.2.a.i		1	5.b	even	2	1
9025.2.a.j		1	19.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(9025))\):

\( T_{2} + 2 \)

\( T_{3} \)

\( T_{7} - 4 \)

\( T_{11} + 1 \)

\( T_{29} - 9 \)

Hecke characteristic polynomials

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