Newform orbit 4725.2.a.ba

• Label: 4725.2.a.ba
• Level: $4725$
• Weight: $2$
• Character orbit: 4725.a
• Self dual: yes
• Analytic conductor: $37.729$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $2$

Newspace parameters

Level:	\( N \)	\(=\)	\( 4725 = 3^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4725.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(37.7293149551\)
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 189)
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.

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

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

1.00000

0

0

−1.00000

1.73205

0

0

1.2

1.73205

0

1.00000

0

0

−1.00000

−1.73205

0

0

Atkin-Lehner signs

\( p \)	Sign
\(3\)	\(-1\)
\(5\)	\(1\)
\(7\)	\(1\)

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
3.b	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	4725.2.a.ba		2
3.b	odd	2	1	inner	4725.2.a.ba		2
5.b	even	2	1		189.2.a.e	✓	2
15.d	odd	2	1		189.2.a.e	✓	2
20.d	odd	2	1		3024.2.a.bg		2
35.c	odd	2	1		1323.2.a.t		2
45.h	odd	6	2		567.2.f.k		4
45.j	even	6	2		567.2.f.k		4
60.h	even	2	1		3024.2.a.bg		2
105.g	even	2	1		1323.2.a.t		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
189.2.a.e	✓	2	5.b	even	2	1
189.2.a.e	✓	2	15.d	odd	2	1
567.2.f.k		4	45.h	odd	6	2
567.2.f.k		4	45.j	even	6	2
1323.2.a.t		2	35.c	odd	2	1
1323.2.a.t		2	105.g	even	2	1
3024.2.a.bg		2	20.d	odd	2	1
3024.2.a.bg		2	60.h	even	2	1
4725.2.a.ba		2	1.a	even	1	1	trivial
4725.2.a.ba		2	3.b	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4725))\):

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

\( T_{11}^{2} - 3 \)

\( T_{13} + 2 \)

\( T_{37} - 7 \)

Hecke characteristic polynomials

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