Newform orbit 1805.2.a.o

• Label: 1805.2.a.o
• Level: $1805$
• Weight: $2$
• Character orbit: 1805.a
• Self dual: yes
• Analytic conductor: $14.413$
• Analytic rank: $0$
• Dimension: $4$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1805 = 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1805.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(14.4129975648\)
Analytic rank:	\(0\)
Dimension:	\(4\)
Coefficient field:	4.4.7537.1
Defining polynomial:	\( x^{4} - x^{3} - 5x^{2} + 4x + 3 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2,\beta_3\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	\( q - \beta_{2} q^{2} + ( - \beta_1 + 1) q^{3} + (\beta_{3} - \beta_{2} + 1) q^{4} + q^{5} + (\beta_{3} - \beta_{2} + \beta_1) q^{6} + ( - \beta_{3} - 1) q^{7} + (2 \beta_{3} - \beta_{2} - \beta_1 + 3) q^{8} + (\beta_{2} - 2 \beta_1 + 1) q^{9}+O(q^{10}) \)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 3 q^{3} + 5 q^{4} + 4 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} + q^{9}+O(q^{10}) \)

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{4} - x^{3} - 5x^{2} + 4x + 3 \) :

\(\beta_{1}\)	\(=\)	\( \nu \)
\(\beta_{2}\)	\(=\)	\( \nu^{2} - 3 \)
\(\beta_{3}\)	\(=\)	\( \nu^{3} - 4\nu \)

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

2.15976
−2.04717
1.37933
−0.491918

−1.66454

−1.15976

0.770710

1.00000

1.93047

−2.43525

2.04621

−1.65497

−1.66454

1.2

−1.19091

3.04717

−0.581734

1.00000

−3.62891

−0.609175

3.07461

6.28525

−1.19091

1.3

1.09744

−0.379334

−0.795629

1.00000

−0.416295

1.89307

−3.06803

−2.85611

1.09744

1.4

2.75802

1.49192

5.60665

1.00000

4.11474

−2.84864

9.94721

−0.774179

2.75802

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	1805.2.a.o		4
5.b	even	2	1		9025.2.a.bg		4
19.b	odd	2	1		1805.2.a.i		4
19.c	even	3	2		95.2.e.c	✓	8
57.h	odd	6	2		855.2.k.h		8
76.g	odd	6	2		1520.2.q.o		8
95.d	odd	2	1		9025.2.a.bp		4
95.i	even	6	2		475.2.e.e		8
95.m	odd	12	4		475.2.j.c		16

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.2.e.c	✓	8	19.c	even	3	2
475.2.e.e		8	95.i	even	6	2
475.2.j.c		16	95.m	odd	12	4
855.2.k.h		8	57.h	odd	6	2
1520.2.q.o		8	76.g	odd	6	2
1805.2.a.i		4	19.b	odd	2	1
1805.2.a.o		4	1.a	even	1	1	trivial
9025.2.a.bg		4	5.b	even	2	1
9025.2.a.bp		4	95.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 \(S_{2}^{\mathrm{new}}(\Gamma_0(1805))\):

\( T_{2}^{4} - T_{2}^{3} - 6T_{2}^{2} + T_{2} + 6 \)

\( T_{3}^{4} - 3T_{3}^{3} - 2T_{3}^{2} + 5T_{3} + 2 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{4} - T^{3} - 6 T^{2} + T + 6 \)
$3$	\( T^{4} - 3 T^{3} - 2 T^{2} + 5 T + 2 \)
$5$	\( (T - 1)^{4} \)
$7$	\( T^{4} + 4 T^{3} - T^{2} - 15 T - 8 \)
$11$	\( T^{4} + 2 T^{3} - 25 T^{2} - 19 T + 3 \)