Newform orbit 2023.2.a.i

• Label: 2023.2.a.i
• Level: $2023$
• Weight: $2$
• Character orbit: 2023.a
• Self dual: yes
• Analytic conductor: $16.154$
• Analytic rank: $0$
• Dimension: $5$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2023 = 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2023.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(16.1537363289\)
Analytic rank:	\(0\)
Dimension:	\(5\)
Coefficient field:	5.5.240133.1
Defining polynomial:	\( x^{5} - 2x^{4} - 4x^{3} + 6x^{2} + 2x - 1 \)
Coefficient ring:	\(\Z[a_1, a_2]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 119)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2,\beta_3,\beta_4\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.

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

Basis of coefficient ring in terms of a root \(\nu\) of \( x^{5} - 2x^{4} - 4x^{3} + 6x^{2} + 2x - 1 \) :

\(\beta_{1}\)	\(=\)	\( \nu \)
\(\beta_{2}\)	\(=\)	\( \nu^{2} - \nu - 2 \)
\(\beta_{3}\)	\(=\)	\( \nu^{3} - \nu^{2} - 4\nu + 1 \)
\(\beta_{4}\)	\(=\)	\( \nu^{4} - 2\nu^{3} - 4\nu^{2} + 6\nu + 2 \)

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

−1.75413
−0.526523
0.295797
1.43621
2.54865

−1.75413

−1.18405

1.07697

0.542135

2.07697

1.00000

1.61911

−1.59803

−0.950975

1.2

−0.526523

1.37273

−1.72277

3.68290

−0.722774

1.00000

1.96012

−1.11561

−1.93913

1.3

0.295797

−3.08490

−1.91250

0.755196

−0.912504

1.00000

−1.15731

6.51658

0.223385

1.4

1.43621

0.739927

0.0626866

−2.84507

1.06269

1.00000

−2.78238

−2.45251

−4.08610

1.5

2.54865

2.15629

4.49562

1.86484

5.49562

1.00000

6.36046

1.64957

4.75282

Atkin-Lehner signs

\( p \)	Sign
\(7\)	\(-1\)
\(17\)	\(1\)

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	2023.2.a.i		5
17.b	even	2	1		2023.2.a.h		5
17.c	even	4	2		119.2.b.a	✓	10
51.f	odd	4	2		1071.2.f.c		10
68.f	odd	4	2		1904.2.c.i		10
119.f	odd	4	2		833.2.b.a		10
119.m	odd	12	4		833.2.j.d		20
119.n	even	12	4		833.2.j.c		20

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
119.2.b.a	✓	10	17.c	even	4	2
833.2.b.a		10	119.f	odd	4	2
833.2.j.c		20	119.n	even	12	4
833.2.j.d		20	119.m	odd	12	4
1071.2.f.c		10	51.f	odd	4	2
1904.2.c.i		10	68.f	odd	4	2
2023.2.a.h		5	17.b	even	2	1
2023.2.a.i		5	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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2023))\):

\( T_{2}^{5} - 2T_{2}^{4} - 4T_{2}^{3} + 6T_{2}^{2} + 2T_{2} - 1 \)

\( T_{3}^{5} - 9T_{3}^{3} + 6T_{3}^{2} + 11T_{3} - 8 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	T^5 - 2*T^4 - 4*T^3 + 6*T^2 + 2*T - 1
$3$	T^5 - 9*T^3 + 6*T^2 + 11*T - 8
$5$	T^5 - 4*T^4 - 5*T^3 + 30*T^2 - 29*T + 8
$7$	\( (T - 1)^{5} \)
$11$	T^5 - 40*T^3 + 40*T^2 + 368*T - 640