Newform orbit 2890.2.a.t

• Label: 2890.2.a.t
• Level: $2890$
• Weight: $2$
• Character orbit: 2890.a
• Self dual: yes
• Analytic conductor: $23.077$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 2890 = 2 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2890.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(23.0767661842\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{2}) \)
Defining polynomial:	\( x^{2} - 2 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 170)
Fricke sign:	\(1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{2}\). We also show the integral \(q\)-expansion of the trace form.

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

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

−1.41421
1.41421

1.00000

−2.41421

1.00000

1.00000

−2.41421

−0.585786

1.00000

2.82843

1.00000

1.2

1.00000

0.414214

1.00000

1.00000

0.414214

−3.41421

1.00000

−2.82843

1.00000

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\(-1\)
\(5\)	\(-1\)
\(17\)	\(1\)

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	2890.2.a.t		2
17.b	even	2	1		2890.2.a.v		2
17.c	even	4	2		2890.2.b.j		4
17.d	even	8	2		170.2.h.a	✓	4
51.g	odd	8	2		1530.2.q.c		4
68.g	odd	8	2		1360.2.bt.a		4
85.k	odd	8	2		850.2.g.e		4
85.m	even	8	2		850.2.h.g		4
85.n	odd	8	2		850.2.g.h		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
170.2.h.a	✓	4	17.d	even	8	2
850.2.g.e		4	85.k	odd	8	2
850.2.g.h		4	85.n	odd	8	2
850.2.h.g		4	85.m	even	8	2
1360.2.bt.a		4	68.g	odd	8	2
1530.2.q.c		4	51.g	odd	8	2
2890.2.a.t		2	1.a	even	1	1	trivial
2890.2.a.v		2	17.b	even	2	1
2890.2.b.j		4	17.c	even	4	2

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2890))\):

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

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

\( T_{13} + 1 \)

Hecke characteristic polynomials

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