Properties

Label 2800.2.a.x
Level 2800
Weight 2
Character orbit 2800.a
Self dual yes
Analytic conductor 22.358
Analytic rank 1
Dimension 1
CM no
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 2800 = 2^{4} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 2800.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(22.3581125660\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 350)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q + q^{3} + q^{7} - 2q^{9} + O(q^{10}) \) \( q + q^{3} + q^{7} - 2q^{9} - 3q^{11} - 2q^{13} - 3q^{17} + 7q^{19} + q^{21} - 5q^{27} - 6q^{29} + 4q^{31} - 3q^{33} - 8q^{37} - 2q^{39} - 9q^{41} + 8q^{43} - 6q^{47} + q^{49} - 3q^{51} + 12q^{53} + 7q^{57} - 12q^{59} - 10q^{61} - 2q^{63} - 7q^{67} - 6q^{71} - 5q^{73} - 3q^{77} - 14q^{79} + q^{81} - 9q^{83} - 6q^{87} - 15q^{89} - 2q^{91} + 4q^{93} + 10q^{97} + 6q^{99} + O(q^{100}) \)

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
0 1.00000 0 0 0 1.00000 0 −2.00000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

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 2800.2.a.x 1
4.b odd 2 1 350.2.a.a 1
5.b even 2 1 2800.2.a.h 1
5.c odd 4 2 2800.2.g.i 2
12.b even 2 1 3150.2.a.x 1
20.d odd 2 1 350.2.a.e yes 1
20.e even 4 2 350.2.c.c 2
28.d even 2 1 2450.2.a.m 1
60.h even 2 1 3150.2.a.m 1
60.l odd 4 2 3150.2.g.f 2
140.c even 2 1 2450.2.a.x 1
140.j odd 4 2 2450.2.c.h 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
350.2.a.a 1 4.b odd 2 1
350.2.a.e yes 1 20.d odd 2 1
350.2.c.c 2 20.e even 4 2
2450.2.a.m 1 28.d even 2 1
2450.2.a.x 1 140.c even 2 1
2450.2.c.h 2 140.j odd 4 2
2800.2.a.h 1 5.b even 2 1
2800.2.a.x 1 1.a even 1 1 trivial
2800.2.g.i 2 5.c odd 4 2
3150.2.a.m 1 60.h even 2 1
3150.2.a.x 1 12.b even 2 1
3150.2.g.f 2 60.l odd 4 2

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(5\) \(1\)
\(7\) \(-1\)

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(2800))\):

\( T_{3} - 1 \)
\( T_{11} + 3 \)
\( T_{13} + 2 \)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ \( 1 - T + 3 T^{2} \)
$5$ 1
$7$ \( 1 - T \)
$11$ \( 1 + 3 T + 11 T^{2} \)
$13$ \( 1 + 2 T + 13 T^{2} \)
$17$ \( 1 + 3 T + 17 T^{2} \)
$19$ \( 1 - 7 T + 19 T^{2} \)
$23$ \( 1 + 23 T^{2} \)
$29$ \( 1 + 6 T + 29 T^{2} \)
$31$ \( 1 - 4 T + 31 T^{2} \)
$37$ \( 1 + 8 T + 37 T^{2} \)
$41$ \( 1 + 9 T + 41 T^{2} \)
$43$ \( 1 - 8 T + 43 T^{2} \)
$47$ \( 1 + 6 T + 47 T^{2} \)
$53$ \( 1 - 12 T + 53 T^{2} \)
$59$ \( 1 + 12 T + 59 T^{2} \)
$61$ \( 1 + 10 T + 61 T^{2} \)
$67$ \( 1 + 7 T + 67 T^{2} \)
$71$ \( 1 + 6 T + 71 T^{2} \)
$73$ \( 1 + 5 T + 73 T^{2} \)
$79$ \( 1 + 14 T + 79 T^{2} \)
$83$ \( 1 + 9 T + 83 T^{2} \)
$89$ \( 1 + 15 T + 89 T^{2} \)
$97$ \( 1 - 10 T + 97 T^{2} \)
show more
show less