Properties

Label 80.4.a.b
Level $80$
Weight $4$
Character orbit 80.a
Self dual yes
Analytic conductor $4.720$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 80.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(4.72015280046\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 40)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

\(f(q)\) \(=\) \( q - 4 q^{3} + 5 q^{5} - 16 q^{7} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 4 q^{3} + 5 q^{5} - 16 q^{7} - 11 q^{9} - 36 q^{11} - 42 q^{13} - 20 q^{15} - 110 q^{17} + 116 q^{19} + 64 q^{21} - 16 q^{23} + 25 q^{25} + 152 q^{27} + 198 q^{29} - 240 q^{31} + 144 q^{33} - 80 q^{35} - 258 q^{37} + 168 q^{39} + 442 q^{41} + 292 q^{43} - 55 q^{45} - 392 q^{47} - 87 q^{49} + 440 q^{51} + 142 q^{53} - 180 q^{55} - 464 q^{57} + 348 q^{59} - 570 q^{61} + 176 q^{63} - 210 q^{65} - 692 q^{67} + 64 q^{69} - 168 q^{71} - 134 q^{73} - 100 q^{75} + 576 q^{77} - 784 q^{79} - 311 q^{81} - 564 q^{83} - 550 q^{85} - 792 q^{87} + 1034 q^{89} + 672 q^{91} + 960 q^{93} + 580 q^{95} - 382 q^{97} + 396 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −4.00000 0 5.00000 0 −16.0000 0 −11.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

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

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 80.4.a.b 1
3.b odd 2 1 720.4.a.d 1
4.b odd 2 1 40.4.a.b 1
5.b even 2 1 400.4.a.p 1
5.c odd 4 2 400.4.c.h 2
8.b even 2 1 320.4.a.j 1
8.d odd 2 1 320.4.a.e 1
12.b even 2 1 360.4.a.f 1
16.e even 4 2 1280.4.d.m 2
16.f odd 4 2 1280.4.d.d 2
20.d odd 2 1 200.4.a.d 1
20.e even 4 2 200.4.c.f 2
28.d even 2 1 1960.4.a.e 1
40.e odd 2 1 1600.4.a.bk 1
40.f even 2 1 1600.4.a.q 1
60.h even 2 1 1800.4.a.h 1
60.l odd 4 2 1800.4.f.d 2
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
40.4.a.b 1 4.b odd 2 1
80.4.a.b 1 1.a even 1 1 trivial
200.4.a.d 1 20.d odd 2 1
200.4.c.f 2 20.e even 4 2
320.4.a.e 1 8.d odd 2 1
320.4.a.j 1 8.b even 2 1
360.4.a.f 1 12.b even 2 1
400.4.a.p 1 5.b even 2 1
400.4.c.h 2 5.c odd 4 2
720.4.a.d 1 3.b odd 2 1
1280.4.d.d 2 16.f odd 4 2
1280.4.d.m 2 16.e even 4 2
1600.4.a.q 1 40.f even 2 1
1600.4.a.bk 1 40.e odd 2 1
1800.4.a.h 1 60.h even 2 1
1800.4.f.d 2 60.l odd 4 2
1960.4.a.e 1 28.d even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(80))\):

\( T_{3} + 4 \) Copy content Toggle raw display
\( T_{7} + 16 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T \) Copy content Toggle raw display
$3$ \( T + 4 \) Copy content Toggle raw display
$5$ \( T - 5 \) Copy content Toggle raw display
$7$ \( T + 16 \) Copy content Toggle raw display
$11$ \( T + 36 \) Copy content Toggle raw display
$13$ \( T + 42 \) Copy content Toggle raw display
$17$ \( T + 110 \) Copy content Toggle raw display
$19$ \( T - 116 \) Copy content Toggle raw display
$23$ \( T + 16 \) Copy content Toggle raw display
$29$ \( T - 198 \) Copy content Toggle raw display
$31$ \( T + 240 \) Copy content Toggle raw display
$37$ \( T + 258 \) Copy content Toggle raw display
$41$ \( T - 442 \) Copy content Toggle raw display
$43$ \( T - 292 \) Copy content Toggle raw display
$47$ \( T + 392 \) Copy content Toggle raw display
$53$ \( T - 142 \) Copy content Toggle raw display
$59$ \( T - 348 \) Copy content Toggle raw display
$61$ \( T + 570 \) Copy content Toggle raw display
$67$ \( T + 692 \) Copy content Toggle raw display
$71$ \( T + 168 \) Copy content Toggle raw display
$73$ \( T + 134 \) Copy content Toggle raw display
$79$ \( T + 784 \) Copy content Toggle raw display
$83$ \( T + 564 \) Copy content Toggle raw display
$89$ \( T - 1034 \) Copy content Toggle raw display
$97$ \( T + 382 \) Copy content Toggle raw display
show more
show less