↑

Properties

Label 820.2.bv.c
Level $820$
Weight $2$
Character orbit 820.bv
Analytic conductor $6.548$
Analytic rank $0$
Dimension $960$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [820,2,Mod(103,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(20)) chi = DirichletCharacter(H, H._module([10, 15, 7])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.103"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 820.bv (of order \(20\), degree \(8\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [960,-10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.54773296574\)
Analytic rank: \(0\)
Dimension: \(960\)
Relative dimension: \(120\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 960 q - 10 q^{2} - 20 q^{5} - 16 q^{6} + 2 q^{8} + 960 q^{9} - 60 q^{10} - 40 q^{12} - 20 q^{13} - 8 q^{14} - 28 q^{16} - 20 q^{17} - 48 q^{18} - 34 q^{20} - 40 q^{21} - 10 q^{22} - 48 q^{24} - 4 q^{25}+ \cdots - 38 q^{98}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
103.1 −1.41421 0.000238105i 0.769778 2.00000 0.000673463i 1.66777 − 1.48948i −1.08863 0.000183288i 0.528714 − 0.171790i −2.82843 + 0.00142863i −2.40744 −2.35823 + 2.10684i
103.2 −1.41382 − 0.0333074i 2.02199 1.99778 + 0.0941813i 2.18809 + 0.460731i −2.85874 − 0.0673473i 1.85095 − 0.601410i −2.82137 − 0.199696i 1.08846 −3.07822 − 0.724271i
103.3 −1.41368 − 0.0389341i −0.208028 1.99697 + 0.110080i 0.208096 + 2.22636i 0.294085 + 0.00809940i 0.894609 − 0.290676i −2.81878 − 0.233368i −2.95672 −0.207499 − 3.15546i
103.4 −1.41297 − 0.0593411i 2.23336 1.99296 + 0.167694i −0.983161 + 2.00833i −3.15566 − 0.132530i −3.76737 + 1.22409i −2.80603 − 0.355211i 1.98789 1.50835 − 2.77937i
103.5 −1.41061 + 0.100844i −2.10001 1.97966 − 0.284503i −2.12586 + 0.693335i 2.96231 − 0.211773i 2.45895 − 0.798960i −2.76385 + 0.600960i 1.41006 2.92885 − 1.19241i
103.6 −1.40188 − 0.186396i −3.23380 1.93051 + 0.522608i 2.23546 + 0.0520929i 4.53339 + 0.602768i 1.29559 − 0.420964i −2.60893 − 1.09247i 7.45749 −3.12413 − 0.489709i
103.7 −1.39595 − 0.226563i −1.94267 1.89734 + 0.632541i 1.06878 + 1.96410i 2.71187 + 0.440138i −3.77593 + 1.22687i −2.50527 − 1.31286i 0.773974 −1.04697 − 2.98393i
103.8 −1.37867 − 0.315075i 1.73013 1.80145 + 0.868769i −1.96065 − 1.07511i −2.38528 − 0.545122i 4.32334 − 1.40474i −2.20988 − 1.76534i −0.00664869 2.36434 + 2.09998i
103.9 −1.37711 + 0.321815i −1.94621 1.79287 − 0.886350i 1.53192 − 1.62887i 2.68014 − 0.626318i −4.55859 + 1.48118i −2.18374 + 1.79757i 0.787715 −1.58543 + 2.73613i
103.10 −1.37675 + 0.323361i 1.07913 1.79087 − 0.890375i −0.990353 − 2.00479i −1.48569 + 0.348949i −0.879997 + 0.285928i −2.17767 + 1.80492i −1.83548 2.01174 + 2.43986i
103.11 −1.37281 + 0.339686i −0.848586 1.76923 − 0.932650i −2.22703 − 0.200823i 1.16495 − 0.288253i −2.45926 + 0.799062i −2.11201 + 1.88134i −2.27990 3.12551 − 0.480799i
103.12 −1.32339 + 0.498625i 2.80709 1.50275 − 1.31975i −0.994212 + 2.00288i −3.71489 + 1.39969i 2.51904 − 0.818484i −1.33066 + 2.49586i 4.87977 0.317048 − 3.14634i
103.13 −1.32035 − 0.506639i −1.63748 1.48663 + 1.33788i 1.37580 − 1.76272i 2.16204 + 0.829612i 1.71329 − 0.556683i −1.28505 − 2.51965i −0.318655 −2.70960 + 1.63037i
103.14 −1.31585 − 0.518216i 0.442072 1.46290 + 1.36378i −2.05932 + 0.871326i −0.581699 − 0.229088i −2.58201 + 0.838946i −1.21822 − 2.55263i −2.80457 3.16128 − 0.0793606i
103.15 −1.31293 − 0.525554i −1.83316 1.44759 + 1.38003i −1.25773 − 1.84882i 2.40682 + 0.963425i 3.32085 − 1.07901i −1.17530 − 2.57268i 0.360477 0.679658 + 3.08838i
103.16 −1.30454 + 0.546054i 3.28938 1.40365 − 1.42470i −0.479772 − 2.18399i −4.29113 + 1.79618i −1.14493 + 0.372010i −1.05315 + 2.62505i 7.82003 1.81846 + 2.58712i
103.17 −1.28771 − 0.584633i 0.0874408 1.31641 + 1.50568i −0.437444 − 2.19286i −0.112599 − 0.0511208i −3.19012 + 1.03653i −0.814885 − 2.70850i −2.99235 −0.718718 + 3.07952i
103.18 −1.28177 + 0.597550i −1.86820 1.28587 − 1.53184i 1.96688 + 1.06367i 2.39460 − 1.11634i 3.59578 − 1.16834i −0.732832 + 2.73184i 0.490153 −3.15668 − 0.188076i
103.19 −1.26962 − 0.622939i 3.09593 1.22389 + 1.58180i 1.18991 + 1.89317i −3.93067 − 1.92858i 1.03218 − 0.335376i −0.568524 − 2.77070i 6.58479 −0.331414 − 3.14486i
103.20 −1.23683 + 0.685742i 1.86820 1.05952 − 1.69630i 1.96688 + 1.06367i −2.31065 + 1.28110i −3.59578 + 1.16834i −0.147221 + 2.82459i 0.490153 −3.16210 + 0.0331839i
See next 80 embeddings (of 960 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 103.120
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
205.t odd 20 1 inner
820.bv even 20 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 820.2.bv.c yes 960
4.b odd 2 1 inner 820.2.bv.c yes 960
5.c odd 4 1 820.2.bk.c ✓ 960
20.e even 4 1 820.2.bk.c ✓ 960
41.g even 20 1 820.2.bk.c ✓ 960
164.n odd 20 1 820.2.bk.c ✓ 960
205.t odd 20 1 inner 820.2.bv.c yes 960
820.bv even 20 1 inner 820.2.bv.c yes 960
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
820.2.bk.c ✓ 960 5.c odd 4 1
820.2.bk.c ✓ 960 20.e even 4 1
820.2.bk.c ✓ 960 41.g even 20 1
820.2.bk.c ✓ 960 164.n odd 20 1
820.2.bv.c yes 960 1.a even 1 1 trivial
820.2.bv.c yes 960 4.b odd 2 1 inner
820.2.bv.c yes 960 205.t odd 20 1 inner
820.2.bv.c yes 960 820.bv even 20 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(820, [\chi])\):

\( T_{3}^{480} - 960 T_{3}^{478} + 457486 T_{3}^{476} - 144292632 T_{3}^{474} + 33885068469 T_{3}^{472} + \cdots + 12\!\cdots\!36 \) Copy content Toggle raw display
\( T_{13}^{480} + 10 T_{13}^{479} - 754 T_{13}^{478} - 8360 T_{13}^{477} + 288494 T_{13}^{476} + \cdots + 33\!\cdots\!00 \) Copy content Toggle raw display