↑

Properties

Label 4205.2.a.y
Level 42054205
Weight 22
Character orbit 4205.a
Self dual yes
Analytic conductor 33.57733.577
Analytic rank 11
Dimension 2424
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4205,2,Mod(1,4205)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4205, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4205.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4205=5⋅292 4205 = 5 \cdot 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4205.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 33.577094049933.5770940499
Analytic rank: 11
Dimension: 2424
Twist minimal: no (minimal twist has level 145)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

qq-expansion

The algebraic qq-expansion of this newform has not been computed, but we have computed the trace expansion.

Tr⁡(f)(q)=\operatorname{Tr}(f)(q) = 24q+14q4+24q5−18q6−38q7+18q9−34q13−10q16+14q20−10q22−44q23−4q24+24q25−44q28−18q30−58q33+8q34−38q35+⋯+22q96+O(q100) 24 q + 14 q^{4} + 24 q^{5} - 18 q^{6} - 38 q^{7} + 18 q^{9} - 34 q^{13} - 10 q^{16} + 14 q^{20} - 10 q^{22} - 44 q^{23} - 4 q^{24} + 24 q^{25} - 44 q^{28} - 18 q^{30} - 58 q^{33} + 8 q^{34} - 38 q^{35}+ \cdots + 22 q^{96}+O(q^{100}) Copy content Toggle raw display

Embeddings

For each embedding ιm\iota_m of the coefficient field, the values ιm(an)\iota_m(a_n) are shown below.

For more information on an embedded modular form you can click on its label.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   a2 a_{2} a3 a_{3} a4 a_{4} a5 a_{5} a6 a_{6} a7 a_{7} a8 a_{8} a9 a_{9} a10 a_{10}
1.1 −2.52311 −0.367113 4.36608 1.00000 0.926266 −5.12713 −5.96987 −2.86523 −2.52311
1.2 −2.46493 1.17334 4.07587 1.00000 −2.89220 −0.528087 −5.11687 −1.62327 −2.46493
1.3 −2.07250 3.28868 2.29525 1.00000 −6.81579 −4.26791 −0.611896 7.81544 −2.07250
1.4 −1.95283 0.620899 1.81353 1.00000 −1.21251 0.126430 0.364137 −2.61448 −1.95283
1.5 −1.86976 −0.995019 1.49598 1.00000 1.86044 0.907041 0.942385 −2.00994 −1.86976
1.6 −1.34022 −1.23909 −0.203815 1.00000 1.66065 −3.86391 2.95359 −1.46465 −1.34022
1.7 −1.29519 −3.05287 −0.322483 1.00000 3.95404 −3.30555 3.00806 6.31999 −1.29519
1.8 −1.26889 2.62094 −0.389926 1.00000 −3.32568 −0.00237662 3.03255 3.86933 −1.26889
1.9 −0.976160 2.48787 −1.04711 1.00000 −2.42856 2.05638 2.97447 3.18951 −0.976160
1.10 −0.946293 1.03726 −1.10453 1.00000 −0.981552 1.25250 2.93779 −1.92409 −0.946293
1.11 −0.110687 −2.50070 −1.98775 1.00000 0.276795 −2.79886 0.441392 3.25348 −0.110687
1.12 −0.0943500 0.232166 −1.99110 1.00000 −0.0219049 −3.44853 0.376560 −2.94610 −0.0943500
1.13 0.0943500 −0.232166 −1.99110 1.00000 −0.0219049 −3.44853 −0.376560 −2.94610 0.0943500
1.14 0.110687 2.50070 −1.98775 1.00000 0.276795 −2.79886 −0.441392 3.25348 0.110687
1.15 0.946293 −1.03726 −1.10453 1.00000 −0.981552 1.25250 −2.93779 −1.92409 0.946293
1.16 0.976160 −2.48787 −1.04711 1.00000 −2.42856 2.05638 −2.97447 3.18951 0.976160
1.17 1.26889 −2.62094 −0.389926 1.00000 −3.32568 −0.00237662 −3.03255 3.86933 1.26889
1.18 1.29519 3.05287 −0.322483 1.00000 3.95404 −3.30555 −3.00806 6.31999 1.29519
1.19 1.34022 1.23909 −0.203815 1.00000 1.66065 −3.86391 −2.95359 −1.46465 1.34022
1.20 1.86976 0.995019 1.49598 1.00000 1.86044 0.907041 −0.942385 −2.00994 1.86976
See all 24 embeddings
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

p p Sign
55 −1 -1
2929 −1 -1

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
29.b even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4205.2.a.y 24
29.b even 2 1 inner 4205.2.a.y 24
29.f odd 28 2 145.2.m.a ✓ 24
145.o even 28 2 725.2.p.b 48
145.s odd 28 2 725.2.q.b 24
145.t even 28 2 725.2.p.b 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
145.2.m.a ✓ 24 29.f odd 28 2
725.2.p.b 48 145.o even 28 2
725.2.p.b 48 145.t even 28 2
725.2.q.b 24 145.s odd 28 2
4205.2.a.y 24 1.a even 1 1 trivial
4205.2.a.y 24 29.b even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on S2new(Γ0(4205))S_{2}^{\mathrm{new}}(\Gamma_0(4205)):

T224−31T222+414T220−3129T218+14790T216−45609T214+⋯+1 T_{2}^{24} - 31 T_{2}^{22} + 414 T_{2}^{20} - 3129 T_{2}^{18} + 14790 T_{2}^{16} - 45609 T_{2}^{14} + \cdots + 1 Copy content Toggle raw display
T324−45T322+845T320−8613T318+52013T316−191573T314+⋯+169 T_{3}^{24} - 45 T_{3}^{22} + 845 T_{3}^{20} - 8613 T_{3}^{18} + 52013 T_{3}^{16} - 191573 T_{3}^{14} + \cdots + 169 Copy content Toggle raw display