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Properties

Label 4655.2.a.bs
Level 46554655
Weight 22
Character orbit 4655.a
Self dual yes
Analytic conductor 37.17037.170
Analytic rank 00
Dimension 2626
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4655,2,Mod(1,4655)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4655, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("4655.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4655=5⋅72⋅19 4655 = 5 \cdot 7^{2} \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4655.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: 37.170362140937.1703621409
Analytic rank: 00
Dimension: 2626
Twist minimal: yes
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) = 26q+4q2+6q3+36q4+26q5−4q6+12q8+44q9+4q10+14q11+20q12+14q13+6q15+64q16+18q17+8q18−26q19+36q20+36q22+⋯+24q99+O(q100) 26 q + 4 q^{2} + 6 q^{3} + 36 q^{4} + 26 q^{5} - 4 q^{6} + 12 q^{8} + 44 q^{9} + 4 q^{10} + 14 q^{11} + 20 q^{12} + 14 q^{13} + 6 q^{15} + 64 q^{16} + 18 q^{17} + 8 q^{18} - 26 q^{19} + 36 q^{20} + 36 q^{22}+ \cdots + 24 q^{99}+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 −2.78329 3.28920 5.74672 1.00000 −9.15481 0 −10.4282 7.81883 −2.78329
1.2 −2.59964 0.401002 4.75812 1.00000 −1.04246 0 −7.17010 −2.83920 −2.59964
1.3 −2.33490 −0.464806 3.45176 1.00000 1.08528 0 −3.38971 −2.78396 −2.33490
1.4 −2.22756 −1.74547 2.96202 1.00000 3.88813 0 −2.14296 0.0466492 −2.22756
1.5 −2.18977 2.55255 2.79510 1.00000 −5.58950 0 −1.74110 3.51550 −2.18977
1.6 −1.87125 0.704568 1.50158 1.00000 −1.31842 0 0.932671 −2.50358 −1.87125
1.7 −1.68247 −3.39985 0.830711 1.00000 5.72015 0 1.96730 8.55898 −1.68247
1.8 −1.21870 2.59660 −0.514774 1.00000 −3.16448 0 3.06475 3.74235 −1.21870
1.9 −0.970750 −1.67805 −1.05764 1.00000 1.62896 0 2.96821 −0.184157 −0.970750
1.10 −0.237306 −2.08918 −1.94369 1.00000 0.495776 0 0.935862 1.36468 −0.237306
1.11 −0.208527 2.42003 −1.95652 1.00000 −0.504642 0 0.825039 2.85657 −0.208527
1.12 −0.162590 3.34603 −1.97356 1.00000 −0.544029 0 0.646060 8.19589 −0.162590
1.13 −0.148061 −1.13846 −1.97808 1.00000 0.168562 0 0.588998 −1.70391 −0.148061
1.14 −0.0673534 0.195526 −1.99546 1.00000 −0.0131693 0 0.269108 −2.96177 −0.0673534
1.15 0.430405 −3.01701 −1.81475 1.00000 −1.29854 0 −1.64189 6.10233 0.430405
1.16 1.09706 0.170744 −0.796456 1.00000 0.187316 0 −3.06788 −2.97085 1.09706
1.17 1.20641 2.57761 −0.544574 1.00000 3.10966 0 −3.06980 3.64407 1.20641
1.18 1.26806 1.15394 −0.392024 1.00000 1.46327 0 −3.03323 −1.66842 1.26806
1.19 1.59222 −1.71325 0.535154 1.00000 −2.72786 0 −2.33235 −0.0647885 1.59222
1.20 1.89552 −0.890414 1.59301 1.00000 −1.68780 0 −0.771462 −2.20716 1.89552
See all 26 embeddings
nn: e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.26
Significant digits:
Format:

Atkin-Lehner signs

p p Sign
55 −1 -1
77 +1 +1
1919 +1 +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 4655.2.a.bs yes 26
7.b odd 2 1 4655.2.a.br ✓ 26
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4655.2.a.br ✓ 26 7.b odd 2 1
4655.2.a.bs yes 26 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on S2new(Γ0(4655))S_{2}^{\mathrm{new}}(\Gamma_0(4655)):

T226−4T225−36T224+156T223+542T222−2628T221+⋯+14 T_{2}^{26} - 4 T_{2}^{25} - 36 T_{2}^{24} + 156 T_{2}^{23} + 542 T_{2}^{22} - 2628 T_{2}^{21} + \cdots + 14 Copy content Toggle raw display
T326−6T325−43T324+308T323+704T322−6760T321+⋯−19612 T_{3}^{26} - 6 T_{3}^{25} - 43 T_{3}^{24} + 308 T_{3}^{23} + 704 T_{3}^{22} - 6760 T_{3}^{21} + \cdots - 19612 Copy content Toggle raw display
T1126−14T1125−103T1124+2276T1123+536T1122−150792T1121+⋯−32130496 T_{11}^{26} - 14 T_{11}^{25} - 103 T_{11}^{24} + 2276 T_{11}^{23} + 536 T_{11}^{22} - 150792 T_{11}^{21} + \cdots - 32130496 Copy content Toggle raw display
T1326−14T1325−121T1324+2368T1323+4328T1322+⋯−3138774099712 T_{13}^{26} - 14 T_{13}^{25} - 121 T_{13}^{24} + 2368 T_{13}^{23} + 4328 T_{13}^{22} + \cdots - 3138774099712 Copy content Toggle raw display
T1726−18T1725−129T1724+3896T1723+650T1722+⋯−6892135972864 T_{17}^{26} - 18 T_{17}^{25} - 129 T_{17}^{24} + 3896 T_{17}^{23} + 650 T_{17}^{22} + \cdots - 6892135972864 Copy content Toggle raw display