↑

Properties

Label 8281.2.a.cw
Level 82818281
Weight 22
Character orbit 8281.a
Self dual yes
Analytic conductor 66.12466.124
Analytic rank 00
Dimension 2424
CM no
Inner twists 11

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8281,2,Mod(1,8281)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8281, 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("8281.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 8281=72⋅132 8281 = 7^{2} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 8281.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: 66.124117913866.1241179138
Analytic rank: 00
Dimension: 2424
Twist minimal: no (minimal twist has level 1183)
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+q2+23q4+13q5+14q6+26q9−5q10+q11−5q12−5q15+17q16+5q17+24q19+34q20−14q22+11q23+32q24+33q25+21q27+⋯+39q99+O(q100) 24 q + q^{2} + 23 q^{4} + 13 q^{5} + 14 q^{6} + 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 5 q^{15} + 17 q^{16} + 5 q^{17} + 24 q^{19} + 34 q^{20} - 14 q^{22} + 11 q^{23} + 32 q^{24} + 33 q^{25} + 21 q^{27}+ \cdots + 39 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 −2.74249 −2.41352 5.52124 0.624420 6.61904 0 −9.65697 2.82506 −1.71247
1.2 −2.43473 −1.95805 3.92789 4.14976 4.76731 0 −4.69388 0.833959 −10.1035
1.3 −2.38490 −0.705442 3.68772 −0.769810 1.68241 0 −4.02505 −2.50235 1.83592
1.4 −2.06809 2.54401 2.27701 0.855789 −5.26125 0 −0.572885 3.47198 −1.76985
1.5 −1.76732 2.32802 1.12344 4.06760 −4.11437 0 1.54917 2.41970 −7.18877
1.6 −1.57441 −2.20221 0.478777 −3.76060 3.46719 0 2.39503 1.84974 5.92074
1.7 −1.54383 1.35319 0.383396 0.341965 −2.08910 0 2.49575 −1.16886 −0.527934
1.8 −1.20612 −1.03207 −0.545276 3.02929 1.24480 0 3.06991 −1.93483 −3.65368
1.9 −1.09197 −1.39541 −0.807612 −1.62650 1.52374 0 3.06581 −1.05283 1.77608
1.10 −0.877203 0.755024 −1.23052 −0.265839 −0.662309 0 2.83382 −2.42994 0.233195
1.11 −0.00236726 3.09829 −1.99999 −1.13142 −0.00733446 0 0.00946903 6.59939 0.00267836
1.12 0.136454 −2.96681 −1.98138 3.29030 −0.404833 0 −0.543274 5.80198 0.448974
1.13 0.254753 1.57524 −1.93510 0.518004 0.401297 0 −1.00248 −0.518622 0.131963
1.14 0.588471 −0.773677 −1.65370 −2.69602 −0.455287 0 −2.15010 −2.40142 −1.58653
1.15 0.617518 −3.07329 −1.61867 1.39605 −1.89781 0 −2.23459 6.44510 0.862085
1.16 1.02884 −2.66326 −0.941498 1.49113 −2.74006 0 −3.02632 4.09295 1.53412
1.17 1.18747 2.93451 −0.589922 3.40390 3.48463 0 −3.07545 5.61133 4.04203
1.18 1.36142 1.31293 −0.146524 −3.05867 1.78745 0 −2.92233 −1.27622 −4.16415
1.19 1.75182 −0.671818 1.06888 −2.67750 −1.17690 0 −1.63116 −2.54866 −4.69050
1.20 1.94710 1.73455 1.79121 3.71933 3.37734 0 −0.406541 0.00865975 7.24191
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
77 −1 -1
1313 +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 8281.2.a.cw 24
7.b odd 2 1 8281.2.a.cv 24
7.d odd 6 2 1183.2.e.k ✓ 48
13.b even 2 1 8281.2.a.ct 24
91.b odd 2 1 8281.2.a.cu 24
91.s odd 6 2 1183.2.e.l yes 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1183.2.e.k ✓ 48 7.d odd 6 2
1183.2.e.l yes 48 91.s odd 6 2
8281.2.a.ct 24 13.b even 2 1
8281.2.a.cu 24 91.b odd 2 1
8281.2.a.cv 24 7.b odd 2 1
8281.2.a.cw 24 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(8281))S_{2}^{\mathrm{new}}(\Gamma_0(8281)):

T224−T223−35T222+34T221+527T220−496T219−4477T218+⋯−1 T_{2}^{24} - T_{2}^{23} - 35 T_{2}^{22} + 34 T_{2}^{21} + 527 T_{2}^{20} - 496 T_{2}^{19} - 4477 T_{2}^{18} + \cdots - 1 Copy content Toggle raw display
T324−49T322−7T321+1030T320+282T319−12168T318+⋯−28469 T_{3}^{24} - 49 T_{3}^{22} - 7 T_{3}^{21} + 1030 T_{3}^{20} + 282 T_{3}^{19} - 12168 T_{3}^{18} + \cdots - 28469 Copy content Toggle raw display
T524−13T523+8T522+560T521−1887T520−8750T519+⋯+346087 T_{5}^{24} - 13 T_{5}^{23} + 8 T_{5}^{22} + 560 T_{5}^{21} - 1887 T_{5}^{20} - 8750 T_{5}^{19} + \cdots + 346087 Copy content Toggle raw display
T1124−T1123−124T1122+117T1121+6433T1120−5835T1119+⋯+64936579 T_{11}^{24} - T_{11}^{23} - 124 T_{11}^{22} + 117 T_{11}^{21} + 6433 T_{11}^{20} - 5835 T_{11}^{19} + \cdots + 64936579 Copy content Toggle raw display
T1724−5T1723−178T1722+992T1721+12871T1720−81819T1719+⋯−85617259 T_{17}^{24} - 5 T_{17}^{23} - 178 T_{17}^{22} + 992 T_{17}^{21} + 12871 T_{17}^{20} - 81819 T_{17}^{19} + \cdots - 85617259 Copy content Toggle raw display