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Properties

Label 920.2.bn.b
Level $920$
Weight $2$
Character orbit 920.bn
Analytic conductor $7.346$
Analytic rank $0$
Dimension $1360$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [920,2,Mod(19,920)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(920, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 11, 11, 15]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("920.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 920.bn (of order \(22\), degree \(10\), minimal)

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: no
Analytic conductor: \(7.34623698596\)
Analytic rank: \(0\)
Dimension: \(1360\)
Relative dimension: \(136\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 1360 q - 14 q^{4} - 30 q^{6} + 108 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 1360 q - 14 q^{4} - 30 q^{6} + 108 q^{9} - 11 q^{10} - 44 q^{11} - 22 q^{14} + 2 q^{16} - 44 q^{19} - 11 q^{20} - 48 q^{24} - 38 q^{25} - 62 q^{26} - 11 q^{30} - 44 q^{34} + 142 q^{35} + 26 q^{36} - 11 q^{40} - 28 q^{41} + 110 q^{44} + 10 q^{46} + 28 q^{49} - 15 q^{50} - 44 q^{51} - 34 q^{54} - 22 q^{56} - 288 q^{59} - 11 q^{60} - 26 q^{64} - 22 q^{65} - 88 q^{66} - 14 q^{70} - 22 q^{74} - 30 q^{75} - 132 q^{76} + 88 q^{80} - 116 q^{81} - 22 q^{84} - 242 q^{86} - 44 q^{89} + 220 q^{90} - 126 q^{94} - 456 q^{96} - 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
19.1 −1.41420 + 0.00554958i −0.584296 − 1.98993i 1.99994 − 0.0156965i 2.08517 − 0.807517i 0.837356 + 2.81092i 4.91151 − 0.706168i −2.82823 + 0.0332968i −1.09465 + 0.703491i −2.94437 + 1.15357i
19.2 −1.41417 − 0.0108588i 0.478329 + 1.62904i 1.99976 + 0.0307124i 2.22398 + 0.232227i −0.658749 − 2.30893i −0.723559 + 0.104032i −2.82768 − 0.0651476i 0.0987956 − 0.0634920i −3.14256 − 0.352558i
19.3 −1.41347 − 0.0456997i 0.704456 + 2.39916i 1.99582 + 0.129191i 0.631350 + 2.14509i −0.886090 − 3.42334i −0.0296572 + 0.00426407i −2.81514 − 0.273816i −2.73593 + 1.75827i −0.794367 − 3.06088i
19.4 −1.41347 − 0.0457448i −0.250155 − 0.851949i 1.99581 + 0.129318i 1.59726 − 1.56485i 0.314615 + 1.21565i −3.34301 + 0.480652i −2.81512 − 0.274086i 1.86052 − 1.19568i −2.32927 + 2.13881i
19.5 −1.40617 + 0.150620i −0.908709 − 3.09478i 1.95463 − 0.423596i 0.935307 + 2.03106i 1.74394 + 4.21492i −2.14637 + 0.308602i −2.68474 + 0.890054i −6.22815 + 4.00259i −1.62112 − 2.71514i
19.6 −1.40442 − 0.166141i 0.699851 + 2.38347i 1.94479 + 0.466662i −2.21875 − 0.277747i −0.586894 − 3.46367i −3.55256 + 0.510782i −2.65378 − 0.978500i −2.66740 + 1.71423i 3.06991 + 0.758698i
19.7 −1.39931 − 0.204756i −0.145818 − 0.496611i 1.91615 + 0.573034i −1.52876 + 1.63184i 0.102361 + 0.724771i −1.67327 + 0.240580i −2.56396 − 1.19420i 2.29840 − 1.47709i 2.47334 − 1.97043i
19.8 −1.39090 − 0.255704i 0.168318 + 0.573239i 1.86923 + 0.711321i −0.387371 − 2.20226i −0.0875347 − 0.840360i 1.56888 − 0.225570i −2.41803 − 1.46735i 2.22349 − 1.42895i −0.0243314 + 3.16218i
19.9 −1.38144 + 0.302709i 0.912518 + 3.10775i 1.81673 − 0.836346i −1.96027 − 1.07579i −2.20133 − 4.01693i 3.50279 − 0.503625i −2.25653 + 1.70530i −6.30166 + 4.04983i 3.03365 + 0.892744i
19.10 −1.37482 − 0.331479i −0.239981 − 0.817301i 1.78024 + 0.911445i 1.21441 + 1.87756i 0.0590124 + 1.20319i 3.31712 − 0.476929i −2.14538 − 1.84318i 1.91337 − 1.22965i −1.04722 − 2.98385i
19.11 −1.36751 + 0.360433i 0.00164177 + 0.00559137i 1.74018 − 0.985792i −1.63648 − 1.52379i −0.00426046 − 0.00705451i 2.09955 − 0.301870i −2.02440 + 1.97530i 2.52373 − 1.62190i 2.78712 + 1.49397i
19.12 −1.36375 − 0.374409i −0.750395 − 2.55561i 1.71964 + 1.02120i −2.22304 − 0.241029i 0.0665089 + 3.76617i 3.18642 − 0.458138i −1.96281 − 2.03651i −3.44429 + 2.21351i 2.94143 + 1.16103i
19.13 −1.35904 + 0.391149i −0.625856 − 2.13147i 1.69401 − 1.06318i −1.56717 + 1.59499i 1.68429 + 2.65196i 1.59254 − 0.228972i −1.88637 + 2.10751i −1.62771 + 1.04607i 1.50597 − 2.78066i
19.14 −1.35197 − 0.414945i −0.882555 − 3.00571i 1.65564 + 1.12199i 0.408299 − 2.19847i −0.0540152 + 4.42983i −0.897632 + 0.129060i −1.77281 − 2.20389i −5.73161 + 3.68348i −1.46425 + 2.80285i
19.15 −1.33948 + 0.453639i −0.467658 − 1.59270i 1.58842 − 1.21528i −1.79244 − 1.33685i 1.34893 + 1.92124i −1.05446 + 0.151608i −1.57636 + 2.34842i 0.205785 − 0.132250i 3.00739 + 0.977560i
19.16 −1.32268 − 0.500510i 0.648024 + 2.20697i 1.49898 + 1.32403i 1.01999 − 1.98988i 0.247478 − 3.24346i 2.81267 − 0.404401i −1.31999 − 2.50153i −1.92701 + 1.23841i −2.34508 + 2.12146i
19.17 −1.31812 + 0.512405i 0.409210 + 1.39364i 1.47488 − 1.35082i −0.186213 + 2.22830i −1.25350 − 1.62730i 4.16853 − 0.599344i −1.25190 + 2.53628i 0.748979 − 0.481340i −0.896342 − 3.03258i
19.18 −1.31347 + 0.524206i 0.267502 + 0.911029i 1.45042 − 1.37706i −1.99279 + 1.01430i −0.828924 − 1.05638i −2.33579 + 0.335836i −1.18322 + 2.56905i 1.76534 − 1.13452i 2.08577 − 2.37688i
19.19 −1.27432 − 0.613270i −0.260073 − 0.885729i 1.24780 + 1.56301i −0.244514 + 2.22266i −0.211773 + 1.28820i 0.425779 − 0.0612178i −0.631554 − 2.75702i 1.80688 − 1.16121i 1.67468 − 2.68243i
19.20 −1.25631 + 0.649374i 0.267502 + 0.911029i 1.15663 − 1.63163i 1.99279 − 1.01430i −0.927664 − 0.970826i 2.33579 − 0.335836i −0.393545 + 2.80091i 1.76534 − 1.13452i −1.84490 + 2.56834i
See next 80 embeddings (of 1360 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 19.136
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
8.d odd 2 1 inner
23.d odd 22 1 inner
40.e odd 2 1 inner
115.i odd 22 1 inner
184.j even 22 1 inner
920.bn even 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 920.2.bn.b ✓ 1360
5.b even 2 1 inner 920.2.bn.b ✓ 1360
8.d odd 2 1 inner 920.2.bn.b ✓ 1360
23.d odd 22 1 inner 920.2.bn.b ✓ 1360
40.e odd 2 1 inner 920.2.bn.b ✓ 1360
115.i odd 22 1 inner 920.2.bn.b ✓ 1360
184.j even 22 1 inner 920.2.bn.b ✓ 1360
920.bn even 22 1 inner 920.2.bn.b ✓ 1360
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
920.2.bn.b ✓ 1360 1.a even 1 1 trivial
920.2.bn.b ✓ 1360 5.b even 2 1 inner
920.2.bn.b ✓ 1360 8.d odd 2 1 inner
920.2.bn.b ✓ 1360 23.d odd 22 1 inner
920.2.bn.b ✓ 1360 40.e odd 2 1 inner
920.2.bn.b ✓ 1360 115.i odd 22 1 inner
920.2.bn.b ✓ 1360 184.j even 22 1 inner
920.2.bn.b ✓ 1360 920.bn even 22 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{680} - 129 T_{3}^{678} + 8812 T_{3}^{676} - 423948 T_{3}^{674} + 16125020 T_{3}^{672} + \cdots + 28\!\cdots\!56 \) acting on \(S_{2}^{\mathrm{new}}(920, [\chi])\). Copy content Toggle raw display