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Properties

Label 880.2.cz.a
Level $880$
Weight $2$
Character orbit 880.cz
Analytic conductor $7.027$
Analytic rank $0$
Dimension $1120$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [880,2,Mod(147,880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(880, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 15, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.147");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.cz (of order \(20\), degree \(8\), 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: \(7.02683537787\)
Analytic rank: \(0\)
Dimension: \(1120\)
Relative dimension: \(140\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9} - 8 q^{10} - 16 q^{11} - 44 q^{12} - 12 q^{13} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 10 q^{18} - 6 q^{20} - 32 q^{21} - 10 q^{22} - 32 q^{23} - 24 q^{24} + 20 q^{26} - 22 q^{28} + 36 q^{30} - 36 q^{32} - 16 q^{33} - 32 q^{34} + 14 q^{35} + 20 q^{36} - 12 q^{37} - 26 q^{38} - 88 q^{40} - 6 q^{42} + 32 q^{43} + 80 q^{44} - 8 q^{45} - 12 q^{46} - 18 q^{48} + 16 q^{50} - 12 q^{51} + 34 q^{52} - 168 q^{54} - 16 q^{55} - 80 q^{56} - 24 q^{57} + 38 q^{58} + 16 q^{59} - 32 q^{60} - 12 q^{61} + 96 q^{62} + 36 q^{63} - 32 q^{65} - 24 q^{66} - 32 q^{67} - 38 q^{68} + 36 q^{69} - 42 q^{70} - 56 q^{71} - 76 q^{72} + 100 q^{74} + 30 q^{75} - 32 q^{76} - 108 q^{78} + 102 q^{80} - 240 q^{81} - 18 q^{82} + 24 q^{84} + 14 q^{85} - 4 q^{86} - 32 q^{87} - 98 q^{88} - 44 q^{90} - 28 q^{91} - 48 q^{92} - 36 q^{93} - 48 q^{94} - 120 q^{95} + 20 q^{96} - 12 q^{97} - 284 q^{98} + 20 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
147.1 −1.41413 − 0.0150371i −2.10316 − 0.683359i 1.99955 + 0.0425289i −1.38641 + 1.75439i 2.96388 + 0.997986i 1.01174 − 1.98566i −2.82699 − 0.0902090i 1.52926 + 1.11107i 1.98695 − 2.46009i
147.2 −1.41268 + 0.0659259i 1.21781 + 0.395691i 1.99131 − 0.186264i 0.316497 − 2.21356i −1.74646 − 0.478698i −0.197314 + 0.387250i −2.80079 + 0.394409i −1.10056 − 0.799601i −0.301177 + 3.14790i
147.3 −1.40971 − 0.112723i 3.17223 + 1.03072i 1.97459 + 0.317814i −0.236708 + 2.22350i −4.35575 − 1.81060i 1.59029 − 3.12112i −2.74778 − 0.670609i 6.57359 + 4.77599i 0.584331 − 3.10782i
147.4 −1.40684 + 0.144252i −0.632130 − 0.205391i 1.95838 − 0.405878i −1.44037 − 1.71036i 0.918932 + 0.197766i 0.916346 − 1.79843i −2.69658 + 0.853504i −2.06965 − 1.50369i 2.27309 + 2.19843i
147.5 −1.40420 + 0.167990i −2.83045 − 0.919670i 1.94356 − 0.471782i 2.03468 − 0.927412i 4.12902 + 0.815915i 0.267981 − 0.525942i −2.64989 + 0.988974i 4.73863 + 3.44281i −2.70130 + 1.64408i
147.6 −1.39911 − 0.206162i −0.0920952 − 0.0299235i 1.91499 + 0.576884i 1.71727 + 1.43213i 0.122682 + 0.0608527i 0.0857610 − 0.168315i −2.56035 − 1.20192i −2.41946 − 1.75784i −2.10739 − 2.35774i
147.7 −1.39775 + 0.215188i −0.244411 − 0.0794140i 1.90739 − 0.601556i −1.24889 + 1.85480i 0.358714 + 0.0584063i −0.794532 + 1.55936i −2.53660 + 1.25127i −2.37362 − 1.72454i 1.34649 − 2.86129i
147.8 −1.39395 − 0.238551i 2.05504 + 0.667722i 1.88619 + 0.665057i −1.84711 + 1.26023i −2.70533 − 1.42100i −1.78083 + 3.49508i −2.47060 − 1.37701i 1.35028 + 0.981035i 2.87541 − 1.31606i
147.9 −1.38758 + 0.273165i 3.23110 + 1.04985i 1.85076 − 0.758078i 1.22816 − 1.86859i −4.77019 − 0.574124i −1.11586 + 2.18999i −2.36100 + 1.55746i 6.91076 + 5.02096i −1.19374 + 2.92831i
147.10 −1.37402 − 0.334786i 1.60229 + 0.520616i 1.77584 + 0.920003i −2.17953 − 0.499665i −2.02728 − 1.25176i −0.189760 + 0.372425i −2.13202 − 1.85862i −0.130751 − 0.0949961i 2.82742 + 1.41622i
147.11 −1.37387 + 0.335364i −0.627369 − 0.203845i 1.77506 − 0.921497i 2.17496 + 0.519173i 0.930289 + 0.0696596i −1.59597 + 3.13227i −2.12967 + 1.86131i −2.07501 − 1.50758i −3.16224 + 0.0161265i
147.12 −1.36224 − 0.379880i −0.667841 − 0.216995i 1.71138 + 1.03497i 1.40511 − 1.73944i 0.827327 + 0.549298i −1.85119 + 3.63317i −1.93814 − 2.06000i −2.02813 − 1.47352i −2.57488 + 1.83576i
147.13 −1.35538 − 0.403653i −1.75079 − 0.568865i 1.67413 + 1.09421i −1.92180 − 1.14311i 2.14336 + 1.47774i −1.46716 + 2.87945i −1.82741 − 2.15884i 0.314596 + 0.228567i 2.14335 + 2.32509i
147.14 −1.34772 + 0.428541i 1.01739 + 0.330571i 1.63271 − 1.15511i 2.08932 − 0.796707i −1.51283 − 0.00952347i 1.91412 − 3.75668i −1.70542 + 2.25644i −1.50124 − 1.09071i −2.47440 + 1.96910i
147.15 −1.34050 + 0.450607i 1.28705 + 0.418188i 1.59391 − 1.20808i −0.572291 + 2.16159i −1.91373 + 0.0193706i 1.46910 − 2.88327i −1.59227 + 2.33766i −0.945436 − 0.686899i −0.206870 − 3.15550i
147.16 −1.33566 − 0.464780i −1.16338 − 0.378006i 1.56796 + 1.24157i 1.32745 + 1.79941i 1.37819 + 1.04560i 1.69448 − 3.32560i −1.51720 − 2.38707i −1.21648 − 0.883825i −0.936689 − 3.02037i
147.17 −1.33136 + 0.476942i −3.03795 − 0.987091i 1.54505 − 1.26996i −2.16215 − 0.570187i 4.51540 − 0.134750i −0.949601 + 1.86370i −1.45133 + 2.42768i 5.82776 + 4.23412i 3.15055 − 0.272092i
147.18 −1.31807 − 0.512538i −2.05099 − 0.666407i 1.47461 + 1.35112i 1.53087 − 1.62985i 2.36179 + 1.92958i 1.47433 − 2.89354i −1.25114 − 2.53666i 1.33541 + 0.970234i −2.85316 + 1.36363i
147.19 −1.30770 − 0.538453i 1.53053 + 0.497299i 1.42014 + 1.40827i 0.0833910 − 2.23451i −1.73369 − 1.47443i 0.776456 − 1.52388i −1.09882 − 2.60626i −0.331840 − 0.241096i −1.31223 + 2.87716i
147.20 −1.30622 + 0.542022i 1.96226 + 0.637577i 1.41243 − 1.41600i 1.91146 + 1.16031i −2.90872 + 0.230771i −1.01416 + 1.99041i −1.07744 + 2.61517i 1.01691 + 0.738825i −3.12570 − 0.479575i
See next 80 embeddings (of 1120 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 147.140
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner
80.j even 4 1 inner
880.cz even 20 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 880.2.cz.a yes 1120
5.c odd 4 1 880.2.ch.a ✓ 1120
11.c even 5 1 inner 880.2.cz.a yes 1120
16.f odd 4 1 880.2.ch.a ✓ 1120
55.k odd 20 1 880.2.ch.a ✓ 1120
80.j even 4 1 inner 880.2.cz.a yes 1120
176.v odd 20 1 880.2.ch.a ✓ 1120
880.cz even 20 1 inner 880.2.cz.a yes 1120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
880.2.ch.a ✓ 1120 5.c odd 4 1
880.2.ch.a ✓ 1120 16.f odd 4 1
880.2.ch.a ✓ 1120 55.k odd 20 1
880.2.ch.a ✓ 1120 176.v odd 20 1
880.2.cz.a yes 1120 1.a even 1 1 trivial
880.2.cz.a yes 1120 11.c even 5 1 inner
880.2.cz.a yes 1120 80.j even 4 1 inner
880.2.cz.a yes 1120 880.cz even 20 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(880, [\chi])\).