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Properties

Label 880.2.cu.a
Level $880$
Weight $2$
Character orbit 880.cu
Analytic conductor $7.027$
Analytic rank $0$
Dimension $768$
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(141,880)]
 
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([0, 15, 0, 12]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.141");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.cu (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: \(768\)
Relative dimension: \(96\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 768 q + 8 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 768 q + 8 q^{4} + 8 q^{11} - 20 q^{14} - 40 q^{16} + 60 q^{18} - 8 q^{20} - 100 q^{22} + 32 q^{24} + 32 q^{26} + 48 q^{28} + 32 q^{29} - 40 q^{32} - 40 q^{34} - 48 q^{37} - 40 q^{42} - 16 q^{43} - 48 q^{44} - 64 q^{46} + 40 q^{48} + 192 q^{49} + 8 q^{50} - 112 q^{52} + 48 q^{53} - 32 q^{54} + 152 q^{56} + 40 q^{58} - 16 q^{59} - 84 q^{60} + 88 q^{62} - 80 q^{63} + 80 q^{64} - 40 q^{66} - 80 q^{67} - 156 q^{68} + 8 q^{70} - 60 q^{72} - 68 q^{74} - 256 q^{76} - 16 q^{77} + 56 q^{78} + 48 q^{80} + 192 q^{81} - 120 q^{82} - 112 q^{84} - 192 q^{86} + 160 q^{91} - 104 q^{92} - 192 q^{94} - 64 q^{95} - 152 q^{96} - 192 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
141.1 −1.41151 − 0.0874094i −2.69534 − 0.426899i 1.98472 + 0.246758i 0.891007 + 0.453990i 3.76718 + 0.838170i 1.01368 − 1.39521i −2.77988 − 0.521785i 4.22943 + 1.37422i −1.21798 − 0.718694i
141.2 −1.41049 − 0.102598i −1.04525 − 0.165551i 1.97895 + 0.289426i 0.891007 + 0.453990i 1.45732 + 0.340747i −1.77469 + 2.44265i −2.76159 − 0.611267i −1.78804 − 0.580969i −1.21017 − 0.731763i
141.3 −1.41014 − 0.107272i −0.733140 − 0.116118i 1.97699 + 0.302538i −0.891007 − 0.453990i 1.02137 + 0.242388i 2.00916 − 2.76537i −2.75537 − 0.638696i −2.32916 − 0.756790i 1.20774 + 0.735770i
141.4 −1.40709 + 0.141758i 2.06122 + 0.326465i 1.95981 − 0.398932i 0.891007 + 0.453990i −2.94660 − 0.167172i −1.56009 + 2.14728i −2.70108 + 0.839151i 1.28887 + 0.418780i −1.31808 − 0.512499i
141.5 −1.37889 − 0.314091i −1.78433 − 0.282610i 1.80269 + 0.866195i −0.891007 − 0.453990i 2.37164 + 0.950131i −2.66945 + 3.67418i −2.21366 − 1.76060i 0.250796 + 0.0814885i 1.08601 + 0.905861i
141.6 −1.37887 − 0.314201i 1.48182 + 0.234697i 1.80256 + 0.866482i −0.891007 − 0.453990i −1.96949 − 0.789206i 0.0548045 − 0.0754320i −2.21324 − 1.76113i −0.712458 − 0.231492i 1.08594 + 0.905948i
141.7 −1.37398 + 0.334921i 0.881329 + 0.139589i 1.77566 − 0.920352i 0.891007 + 0.453990i −1.25768 + 0.103383i 1.01669 − 1.39936i −2.13147 + 1.85925i −2.09591 − 0.681004i −1.37628 − 0.325358i
141.8 −1.37340 + 0.337296i 1.44142 + 0.228299i 1.77246 − 0.926486i −0.891007 − 0.453990i −2.05666 + 0.172640i −1.18867 + 1.63606i −2.12180 + 1.87028i −0.827592 − 0.268901i 1.37684 + 0.322978i
141.9 −1.36523 + 0.368999i −1.19376 − 0.189073i 1.72768 − 1.00753i −0.891007 − 0.453990i 1.69952 − 0.182370i −1.64692 + 2.26679i −1.98689 + 2.01302i −1.46385 − 0.475634i 1.38395 + 0.291018i
141.10 −1.33582 + 0.464313i 2.95242 + 0.467617i 1.56883 − 1.24048i 0.891007 + 0.453990i −4.16101 + 0.746192i 0.365653 − 0.503278i −1.51970 + 2.38548i 5.64492 + 1.83415i −1.40102 − 0.192744i
141.11 −1.32551 + 0.492987i −0.458307 − 0.0725887i 1.51393 − 1.30691i 0.891007 + 0.453990i 0.643274 − 0.129723i 1.91670 − 2.63812i −1.36243 + 2.47867i −2.64839 − 0.860515i −1.40485 − 0.162512i
141.12 −1.28822 + 0.583516i −2.94887 − 0.467055i 1.31902 − 1.50339i 0.891007 + 0.453990i 4.07133 − 1.11904i −1.54661 + 2.12873i −0.821933 + 2.70637i 5.62452 + 1.82752i −1.41272 − 0.0649232i
141.13 −1.28378 − 0.593220i 3.12629 + 0.495156i 1.29618 + 1.52313i −0.891007 − 0.453990i −3.71973 − 2.49025i −2.65390 + 3.65279i −0.760463 − 2.72428i 6.67535 + 2.16895i 0.874540 + 1.11139i
141.14 −1.26524 − 0.631804i −1.57300 − 0.249139i 1.20165 + 1.59876i 0.891007 + 0.453990i 1.83281 + 1.30905i 0.992970 − 1.36671i −0.510263 − 2.78202i −0.440910 − 0.143260i −0.840501 − 1.13735i
141.15 −1.23315 + 0.692344i 2.25820 + 0.357664i 1.04132 − 1.70753i −0.891007 − 0.453990i −3.03233 + 1.12240i 2.28835 − 3.14964i −0.101909 + 2.82659i 2.11838 + 0.688305i 1.41306 − 0.0570440i
141.16 −1.21846 + 0.717874i 2.07316 + 0.328357i 0.969314 − 1.74941i −0.891007 − 0.453990i −2.76180 + 1.08818i −1.38082 + 1.90053i 0.0747799 + 2.82744i 1.33702 + 0.434424i 1.41157 − 0.0864589i
141.17 −1.21175 − 0.729149i −1.50993 − 0.239149i 0.936682 + 1.76710i −0.891007 − 0.453990i 1.65528 + 1.39075i 2.76497 − 3.80566i 0.153450 − 2.82426i −0.630476 − 0.204854i 0.748651 + 1.19980i
141.18 −1.19363 − 0.758451i 0.568749 + 0.0900810i 0.849505 + 1.81062i 0.891007 + 0.453990i −0.610554 − 0.538892i 0.275503 − 0.379198i 0.359270 − 2.80552i −2.53781 − 0.824584i −0.719203 − 1.21768i
141.19 −1.12295 − 0.859641i 2.75108 + 0.435729i 0.522035 + 1.93067i 0.891007 + 0.453990i −2.71476 − 2.85425i −0.219012 + 0.301444i 1.07346 − 2.61681i 4.52543 + 1.47040i −0.610287 − 1.27575i
141.20 −1.11742 − 0.866824i 0.589136 + 0.0933099i 0.497233 + 1.93720i −0.891007 − 0.453990i −0.577426 − 0.614943i 0.0227063 − 0.0312526i 1.12360 − 2.59567i −2.51480 − 0.817107i 0.602094 + 1.27964i
See next 80 embeddings (of 768 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 141.96
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner
16.e even 4 1 inner
176.w 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.cu.a ✓ 768
11.c even 5 1 inner 880.2.cu.a ✓ 768
16.e even 4 1 inner 880.2.cu.a ✓ 768
176.w even 20 1 inner 880.2.cu.a ✓ 768
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
880.2.cu.a ✓ 768 1.a even 1 1 trivial
880.2.cu.a ✓ 768 11.c even 5 1 inner
880.2.cu.a ✓ 768 16.e even 4 1 inner
880.2.cu.a ✓ 768 176.w even 20 1 inner

Hecke kernels

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