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Properties

Label 880.2.ci.a
Level $880$
Weight $2$
Character orbit 880.ci
Analytic conductor $7.027$
Analytic rank $0$
Dimension $1120$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [880,2,Mod(19,880)]
 
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, 10, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.19");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.ci (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.

\(\operatorname{Tr}(f)(q) = \) \( 1120 q - 12 q^{4} - 6 q^{5} - 20 q^{6}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 1120 q - 12 q^{4} - 6 q^{5} - 20 q^{6} - 16 q^{11} - 4 q^{14} - 12 q^{16} - 20 q^{19} - 6 q^{20} - 20 q^{24} - 40 q^{26} - 20 q^{29} - 50 q^{30} - 16 q^{34} - 10 q^{35} - 44 q^{36} - 40 q^{39} - 10 q^{40} - 44 q^{44} - 24 q^{45} + 20 q^{46} - 256 q^{49} - 10 q^{50} - 20 q^{51} - 48 q^{55} - 24 q^{56} - 28 q^{59} - 46 q^{60} - 20 q^{61} - 36 q^{64} - 28 q^{66} + 24 q^{69} - 72 q^{70} + 8 q^{71} - 20 q^{74} - 42 q^{75} - 32 q^{80} + 192 q^{81} + 120 q^{84} - 10 q^{85} - 4 q^{86} - 260 q^{90} + 60 q^{91} + 120 q^{94} - 20 q^{96} - 96 q^{99}+O(q^{100}) \) 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 −1.41347 − 0.0457485i 1.26170 − 2.47623i 1.99581 + 0.129329i −1.03136 + 1.98401i −1.89666 + 3.44236i −0.865735 + 2.66446i −2.81511 − 0.274108i −2.77646 − 3.82146i 1.54857 − 2.75716i
19.2 −1.41046 − 0.102994i −1.51145 + 2.96639i 1.97878 + 0.290539i 1.02100 + 1.98936i 2.43736 − 4.02830i 1.27622 − 3.92780i −2.76107 − 0.613597i −4.75165 − 6.54008i −1.23518 − 2.91107i
19.3 −1.40987 − 0.110725i −1.08392 + 2.12732i 1.97548 + 0.312217i 1.74350 − 1.40008i 1.76374 − 2.87923i −0.0973813 + 0.299709i −2.75060 − 0.658921i −1.58725 − 2.18466i −2.61313 + 1.78088i
19.4 −1.40921 + 0.118810i −1.18872 + 2.33298i 1.97177 − 0.334857i −1.83624 + 1.27601i 1.39797 − 3.42891i −0.942229 + 2.89988i −2.73886 + 0.706152i −2.26642 − 3.11946i 2.43606 − 2.01634i
19.5 −1.40606 + 0.151618i 0.551748 − 1.08287i 1.95402 − 0.426369i 1.86886 + 1.22775i −0.611610 + 1.60623i 0.853323 − 2.62626i −2.68283 + 0.895767i 0.895183 + 1.23211i −2.81388 − 1.44294i
19.6 −1.40434 + 0.166832i 0.650593 − 1.27686i 1.94433 − 0.468576i −1.86028 − 1.24071i −0.700632 + 1.90168i −0.338579 + 1.04204i −2.65233 + 0.982416i 0.556255 + 0.765619i 2.81945 + 1.43202i
19.7 −1.40429 − 0.167283i 0.0366747 − 0.0719781i 1.94403 + 0.469826i 2.14477 − 0.632412i −0.0635424 + 0.0949427i 0.173615 − 0.534332i −2.65138 − 0.984973i 1.75952 + 2.42177i −3.11767 + 0.529302i
19.8 −1.40250 + 0.181633i −0.762615 + 1.49672i 1.93402 − 0.509481i −1.30317 − 1.81707i 0.797715 − 2.23766i 1.54956 − 4.76906i −2.61993 + 1.06583i 0.104778 + 0.144215i 2.15774 + 2.31174i
19.9 −1.39287 − 0.244778i 1.09045 − 2.14014i 1.88017 + 0.681886i −1.51776 + 1.64208i −2.04272 + 2.71401i 0.472477 − 1.45414i −2.45192 − 1.41000i −1.62774 − 2.24039i 2.51598 − 1.91568i
19.10 −1.38033 − 0.307698i 0.743766 − 1.45972i 1.81064 + 0.849452i 0.658745 − 2.13683i −1.47580 + 1.78605i 0.874556 − 2.69161i −2.23792 − 1.72966i 0.185751 + 0.255664i −1.56679 + 2.74685i
19.11 −1.37678 + 0.323233i −0.254594 + 0.499668i 1.79104 − 0.890041i 0.865933 + 2.06159i 0.189010 − 0.770226i −0.470469 + 1.44796i −2.17818 + 1.80431i 1.57851 + 2.17263i −1.85857 − 2.55846i
19.12 −1.36796 − 0.358721i −0.721124 + 1.41529i 1.74264 + 0.981433i −2.22222 + 0.248447i 1.49416 − 1.67737i 0.304036 − 0.935728i −2.03180 − 1.96768i 0.280342 + 0.385858i 3.12904 + 0.457292i
19.13 −1.36117 − 0.383701i 0.988460 − 1.93996i 1.70555 + 1.04456i 2.17320 + 0.526511i −2.08982 + 2.26134i −1.42379 + 4.38197i −1.92073 − 2.07624i −1.02305 − 1.40810i −2.75606 − 1.55053i
19.14 −1.32875 + 0.484168i −0.730457 + 1.43360i 1.53116 − 1.28668i −0.745913 − 2.10799i 0.276492 − 2.25856i 0.108835 − 0.334961i −1.41157 + 2.45102i 0.241708 + 0.332683i 2.01175 + 2.43985i
19.15 −1.31638 + 0.516853i 1.07083 − 2.10162i 1.46573 − 1.36075i 0.877480 − 2.05670i −0.323392 + 3.31999i 0.492471 − 1.51567i −1.22615 + 2.54884i −1.50677 − 2.07389i −0.0920871 + 3.16094i
19.16 −1.31364 − 0.523783i −0.206033 + 0.404363i 1.45130 + 1.37613i −0.0489094 + 2.23553i 0.482452 − 0.423270i −1.36186 + 4.19139i −1.18570 − 2.56790i 1.64230 + 2.26043i 1.23518 − 2.91107i
19.17 −1.30199 − 0.552100i 0.147492 − 0.289469i 1.39037 + 1.43766i −1.92909 − 1.13076i −0.351849 + 0.295456i −0.143510 + 0.441680i −1.01652 − 2.63945i 1.70132 + 2.34166i 1.88736 + 2.53729i
19.18 −1.29736 − 0.562907i −0.320799 + 0.629604i 1.36627 + 1.46058i −0.202711 + 2.22686i 0.770600 − 0.636241i 1.05261 − 3.23961i −0.950369 − 2.66398i 1.46987 + 2.02310i 1.51650 − 2.77493i
19.19 −1.29544 + 0.567311i 0.383354 − 0.752375i 1.35632 − 1.46983i −2.22879 + 0.180256i −0.0697806 + 1.19214i −0.955646 + 2.94118i −0.923170 + 2.67353i 1.34425 + 1.85020i 2.78500 − 1.49793i
19.20 −1.28334 + 0.594180i −0.0255399 + 0.0501249i 1.29390 − 1.52506i 1.09486 − 1.94969i 0.00299309 − 0.0795023i −1.02881 + 3.16634i −0.754348 + 2.72598i 1.76150 + 2.42449i −0.246614 + 3.15265i
See next 80 embeddings (of 1120 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 19.140
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
11.d odd 10 1 inner
16.f odd 4 1 inner
55.h odd 10 1 inner
80.k odd 4 1 inner
176.x even 20 1 inner
880.ci 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.ci.a ✓ 1120
5.b even 2 1 inner 880.2.ci.a ✓ 1120
11.d odd 10 1 inner 880.2.ci.a ✓ 1120
16.f odd 4 1 inner 880.2.ci.a ✓ 1120
55.h odd 10 1 inner 880.2.ci.a ✓ 1120
80.k odd 4 1 inner 880.2.ci.a ✓ 1120
176.x even 20 1 inner 880.2.ci.a ✓ 1120
880.ci even 20 1 inner 880.2.ci.a ✓ 1120
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
880.2.ci.a ✓ 1120 1.a even 1 1 trivial
880.2.ci.a ✓ 1120 5.b even 2 1 inner
880.2.ci.a ✓ 1120 11.d odd 10 1 inner
880.2.ci.a ✓ 1120 16.f odd 4 1 inner
880.2.ci.a ✓ 1120 55.h odd 10 1 inner
880.2.ci.a ✓ 1120 80.k odd 4 1 inner
880.2.ci.a ✓ 1120 176.x even 20 1 inner
880.2.ci.a ✓ 1120 880.ci even 20 1 inner

Hecke kernels

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