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Properties

Label 431.2.g.a
Level $431$
Weight $2$
Character orbit 431.g
Analytic conductor $3.442$
Analytic rank $0$
Dimension $5880$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [431,2,Mod(5,431)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(431, base_ring=CyclotomicField(430))
 
chi = DirichletCharacter(H, H._module([342]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("431.5");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 431.g (of order \(215\), degree \(168\), 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: \(3.44155232712\)
Analytic rank: \(0\)
Dimension: \(5880\)
Relative dimension: \(35\) over \(\Q(\zeta_{215})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{215}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 5880 q - 166 q^{2} - 164 q^{3} - 302 q^{4} - 169 q^{5} - 148 q^{6} - 171 q^{7} - 160 q^{8} - 300 q^{9} - 157 q^{10} - 83 q^{11} - 142 q^{12} - 177 q^{13} - 164 q^{14} - 166 q^{15} - 298 q^{16} - 176 q^{17}+ \cdots - 72 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1 −2.66233 + 0.194857i 1.26549 − 1.76883i 5.07134 − 0.746346i −2.12116 − 0.0620067i −3.02449 + 4.95581i 0.780844 − 0.584937i −8.14496 + 1.81437i −0.558663 − 1.63758i 5.65931 − 0.248241i
5.2 −2.59031 + 0.189586i −0.459563 + 0.642351i 4.69509 − 0.690974i 0.806183 + 0.0235667i 1.06863 − 1.75102i 0.854837 − 0.640366i −6.96055 + 1.55053i 0.767224 + 2.24892i −2.09274 + 0.0917963i
5.3 −2.39071 + 0.174978i −1.55868 + 2.17864i 3.70621 − 0.545441i 1.90733 + 0.0557560i 3.34515 − 5.48123i −1.73456 + 1.29938i −4.08552 + 0.910089i −1.34833 − 3.95228i −4.56964 + 0.200444i
5.4 −2.34608 + 0.171711i 1.05945 − 1.48084i 3.49590 − 0.514490i −0.0559383 − 0.00163521i −2.23127 + 3.65607i −2.34018 + 1.75305i −3.52117 + 0.784373i −0.101806 − 0.298418i 0.131516 − 0.00576887i
5.5 −2.24045 + 0.163980i −0.268343 + 0.375075i 3.01406 − 0.443577i −3.36556 − 0.0983834i 0.539706 − 0.884342i 1.32859 − 0.995260i −2.29471 + 0.511169i 0.899968 + 2.63802i 7.55651 − 0.331461i
5.6 −1.87779 + 0.137437i −0.905959 + 1.26630i 1.52854 − 0.224954i −3.05565 − 0.0893241i 1.52717 − 2.50236i −3.23949 + 2.42673i 0.836183 − 0.186268i 0.185891 + 0.544891i 5.75016 − 0.252227i
5.7 −1.81442 + 0.132799i 0.702660 − 0.982138i 1.29581 − 0.190704i 2.08075 + 0.0608255i −1.14450 + 1.87533i 3.85368 − 2.88683i 1.22568 − 0.273032i 0.497776 + 1.45910i −3.78345 + 0.165958i
5.8 −1.78889 + 0.130930i 0.416164 − 0.581690i 1.20429 − 0.177235i 3.47349 + 0.101539i −0.668310 + 1.09507i −2.67429 + 2.00333i 1.37039 − 0.305266i 0.803470 + 2.35516i −6.22698 + 0.273142i
5.9 −1.47323 + 0.107827i −1.74955 + 2.44542i 0.180102 − 0.0265055i −2.15511 − 0.0629990i 2.31381 − 3.79132i 1.47005 − 1.10123i 2.62119 − 0.583896i −1.95051 − 5.71742i 3.18177 − 0.139566i
5.10 −1.33250 + 0.0975262i 1.69925 − 2.37511i −0.212651 + 0.0312957i −1.49743 − 0.0437735i −2.03261 + 3.33055i 1.96607 − 1.47280i 2.88850 − 0.643440i −1.78508 − 5.23249i 1.99959 − 0.0877105i
5.11 −1.29290 + 0.0946282i 1.33541 − 1.86657i −0.316048 + 0.0465126i −2.39201 − 0.0699244i −1.54993 + 2.53965i −2.75421 + 2.06321i 2.93491 − 0.653779i −0.732097 − 2.14595i 3.09926 − 0.135947i
5.12 −1.21343 + 0.0888114i −1.11023 + 1.55182i −0.514168 + 0.0756698i 3.76433 + 0.110040i 1.20936 − 1.98162i 0.698634 − 0.523353i 2.99232 − 0.666567i −0.206884 − 0.606428i −4.57751 + 0.200789i
5.13 −0.938919 + 0.0687200i −1.08710 + 1.51949i −1.10184 + 0.162157i 0.355845 + 0.0104022i 0.916283 − 1.50139i 1.57666 − 1.18109i 2.86121 − 0.637362i −0.158420 − 0.464367i −0.334825 + 0.0146868i
5.14 −0.637787 + 0.0466800i 0.0585875 − 0.0818903i −1.57409 + 0.231659i −0.920024 − 0.0268946i −0.0335437 + 0.0549634i 0.775804 − 0.581162i 2.24151 − 0.499318i 0.965368 + 2.82972i 0.588035 − 0.0257937i
5.15 −0.401820 + 0.0294094i 0.932471 − 1.30336i −1.81809 + 0.267568i 1.10023 + 0.0321624i −0.336354 + 0.551137i 0.145881 − 0.109281i 1.50919 − 0.336186i 0.139408 + 0.408637i −0.443039 + 0.0194336i
5.16 −0.368842 + 0.0269958i 0.224442 − 0.313712i −1.84337 + 0.271288i −3.72788 − 0.108975i −0.0743147 + 0.121769i 2.78896 − 2.08924i 1.39455 − 0.310650i 0.920600 + 2.69850i 1.37794 − 0.0604424i
5.17 −0.367429 + 0.0268924i −0.745733 + 1.04234i −1.84441 + 0.271440i −1.79441 − 0.0524548i 0.245973 − 0.403042i −3.63620 + 2.72391i 1.38959 − 0.309543i 0.438279 + 1.28470i 0.660728 − 0.0289823i
5.18 −0.157447 + 0.0115237i 1.60827 − 2.24795i −1.95403 + 0.287574i 3.23009 + 0.0944234i −0.227314 + 0.372467i −0.366625 + 0.274642i 0.612527 − 0.136446i −1.49811 − 4.39131i −0.509658 + 0.0223558i
5.19 0.154754 − 0.0113265i −1.86776 + 2.61064i −1.95487 + 0.287697i 2.55594 + 0.0747164i −0.259472 + 0.425161i −3.34637 + 2.50679i −0.602174 + 0.134140i −2.35831 − 6.91277i 0.396387 − 0.0173872i
5.20 0.183861 − 0.0134569i 0.342119 − 0.478194i −1.94506 + 0.286254i 1.14690 + 0.0335267i 0.0564672 − 0.0925251i −2.02516 + 1.51707i −0.713653 + 0.158973i 0.857017 + 2.51212i 0.211321 − 0.00926944i
See next 80 embeddings (of 5880 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 5.35
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
431.g even 215 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 431.2.g.a ✓ 5880
431.g even 215 1 inner 431.2.g.a ✓ 5880
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
431.2.g.a ✓ 5880 1.a even 1 1 trivial
431.2.g.a ✓ 5880 431.g even 215 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(431, [\chi])\).