↑

Properties

Label 531.2.e.c
Level $531$
Weight $2$
Character orbit 531.e
Analytic conductor $4.240$
Analytic rank $0$
Dimension $70$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [531,2,Mod(178,531)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("531.178"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(531, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 531 = 3^{2} \cdot 59 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 531.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [70] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.24005634733\)
Analytic rank: \(0\)
Dimension: \(70\)
Relative dimension: \(35\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 70 q - 44 q^{4} - 2 q^{5} + 4 q^{6} - 11 q^{7} + 2 q^{9} + 20 q^{10} + 2 q^{11} - 23 q^{13} + 2 q^{14} - 5 q^{15} - 62 q^{16} - 4 q^{17} - q^{18} + 46 q^{19} + q^{20} + 16 q^{21} - 16 q^{22} - 42 q^{24}+ \cdots - 37 q^{99}+O(q^{100}) \) 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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
178.1 −1.36765 + 2.36884i 1.11876 − 1.32226i −2.74094 − 4.74745i −0.481876 − 0.834633i 1.60216 + 4.45856i −2.03762 + 3.52926i 9.52400 −0.496757 − 2.95859i 2.63615
178.2 −1.35970 + 2.35506i −1.73198 − 0.0157407i −2.69755 − 4.67229i −0.681686 − 1.18072i 2.39204 − 4.05752i −0.00560744 + 0.00971238i 9.23261 2.99950 + 0.0545251i 3.70755
178.3 −1.27943 + 2.21603i −1.09942 − 1.33839i −2.27387 − 3.93846i 2.08497 + 3.61127i 4.37254 − 0.723979i 0.121324 − 0.210140i 6.51929 −0.582558 + 2.94289i −10.6703
178.4 −1.26704 + 2.19458i 1.43227 + 0.973965i −2.21079 − 3.82920i −1.66286 − 2.88017i −3.95219 + 1.90917i 0.344695 − 0.597030i 6.13647 1.10278 + 2.78996i 8.42767
178.5 −1.20592 + 2.08871i −0.403448 + 1.68441i −1.90848 − 3.30558i −0.492905 − 0.853736i −3.03172 − 2.87394i −1.22137 + 2.11547i 4.38219 −2.67446 − 1.35914i 2.37761
178.6 −1.07489 + 1.86177i −1.42029 + 0.991352i −1.31079 − 2.27035i 1.98013 + 3.42968i −0.319010 − 3.70984i 0.972980 − 1.68525i 1.33624 1.03444 − 2.81601i −8.51369
178.7 −1.01170 + 1.75231i 0.120579 + 1.72785i −1.04706 − 1.81356i −0.332631 − 0.576133i −3.14971 − 1.53677i 2.53455 − 4.38996i 0.190436 −2.97092 + 0.416684i 1.34609
178.8 −0.933943 + 1.61764i −0.967970 − 1.43633i −0.744497 − 1.28951i −2.12329 − 3.67765i 3.22748 − 0.224377i −2.14753 + 3.71963i −0.954499 −1.12607 + 2.78064i 7.93212
178.9 −0.852080 + 1.47585i 1.68851 + 0.385930i −0.452081 − 0.783028i 0.598654 + 1.03690i −2.00832 + 2.16313i −1.77014 + 3.06597i −1.86748 2.70212 + 1.30329i −2.04041
178.10 −0.823419 + 1.42620i 1.38056 − 1.04597i −0.356037 − 0.616675i −1.83657 − 3.18104i 0.354996 + 2.83023i 0.170215 − 0.294822i −2.12100 0.811873 − 2.88806i 6.04908
178.11 −0.680492 + 1.17865i 1.42160 + 0.989476i 0.0738604 + 0.127930i 1.41489 + 2.45066i −2.13363 + 1.00223i 1.88660 − 3.26769i −2.92301 1.04188 + 2.81327i −3.85129
178.12 −0.658952 + 1.14134i 0.247062 − 1.71434i 0.131565 + 0.227877i −0.00857333 − 0.0148494i 1.79384 + 1.41165i 0.466147 − 0.807391i −2.98259 −2.87792 − 0.847097i 0.0225977
178.13 −0.435793 + 0.754815i −1.73188 − 0.0240310i 0.620170 + 1.07417i 1.49965 + 2.59747i 0.772881 − 1.29678i −2.55575 + 4.42668i −2.82423 2.99885 + 0.0832378i −2.61414
178.14 −0.370535 + 0.641786i 1.00327 − 1.41189i 0.725407 + 1.25644i −0.385363 − 0.667469i 0.534386 + 1.16704i 1.09630 − 1.89884i −2.55730 −0.986889 − 2.83303i 0.571163
178.15 −0.337827 + 0.585134i 1.34781 + 1.08784i 0.771745 + 1.33670i 0.285666 + 0.494788i −1.09186 + 0.421147i 0.955260 − 1.65456i −2.39418 0.633191 + 2.93242i −0.386023
178.16 −0.165394 + 0.286472i −1.73198 + 0.0151216i 0.945289 + 1.63729i −1.11365 − 1.92889i 0.282129 − 0.498666i −0.918849 + 1.59149i −1.28696 2.99954 − 0.0523808i 0.736763
178.17 −0.0850038 + 0.147231i −0.851268 − 1.50842i 0.985549 + 1.70702i −0.898112 − 1.55558i 0.294448 + 0.00288878i −0.295719 + 0.512201i −0.675117 −1.55068 + 2.56815i 0.305372
178.18 −0.0534806 + 0.0926312i −0.866843 − 1.49953i 0.994280 + 1.72214i 1.65422 + 2.86520i 0.185262 0.000101013i −0.0849628 + 0.147160i −0.426621 −1.49717 + 2.59971i −0.353876
178.19 0.0421922 − 0.0730791i −1.04391 + 1.38212i 0.996440 + 1.72588i −1.87462 − 3.24694i 0.0569587 + 0.134603i −0.622152 + 1.07760i 0.336937 −0.820488 − 2.88562i −0.316378
178.20 0.208865 − 0.361765i 1.01409 + 1.40415i 0.912751 + 1.58093i 0.573905 + 0.994032i 0.719778 − 0.0735848i −1.97064 + 3.41324i 1.59803 −0.943248 + 2.84786i 0.479474
See all 70 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 178.35
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
9.c even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 531.2.e.c ✓ 70
9.c even 3 1 inner 531.2.e.c ✓ 70
9.c even 3 1 4779.2.a.n 35
9.d odd 6 1 4779.2.a.m 35
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
531.2.e.c ✓ 70 1.a even 1 1 trivial
531.2.e.c ✓ 70 9.c even 3 1 inner
4779.2.a.m 35 9.d odd 6 1
4779.2.a.n 35 9.c even 3 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{70} + 57 T_{2}^{68} + 1776 T_{2}^{66} - 2 T_{2}^{65} + 38265 T_{2}^{64} - 137 T_{2}^{63} + \cdots + 1327104 \) acting on \(S_{2}^{\mathrm{new}}(531, [\chi])\). Copy content Toggle raw display