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Properties

Label 583.2.q.b
Level $583$
Weight $2$
Character orbit 583.q
Analytic conductor $4.655$
Analytic rank $0$
Dimension $1200$
Inner twists $4$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [583,2,Mod(21,583)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(583, base_ring=CyclotomicField(52)) chi = DirichletCharacter(H, H._module([26, 31])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("583.21"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 583 = 11 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 583.q (of order \(52\), degree \(24\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [1200] 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: \(4.65527843784\)
Analytic rank: \(0\)
Dimension: \(1200\)
Relative dimension: \(50\) over \(\Q(\zeta_{52})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{52}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 1200 q - 48 q^{3} - 52 q^{4} - 44 q^{5} - 52 q^{9} - 26 q^{11} - 64 q^{12} - 28 q^{14} - 28 q^{15} + 72 q^{16} - 52 q^{20} - 12 q^{22} - 68 q^{23} - 52 q^{25} - 80 q^{26} - 72 q^{27} - 56 q^{31} - 28 q^{33}+ \cdots - 258 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
21.1 −2.63308 − 0.820501i 0.403759 + 0.181717i 4.61393 + 3.18477i −0.283130 − 0.0171262i −0.914031 − 0.809761i 3.70955 − 1.94692i −6.13398 − 7.82944i −1.85937 − 2.09879i 0.731452 + 0.277403i
21.2 −2.60743 − 0.812509i −2.20132 − 0.990735i 4.49257 + 3.10100i 3.69706 + 0.223631i 4.93482 + 4.37187i 0.174868 − 0.0917780i −5.82585 − 7.43615i 1.87490 + 2.11633i −9.45814 − 3.58700i
21.3 −2.47569 − 0.771456i −2.48881 − 1.12012i 3.88793 + 2.68364i −2.45216 − 0.148328i 5.29741 + 4.69309i −3.21326 + 1.68645i −4.35657 − 5.56075i 2.95015 + 3.33003i 5.95636 + 2.25895i
21.4 −2.47515 − 0.771286i 1.76803 + 0.795724i 3.88549 + 2.68196i −3.00149 − 0.181557i −3.76239 − 3.33319i −2.29979 + 1.20703i −4.35087 − 5.55348i 0.503374 + 0.568192i 7.28909 + 2.76439i
21.5 −2.36779 − 0.737832i 0.524586 + 0.236097i 3.41604 + 2.35793i 0.744767 + 0.0450501i −1.06791 − 0.946083i −1.95123 + 1.02408i −3.28968 − 4.19897i −1.76992 − 1.99783i −1.73021 − 0.656182i
21.6 −2.15552 − 0.671688i −1.59813 − 0.719258i 2.54915 + 1.75955i −3.06363 − 0.185315i 2.96168 + 2.62382i 0.802382 − 0.421123i −1.52809 − 1.95046i 0.0473058 + 0.0533972i 6.47925 + 2.45726i
21.7 −2.03884 − 0.635327i −0.112469 − 0.0506184i 2.10724 + 1.45453i 2.63617 + 0.159459i 0.197147 + 0.174657i −0.438250 + 0.230011i −0.738181 − 0.942218i −1.97928 − 2.23415i −5.27340 − 1.99994i
21.8 −1.98213 − 0.617657i 1.92922 + 0.868273i 1.90137 + 1.31242i 1.82279 + 0.110259i −3.28768 − 2.91263i 1.53474 − 0.805493i −0.397353 − 0.507183i 0.978640 + 1.10466i −3.54491 − 1.34441i
21.9 −1.88222 − 0.586525i 2.88560 + 1.29870i 1.55279 + 1.07181i −1.61011 − 0.0973935i −4.66962 − 4.13692i 2.03677 − 1.06898i 0.137657 + 0.175706i 4.65068 + 5.24953i 2.97346 + 1.12768i
21.10 −1.69448 − 0.528021i 0.274146 + 0.123383i 0.946485 + 0.653312i −3.28056 − 0.198437i −0.399385 − 0.353824i 3.24882 − 1.70511i 0.930321 + 1.18747i −1.92944 − 2.17788i 5.45406 + 2.06845i
21.11 −1.67243 − 0.521152i −1.39034 − 0.625743i 0.879470 + 0.607054i 2.82064 + 0.170617i 1.99915 + 1.77109i −2.04730 + 1.07451i 1.00619 + 1.28431i −0.447866 − 0.505536i −4.62842 − 1.75533i
21.12 −1.63961 − 0.510922i −2.35712 − 1.06085i 0.781304 + 0.539295i 1.84800 + 0.111783i 3.32273 + 2.94369i 1.49465 − 0.784451i 1.11277 + 1.42035i 2.44123 + 2.75557i −2.97288 − 1.12747i
21.13 −1.57662 − 0.491293i −0.327795 − 0.147528i 0.598379 + 0.413032i −1.74756 − 0.105708i 0.444327 + 0.393639i −2.46902 + 1.29584i 1.29639 + 1.65472i −1.90368 − 2.14881i 2.70330 + 1.02523i
21.14 −1.41584 − 0.441194i 2.35020 + 1.05774i 0.163990 + 0.113194i −1.38305 − 0.0836588i −2.86084 − 2.53449i −3.89495 + 2.04423i 1.64693 + 2.10216i 2.41526 + 2.72626i 1.92126 + 0.728639i
21.15 −1.23374 − 0.384449i −2.24704 − 1.01131i −0.271652 − 0.187508i −0.397519 − 0.0240455i 2.38347 + 2.11157i −3.64588 + 1.91350i 1.85697 + 2.37025i 2.03708 + 2.29938i 0.481192 + 0.182492i
21.16 −1.19557 − 0.372556i 2.19931 + 0.989829i −0.355368 − 0.245293i 3.46694 + 0.209711i −2.26067 − 2.00278i 1.07166 − 0.562448i 1.87809 + 2.39720i 1.86784 + 2.10835i −4.06686 − 1.54235i
21.17 −1.12153 − 0.349482i −0.626396 − 0.281918i −0.510283 − 0.352223i 1.91299 + 0.115715i 0.603995 + 0.535093i 4.39178 − 2.30499i 1.89814 + 2.42280i −1.67647 − 1.89235i −2.10503 − 0.798334i
21.18 −0.960421 − 0.299279i 0.838375 + 0.377322i −0.813127 − 0.561261i −1.67729 − 0.101457i −0.692268 − 0.613296i 1.27366 − 0.668470i 1.85377 + 2.36617i −1.42887 − 1.61286i 1.58054 + 0.599420i
21.19 −0.926926 − 0.288842i −3.04302 − 1.36955i −0.870206 − 0.600660i −3.15436 − 0.190803i 2.42507 + 2.14842i 2.28573 − 1.19964i 1.83065 + 2.33665i 5.39491 + 6.08959i 2.86874 + 1.08797i
21.20 −0.627538 − 0.195549i 2.10325 + 0.946596i −1.29040 − 0.890701i −4.15485 − 0.251322i −1.13476 − 1.00531i −0.130716 + 0.0686049i 1.44634 + 1.84612i 1.53825 + 1.73633i 2.55818 + 0.970190i
See next 80 embeddings (of 1200 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 21.50
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.b odd 2 1 inner
53.f odd 52 1 inner
583.q even 52 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 583.2.q.b ✓ 1200
11.b odd 2 1 inner 583.2.q.b ✓ 1200
53.f odd 52 1 inner 583.2.q.b ✓ 1200
583.q even 52 1 inner 583.2.q.b ✓ 1200
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
583.2.q.b ✓ 1200 1.a even 1 1 trivial
583.2.q.b ✓ 1200 11.b odd 2 1 inner
583.2.q.b ✓ 1200 53.f odd 52 1 inner
583.2.q.b ✓ 1200 583.q even 52 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{1200} + 26 T_{2}^{1198} - 42 T_{2}^{1196} - 7462 T_{2}^{1194} - 43033 T_{2}^{1192} + \cdots + 58\!\cdots\!01 \) acting on \(S_{2}^{\mathrm{new}}(583, [\chi])\). Copy content Toggle raw display