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Properties

Label 583.2.s.a
Level $583$
Weight $2$
Character orbit 583.s
Analytic conductor $4.655$
Analytic rank $0$
Dimension $2496$
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(15,583)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(583, base_ring=CyclotomicField(130)) chi = DirichletCharacter(H, H._module([26, 30])) 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("583.15"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 583 = 11 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 583.s (of order \(65\), degree \(48\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.65527843784\)
Analytic rank: \(0\)
Dimension: \(2496\)
Relative dimension: \(52\) over \(\Q(\zeta_{65})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{65}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 2496 q - 37 q^{2} - 35 q^{3} + 13 q^{4} - 35 q^{5} - 45 q^{6} - 45 q^{7} - 111 q^{8} + 13 q^{9} - 88 q^{10} - 44 q^{11} - 76 q^{12} - 31 q^{13} - 31 q^{14} + 9 q^{15} - 3 q^{16} - 33 q^{17} - 39 q^{18}+ \cdots + 110 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
15.1 −0.609490 − 2.75799i 0.0232631 − 0.320316i −5.42130 + 2.51914i −0.949471 + 1.92046i −0.897607 + 0.131070i 0.434677 − 0.997856i 6.82210 + 8.92790i 2.86646 + 0.418564i 5.87531 + 1.44813i
15.2 −0.559594 − 2.53221i −0.229369 + 3.15824i −4.28519 + 1.99122i −0.00345901 + 0.00699641i 8.12569 − 1.18652i 1.81697 − 4.17108i 4.29103 + 5.61556i −6.95337 − 1.01534i 0.0196520 + 0.00484378i
15.3 −0.550408 − 2.49064i 0.147978 − 2.03754i −4.08659 + 1.89893i 1.51759 − 3.06958i −5.15623 + 0.752919i 0.760141 − 1.74500i 3.88142 + 5.07952i −1.16115 − 0.169553i −8.48050 − 2.09026i
15.4 −0.541423 − 2.44998i 0.193352 − 2.66232i −3.89553 + 1.81015i −0.110775 + 0.224061i −6.62732 + 0.967730i −1.79525 + 4.12122i 3.49713 + 4.57660i −4.08202 − 0.596062i 0.608922 + 0.150086i
15.5 −0.531942 − 2.40708i −0.0115479 + 0.159005i −3.69732 + 1.71805i 1.06602 − 2.15620i 0.388881 − 0.0567850i 0.610591 − 1.40169i 3.10874 + 4.06832i 2.94337 + 0.429795i −5.75721 − 1.41902i
15.6 −0.506102 − 2.29015i −0.141708 + 1.95121i −3.17490 + 1.47530i 0.560272 − 1.13324i 4.54029 − 0.662980i −0.269187 + 0.617952i 2.13739 + 2.79714i −0.818638 − 0.119539i −2.87885 − 0.709572i
15.7 −0.498228 − 2.25452i −0.214972 + 2.96000i −3.02089 + 1.40373i −1.50022 + 3.03443i 6.78049 − 0.990097i −1.94321 + 4.46088i 1.86606 + 2.44206i −5.74687 − 0.839166i 7.58865 + 1.87043i
15.8 −0.482086 − 2.18148i 0.248217 − 3.41776i −2.71269 + 1.26052i −0.615674 + 1.24530i −7.57544 + 1.10618i 1.02837 − 2.36075i 1.34461 + 1.75965i −8.65097 − 1.26323i 3.01340 + 0.742738i
15.9 −0.473522 − 2.14273i −0.0225380 + 0.310331i −2.55330 + 1.18645i 0.319160 − 0.645552i 0.675627 − 0.0986559i −1.62636 + 3.73352i 1.08655 + 1.42194i 2.87272 + 0.419479i −1.53437 − 0.378188i
15.10 −0.457117 − 2.06849i −0.0710262 + 0.977978i −2.25595 + 1.04828i −1.07149 + 2.16727i 2.05540 − 0.300133i 0.552635 − 1.26864i 0.627167 + 0.820757i 2.01712 + 0.294543i 4.97278 + 1.22568i
15.11 −0.451515 − 2.04314i 0.0736398 − 1.01396i −2.15681 + 1.00222i −1.70356 + 3.44573i −2.10492 + 0.307364i 0.0110242 − 0.0253074i 0.480602 + 0.628952i 1.94582 + 0.284131i 7.80930 + 1.92482i
15.12 −0.361123 − 1.63411i 0.109823 − 1.51219i −0.726158 + 0.337427i 0.473717 − 0.958169i −2.51074 + 0.366621i −0.732224 + 1.68091i −1.21859 − 1.59474i 0.693874 + 0.101320i −1.73682 − 0.428088i
15.13 −0.340607 − 1.54127i −0.183861 + 2.53163i −0.445764 + 0.207135i 0.844150 − 1.70743i 3.96456 − 0.578910i 0.0425969 − 0.0977865i −1.44568 − 1.89193i −3.40682 − 0.497468i −2.91914 − 0.719504i
15.14 −0.328537 − 1.48666i −0.0478455 + 0.658797i −0.288461 + 0.134040i 1.52396 − 3.08246i 0.995124 − 0.145309i 1.38242 − 3.17351i −1.55480 − 2.03472i 2.53679 + 0.370426i −5.08324 − 1.25291i
15.15 −0.319539 − 1.44594i 0.138896 − 1.91249i −0.174893 + 0.0812681i 0.133857 − 0.270747i −2.80974 + 0.410282i 0.965243 − 2.21584i −1.62481 − 2.12635i −0.669826 − 0.0978088i −0.434257 − 0.107035i
15.16 −0.272733 − 1.23414i −0.176989 + 2.43700i 0.365031 − 0.169621i −0.589979 + 1.19333i 3.05587 − 0.446223i −0.576344 + 1.32307i −1.84370 − 2.41280i −2.93914 − 0.429178i 1.63364 + 0.402657i
15.17 −0.259744 − 1.17536i −0.146596 + 2.01852i 0.499736 − 0.232215i −1.33505 + 2.70036i 2.41057 − 0.351995i 2.02132 − 4.64019i −1.86445 − 2.43996i −1.08441 − 0.158347i 3.52068 + 0.867770i
15.18 −0.248897 − 1.12628i 0.177543 − 2.44463i 0.607192 − 0.282146i −1.65787 + 3.35330i −2.79753 + 0.408498i −1.33124 + 3.05603i −1.86957 − 2.44666i −2.97616 − 0.434584i 4.18940 + 1.03259i
15.19 −0.244851 − 1.10797i 0.175706 − 2.41934i 0.646100 − 0.300226i 1.17618 − 2.37902i −2.72359 + 0.397702i −0.0903727 + 0.207462i −1.86874 − 2.44557i −2.85384 − 0.416721i −2.92388 − 0.720671i
15.20 −0.194638 − 0.880753i −0.0162284 + 0.223452i 1.07591 − 0.499946i 1.89522 − 3.83339i 0.199965 − 0.0291991i −2.03274 + 4.66642i −1.74507 − 2.28372i 2.91885 + 0.426215i −3.74515 − 0.923097i
See next 80 embeddings (of 2496 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 15.52
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner
53.d even 13 1 inner
583.s even 65 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 583.2.s.a ✓ 2496
11.c even 5 1 inner 583.2.s.a ✓ 2496
53.d even 13 1 inner 583.2.s.a ✓ 2496
583.s even 65 1 inner 583.2.s.a ✓ 2496
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
583.2.s.a ✓ 2496 1.a even 1 1 trivial
583.2.s.a ✓ 2496 11.c even 5 1 inner
583.2.s.a ✓ 2496 53.d even 13 1 inner
583.2.s.a ✓ 2496 583.s even 65 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(583, [\chi])\).