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Properties

Label 583.2.g.d
Level $583$
Weight $2$
Character orbit 583.g
Analytic conductor $4.655$
Analytic rank $0$
Dimension $104$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [583,2,Mod(213,583)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(583, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([2, 0])) 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("583.213"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 583 = 11 \cdot 53 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 583.g (of order \(5\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [104,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.65527843784\)
Analytic rank: \(0\)
Dimension: \(104\)
Relative dimension: \(26\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 104 q - 4 q^{2} - 2 q^{3} - 26 q^{4} - 2 q^{5} - 3 q^{6} - 13 q^{7} - 12 q^{8} - 26 q^{9} + 48 q^{10} - 4 q^{11} - 14 q^{12} - 24 q^{13} - 4 q^{14} - 6 q^{15} - 22 q^{16} - 15 q^{17} + 30 q^{18} - 29 q^{19}+ \cdots - 62 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
213.1 −2.22499 − 1.61655i −0.951178 + 2.92742i 1.71931 + 5.29150i 1.53808 − 1.11748i 6.84869 − 4.97586i 0.269882 + 0.830612i 3.02878 − 9.32162i −5.23802 − 3.80565i −5.22867
213.2 −2.16595 − 1.57366i 0.0214199 − 0.0659237i 1.59692 + 4.91481i −2.23811 + 1.62608i −0.150136 + 0.109080i 1.28918 + 3.96770i 2.62073 − 8.06579i 2.42316 + 1.76053i 7.40655
213.3 −2.06065 − 1.49715i −0.334839 + 1.03053i 1.38679 + 4.26811i −2.05624 + 1.49395i 2.23285 − 1.62226i −0.996322 − 3.06636i 1.95811 − 6.02645i 1.47718 + 1.07323i 6.47386
213.4 −1.91391 − 1.39054i 0.986579 − 3.03638i 1.11143 + 3.42063i −0.354573 + 0.257613i −6.11043 + 4.43949i 0.412861 + 1.27065i 1.16724 − 3.59241i −5.81919 − 4.22789i 1.03684
213.5 −1.64911 − 1.19815i 0.640713 − 1.97191i 0.665966 + 2.04963i 2.48848 − 1.80798i −3.41924 + 2.48422i 1.32659 + 4.08283i 0.0977049 − 0.300705i −1.05087 − 0.763500i −6.27000
213.6 −1.61381 − 1.17250i −0.689262 + 2.12133i 0.611583 + 1.88226i 2.00474 − 1.45653i 3.59959 − 2.61526i 1.18903 + 3.65947i −0.0128680 + 0.0396036i −1.59791 − 1.16095i −4.94305
213.7 −1.27377 − 0.925449i 0.647284 − 1.99213i 0.148004 + 0.455508i −3.42632 + 2.48936i −2.66811 + 1.93850i 0.947626 + 2.91649i −0.740048 + 2.27763i −1.12257 − 0.815597i 6.66812
213.8 −1.19902 − 0.871136i −0.365075 + 1.12359i 0.0607263 + 0.186896i −2.82543 + 2.05279i 1.41653 − 1.02917i −0.814044 − 2.50537i −0.825966 + 2.54206i 1.29789 + 0.942969i 5.17599
213.9 −1.08667 − 0.789511i 0.841838 − 2.59091i −0.0605134 − 0.186241i 2.86995 − 2.08514i −2.96035 + 2.15082i −1.24061 − 3.81822i −0.911422 + 2.80507i −3.57708 − 2.59890i −4.76492
213.10 −0.924361 − 0.671588i 0.0157293 − 0.0484098i −0.214621 − 0.660534i 1.80997 − 1.31502i −0.0470510 + 0.0341845i −0.413726 − 1.27332i −0.951369 + 2.92801i 2.42495 + 1.76183i −2.55621
213.11 −0.913696 − 0.663839i 0.198485 − 0.610873i −0.223876 − 0.689019i −0.576100 + 0.418561i −0.586876 + 0.426391i 0.583757 + 1.79662i −0.950845 + 2.92640i 2.09328 + 1.52086i 0.804238
213.12 −0.399141 − 0.289993i 0.682376 − 2.10014i −0.542816 − 1.67062i −1.18937 + 0.864127i −0.881390 + 0.640368i −0.309128 − 0.951398i −0.572724 + 1.76266i −1.51789 − 1.10281i 0.725318
213.13 −0.265812 − 0.193124i −0.892021 + 2.74536i −0.584675 − 1.79944i −1.09789 + 0.797664i 0.767304 − 0.557479i −0.498305 − 1.53363i −0.395164 + 1.21619i −4.31423 − 3.13447i 0.445881
213.14 −0.0379428 − 0.0275670i −0.671048 + 2.06527i −0.617354 − 1.90002i −0.0492370 + 0.0357728i 0.0823949 − 0.0598634i −0.289748 − 0.891754i −0.0579395 + 0.178320i −1.38800 − 1.00844i 0.00285434
213.15 0.256862 + 0.186621i −0.350769 + 1.07956i −0.586883 − 1.80624i 3.46328 − 2.51622i −0.291567 + 0.211836i 1.12865 + 3.47362i 0.382560 − 1.17740i 1.38465 + 1.00601i 1.35917
213.16 0.302430 + 0.219728i 0.424657 − 1.30696i −0.574851 − 1.76921i 1.81965 − 1.32205i 0.415605 − 0.301955i −0.484577 − 1.49138i 0.445929 − 1.37243i 0.899238 + 0.653335i 0.840807
213.17 0.857434 + 0.622963i −0.688293 + 2.11835i −0.270923 − 0.833814i −0.404553 + 0.293925i −1.90982 + 1.38756i −1.14671 − 3.52922i 0.942158 − 2.89966i −1.58660 − 1.15273i −0.529981
213.18 0.869775 + 0.631929i −0.974803 + 3.00013i −0.260859 − 0.802841i −2.76514 + 2.00899i −2.74373 + 1.99344i 1.51869 + 4.67405i 0.944899 − 2.90810i −5.62352 − 4.08573i −3.67459
213.19 0.876585 + 0.636877i 0.946657 − 2.91351i −0.255244 − 0.785560i −0.539802 + 0.392189i 2.68537 − 1.95104i 0.330603 + 1.01749i 0.946213 − 2.91214i −5.16533 − 3.75283i −0.722958
213.20 0.988872 + 0.718457i −0.421339 + 1.29675i −0.156348 − 0.481189i 0.530822 − 0.385664i −1.34831 + 0.979604i 1.02386 + 3.15112i 0.946537 − 2.91314i 0.923021 + 0.670614i 0.801998
See next 80 embeddings (of 104 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 213.26
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 583.2.g.d ✓ 104
11.c even 5 1 inner 583.2.g.d ✓ 104
11.c even 5 1 6413.2.a.bi 52
11.d odd 10 1 6413.2.a.bh 52
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
583.2.g.d ✓ 104 1.a even 1 1 trivial
583.2.g.d ✓ 104 11.c even 5 1 inner
6413.2.a.bh 52 11.d odd 10 1
6413.2.a.bi 52 11.c even 5 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{104} + 4 T_{2}^{103} + 47 T_{2}^{102} + 176 T_{2}^{101} + 1217 T_{2}^{100} + 4132 T_{2}^{99} + \cdots + 143496441 \) acting on \(S_{2}^{\mathrm{new}}(583, [\chi])\). Copy content Toggle raw display