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Properties

Label 627.2.br.a
Level $627$
Weight $2$
Character orbit 627.br
Analytic conductor $5.007$
Analytic rank $0$
Dimension $960$
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] = [627,2,Mod(13,627)] 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("627.13"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(627, base_ring=CyclotomicField(90)) chi = DirichletCharacter(H, H._module([0, 9, 25])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 627 = 3 \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 627.br (of order \(90\), degree \(24\), 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: \(5.00662020673\)
Analytic rank: \(0\)
Dimension: \(960\)
Relative dimension: \(40\) over \(\Q(\zeta_{90})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{90}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 960 q + 30 q^{7} - 6 q^{11} - 72 q^{14} - 24 q^{15} + 60 q^{17} - 84 q^{20} - 24 q^{26} - 120 q^{29} + 36 q^{31} + 6 q^{33} + 72 q^{34} - 180 q^{38} - 420 q^{40} + 180 q^{41} - 12 q^{42} + 24 q^{44} + 12 q^{45}+ \cdots + 12 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
13.1 −1.01652 − 2.51598i 0.275637 + 0.961262i −3.85815 + 3.72578i −3.43203 + 1.82485i 2.13832 − 1.67064i 0.00586270 + 0.0131678i 8.33793 + 3.71228i −0.848048 + 0.529919i 8.08001 + 6.77993i
13.2 −1.01449 − 2.51095i −0.275637 − 0.961262i −3.83699 + 3.70534i 0.545691 − 0.290149i −2.13405 + 1.66730i −1.37217 − 3.08195i 8.24846 + 3.67245i −0.848048 + 0.529919i −1.28215 − 1.07585i
13.3 −0.940761 − 2.32846i 0.275637 + 0.961262i −3.09804 + 2.99174i 1.62184 − 0.862349i 1.97896 − 1.54613i 0.881482 + 1.97984i 5.29224 + 2.35626i −0.848048 + 0.529919i −3.53371 − 2.96514i
13.4 −0.917384 − 2.27061i −0.275637 − 0.961262i −2.87538 + 2.77672i 3.73360 − 1.98519i −1.92978 + 1.50771i 1.59593 + 3.58452i 4.46824 + 1.98939i −0.848048 + 0.529919i −7.93272 − 6.65634i
13.5 −0.850346 − 2.10468i 0.275637 + 0.961262i −2.26791 + 2.19010i −0.197965 + 0.105260i 1.78876 − 1.39753i −0.153487 − 0.344737i 2.39053 + 1.06433i −0.848048 + 0.529919i 0.389877 + 0.327146i
13.6 −0.817910 − 2.02440i −0.275637 − 0.961262i −1.99053 + 1.92224i −3.91483 + 2.08155i −1.72053 + 1.34423i −1.55570 − 3.49416i 1.53021 + 0.681292i −0.848048 + 0.529919i 7.41588 + 6.22266i
13.7 −0.709786 − 1.75678i −0.275637 − 0.961262i −1.14381 + 1.10456i 0.378400 − 0.201199i −1.49308 + 1.16653i −1.12211 − 2.52030i −0.709543 − 0.315909i −0.848048 + 0.529919i −0.622046 − 0.521958i
13.8 −0.703526 − 1.74129i 0.275637 + 0.961262i −1.09846 + 1.06077i −1.57431 + 0.837076i 1.47992 − 1.15624i −1.43590 − 3.22508i −0.811452 − 0.361282i −0.848048 + 0.529919i 2.56516 + 2.15243i
13.9 −0.703163 − 1.74039i −0.275637 − 0.961262i −1.09584 + 1.05824i −0.582308 + 0.309619i −1.47915 + 1.15564i 1.10921 + 2.49133i −0.817279 − 0.363876i −0.848048 + 0.529919i 0.948315 + 0.795731i
13.10 −0.677665 − 1.67728i 0.275637 + 0.961262i −0.915359 + 0.883952i 2.69222 − 1.43148i 1.42552 − 1.11373i −1.24825 − 2.80362i −1.20227 − 0.535287i −0.848048 + 0.529919i −4.22541 − 3.54554i
13.11 −0.608457 − 1.50598i −0.275637 − 0.961262i −0.459089 + 0.443337i 2.82466 − 1.50190i −1.27993 + 0.999992i −1.52009 − 3.41417i −2.02067 − 0.899660i −0.848048 + 0.529919i −3.98052 − 3.34005i
13.12 −0.584163 − 1.44585i 0.275637 + 0.961262i −0.310568 + 0.299912i −1.85530 + 0.986480i 1.22883 − 0.960065i 0.516103 + 1.15919i −2.23412 − 0.994695i −0.848048 + 0.529919i 2.51010 + 2.10623i
13.13 −0.460730 − 1.14035i −0.275637 − 0.961262i 0.350563 − 0.338535i −1.94131 + 1.03221i −0.969176 + 0.757204i 0.847956 + 1.90454i −2.79471 − 1.24428i −0.848048 + 0.529919i 2.07150 + 1.73820i
13.14 −0.362912 − 0.898238i 0.275637 + 0.961262i 0.763554 − 0.737355i 3.07774 − 1.63646i 0.763409 − 0.596441i 1.00387 + 2.25473i −2.70947 − 1.20633i −0.848048 + 0.529919i −2.58688 − 2.17065i
13.15 −0.299443 − 0.741148i −0.275637 − 0.961262i 0.979045 − 0.945453i 1.92290 − 1.02242i −0.629900 + 0.492131i 0.311157 + 0.698869i −2.45438 − 1.09276i −0.848048 + 0.529919i −1.33356 − 1.11899i
13.16 −0.276080 − 0.683323i 0.275637 + 0.961262i 1.04797 − 1.01201i −2.45783 + 1.30685i 0.580754 − 0.453735i −0.455816 − 1.02378i −2.32740 − 1.03622i −0.848048 + 0.529919i 1.57156 + 1.31870i
13.17 −0.255346 − 0.632002i 0.275637 + 0.961262i 1.10445 − 1.06656i −2.12636 + 1.13061i 0.537137 − 0.419657i 1.64750 + 3.70034i −2.20150 − 0.980170i −0.848048 + 0.529919i 1.25750 + 1.05517i
13.18 −0.0767456 − 0.189952i −0.275637 − 0.961262i 1.40849 − 1.36016i 2.03434 − 1.08168i −0.161440 + 0.126130i −0.753260 − 1.69185i −0.740776 − 0.329815i −0.848048 + 0.529919i −0.361594 − 0.303413i
13.19 −0.0588394 − 0.145633i −0.275637 − 0.961262i 1.42093 − 1.37218i −3.30090 + 1.75512i −0.123773 + 0.0967019i 1.77441 + 3.98540i −0.570422 − 0.253968i −0.848048 + 0.529919i 0.449826 + 0.377449i
13.20 −0.0426210 − 0.105491i 0.275637 + 0.961262i 1.42937 − 1.38032i 1.04162 − 0.553839i 0.0896563 − 0.0700472i −1.25378 − 2.81603i −0.414411 − 0.184508i −0.848048 + 0.529919i −0.102820 − 0.0862760i
See next 80 embeddings (of 960 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 13.40
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.d odd 10 1 inner
19.f odd 18 1 inner
209.w even 90 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 627.2.br.a ✓ 960
11.d odd 10 1 inner 627.2.br.a ✓ 960
19.f odd 18 1 inner 627.2.br.a ✓ 960
209.w even 90 1 inner 627.2.br.a ✓ 960
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
627.2.br.a ✓ 960 1.a even 1 1 trivial
627.2.br.a ✓ 960 11.d odd 10 1 inner
627.2.br.a ✓ 960 19.f odd 18 1 inner
627.2.br.a ✓ 960 209.w even 90 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(627, [\chi])\).