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Properties

Label 483.2.q.e
Level $483$
Weight $2$
Character orbit 483.q
Analytic conductor $3.857$
Analytic rank $0$
Dimension $60$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [483,2,Mod(64,483)] 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("483.64"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 0, 12])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 483.q (of order \(11\), degree \(10\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [60,-1,6,-3,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.85677441763\)
Analytic rank: \(0\)
Dimension: \(60\)
Relative dimension: \(6\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 60 q - q^{2} + 6 q^{3} - 3 q^{4} + 5 q^{5} + q^{6} + 6 q^{7} + 13 q^{8} - 6 q^{9} - 4 q^{10} - q^{11} + 3 q^{12} + 22 q^{13} + q^{14} + 6 q^{15} - 5 q^{16} + 9 q^{17} - q^{18} - 34 q^{19} + 67 q^{20}+ \cdots - q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
64.1 −1.87100 − 0.549377i 0.654861 − 0.755750i 1.51634 + 0.974491i −0.563341 + 3.91812i −1.64044 + 1.05425i −0.415415 − 0.909632i 0.252236 + 0.291095i −0.142315 − 0.989821i 3.20654 − 7.02134i
64.2 −1.43941 − 0.422649i 0.654861 − 0.755750i 0.210759 + 0.135447i 0.271386 − 1.88753i −1.26203 + 0.811057i −0.415415 − 0.909632i 1.71869 + 1.98348i −0.142315 − 0.989821i −1.18840 + 2.60223i
64.3 0.345617 + 0.101482i 0.654861 − 0.755750i −1.57335 − 1.01113i −0.475765 + 3.30902i 0.303026 − 0.194743i −0.415415 − 0.909632i −0.912937 − 1.05359i −0.142315 − 0.989821i −0.500239 + 1.09537i
64.4 0.888980 + 0.261028i 0.654861 − 0.755750i −0.960357 − 0.617184i 0.251813 − 1.75140i 0.779430 − 0.500909i −0.415415 − 0.909632i −1.90611 − 2.19976i −0.142315 − 0.989821i 0.681020 − 1.49123i
64.5 1.81443 + 0.532766i 0.654861 − 0.755750i 1.32583 + 0.852056i 0.289215 − 2.01153i 1.59084 − 1.02237i −0.415415 − 0.909632i −0.525052 − 0.605943i −0.142315 − 0.989821i 1.59644 − 3.49571i
64.6 2.47754 + 0.727473i 0.654861 − 0.755750i 3.92650 + 2.52341i −0.135670 + 0.943603i 2.17223 − 1.39601i −0.415415 − 0.909632i 4.51049 + 5.20538i −0.142315 − 0.989821i −1.02257 + 2.23912i
85.1 −1.56944 + 1.81123i −0.841254 + 0.540641i −0.532780 − 3.70557i 1.21760 + 2.66617i 0.341071 − 2.37220i 0.959493 − 0.281733i 3.51550 + 2.25928i 0.415415 − 0.909632i −6.73999 − 1.97904i
85.2 −1.10975 + 1.28072i −0.841254 + 0.540641i −0.124067 − 0.862907i −0.209554 − 0.458859i 0.241171 − 1.67738i 0.959493 − 0.281733i −1.60841 − 1.03366i 0.415415 − 0.909632i 0.820221 + 0.240839i
85.3 −0.476363 + 0.549752i −0.841254 + 0.540641i 0.209324 + 1.45588i −1.25822 − 2.75513i 0.103524 − 0.720022i 0.959493 − 0.281733i −2.12399 − 1.36500i 0.415415 − 0.909632i 2.11401 + 0.620729i
85.4 0.451295 − 0.520822i −0.841254 + 0.540641i 0.217041 + 1.50955i 0.918881 + 2.01207i −0.0980757 + 0.682131i 0.959493 − 0.281733i 2.04365 + 1.31337i 0.415415 − 0.909632i 1.46262 + 0.429463i
85.5 0.767372 − 0.885594i −0.841254 + 0.540641i 0.0892119 + 0.620482i −1.61200 − 3.52979i −0.166766 + 1.15988i 0.959493 − 0.281733i 2.58953 + 1.66419i 0.415415 − 0.909632i −4.36297 − 1.28108i
85.6 1.48993 − 1.71948i −0.841254 + 0.540641i −0.452064 − 3.14417i 1.32209 + 2.89498i −0.323794 + 2.25204i 0.959493 − 0.281733i −2.25185 − 1.44718i 0.415415 − 0.909632i 6.94768 + 2.04002i
127.1 −2.26640 + 1.45653i 0.142315 − 0.989821i 2.18428 − 4.78290i 3.84207 − 1.12813i 1.11916 + 2.45062i 0.654861 + 0.755750i 1.24916 + 8.68812i −0.959493 − 0.281733i −7.06452 + 8.15290i
127.2 −1.70473 + 1.09556i 0.142315 − 0.989821i 0.875006 − 1.91600i −0.251997 + 0.0739930i 0.841802 + 1.84329i 0.654861 + 0.755750i 0.0306675 + 0.213297i −0.959493 − 0.281733i 0.348522 − 0.402215i
127.3 −0.539950 + 0.347005i 0.142315 − 0.989821i −0.659696 + 1.44453i −3.99137 + 1.17197i 0.266630 + 0.583838i 0.654861 + 0.755750i −0.327744 − 2.27951i −0.959493 − 0.281733i 1.74846 − 2.01783i
127.4 0.486928 − 0.312930i 0.142315 − 0.989821i −0.691656 + 1.51452i −1.52427 + 0.447565i −0.240447 − 0.526506i 0.654861 + 0.755750i 0.301897 + 2.09974i −0.959493 − 0.281733i −0.602152 + 0.694921i
127.5 0.978856 − 0.629072i 0.142315 − 0.989821i −0.268403 + 0.587721i 2.45426 − 0.720637i −0.483364 − 1.05842i 0.654861 + 0.755750i 0.438177 + 3.04759i −0.959493 − 0.281733i 1.94904 − 2.24931i
127.6 1.96460 − 1.26257i 0.142315 − 0.989821i 1.43472 − 3.14161i 0.650234 − 0.190926i −0.970126 − 2.12428i 0.654861 + 0.755750i −0.483142 − 3.36033i −0.959493 − 0.281733i 1.03639 − 1.19606i
169.1 −0.322450 + 2.24269i −0.415415 − 0.909632i −3.00670 − 0.882847i −0.335539 − 0.387233i 2.17397 − 0.638336i −0.841254 − 0.540641i 1.06701 − 2.33642i −0.654861 + 0.755750i 0.976638 − 0.627647i
169.2 −0.222029 + 1.54425i −0.415415 − 0.909632i −0.416411 − 0.122269i −2.19333 − 2.53124i 1.49693 − 0.439538i −0.841254 − 0.540641i −1.01493 + 2.22239i −0.654861 + 0.755750i 4.39584 − 2.82504i
See all 60 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 64.6
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Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.2.q.e ✓ 60
23.c even 11 1 inner 483.2.q.e ✓ 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.2.q.e ✓ 60 1.a even 1 1 trivial
483.2.q.e ✓ 60 23.c even 11 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{60} + T_{2}^{59} + 8 T_{2}^{58} - 10 T_{2}^{57} + 32 T_{2}^{56} - 136 T_{2}^{55} + 387 T_{2}^{54} + \cdots + 591361 \) acting on \(S_{2}^{\mathrm{new}}(483, [\chi])\). Copy content Toggle raw display