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Properties

Label 483.3.f.a
Level $483$
Weight $3$
Character orbit 483.f
Analytic conductor $13.161$
Analytic rank $0$
Dimension $48$
Inner twists $2$

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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] = [483,3,Mod(22,483)] 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("483.22"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(483, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.f (of order \(2\), degree \(1\), 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: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 4 q^{2} + 116 q^{4} - 24 q^{6} - 4 q^{8} + 144 q^{9} + 16 q^{13} + 324 q^{16} + 12 q^{18} - 4 q^{23} - 24 q^{24} - 176 q^{25} + 136 q^{26} - 128 q^{29} - 8 q^{31} - 252 q^{32} - 56 q^{35} + 348 q^{36}+ \cdots - 28 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
22.1 −3.89548 −1.73205 11.1748 5.58204i 6.74717 2.64575i −27.9492 3.00000 − 21.7447i
22.2 −3.89548 −1.73205 11.1748 − 5.58204i 6.74717 − 2.64575i −27.9492 3.00000 21.7447i
22.3 −3.83573 1.73205 10.7128 − 8.86189i −6.64368 2.64575i −25.7486 3.00000 33.9918i
22.4 −3.83573 1.73205 10.7128 8.86189i −6.64368 − 2.64575i −25.7486 3.00000 − 33.9918i
22.5 −3.28216 1.73205 6.77257 2.78765i −5.68487 2.64575i −9.10001 3.00000 − 9.14952i
22.6 −3.28216 1.73205 6.77257 − 2.78765i −5.68487 − 2.64575i −9.10001 3.00000 9.14952i
22.7 −3.23657 −1.73205 6.47539 4.61855i 5.60591 − 2.64575i −8.01179 3.00000 − 14.9483i
22.8 −3.23657 −1.73205 6.47539 − 4.61855i 5.60591 2.64575i −8.01179 3.00000 14.9483i
22.9 −2.89983 1.73205 4.40899 − 7.66563i −5.02265 − 2.64575i −1.18601 3.00000 22.2290i
22.10 −2.89983 1.73205 4.40899 7.66563i −5.02265 2.64575i −1.18601 3.00000 − 22.2290i
22.11 −2.49369 1.73205 2.21850 2.66866i −4.31920 − 2.64575i 4.44250 3.00000 − 6.65481i
22.12 −2.49369 1.73205 2.21850 − 2.66866i −4.31920 2.64575i 4.44250 3.00000 6.65481i
22.13 −1.75802 −1.73205 −0.909354 0.711109i 3.04499 − 2.64575i 8.63076 3.00000 − 1.25015i
22.14 −1.75802 −1.73205 −0.909354 − 0.711109i 3.04499 2.64575i 8.63076 3.00000 1.25015i
22.15 −1.65091 −1.73205 −1.27448 4.21491i 2.85947 2.64575i 8.70772 3.00000 − 6.95846i
22.16 −1.65091 −1.73205 −1.27448 − 4.21491i 2.85947 − 2.64575i 8.70772 3.00000 6.95846i
22.17 −0.984102 1.73205 −3.03154 − 2.95865i −1.70451 2.64575i 6.91976 3.00000 2.91162i
22.18 −0.984102 1.73205 −3.03154 2.95865i −1.70451 − 2.64575i 6.91976 3.00000 − 2.91162i
22.19 −0.876983 1.73205 −3.23090 8.50705i −1.51898 2.64575i 6.34138 3.00000 − 7.46053i
22.20 −0.876983 1.73205 −3.23090 − 8.50705i −1.51898 − 2.64575i 6.34138 3.00000 7.46053i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 22.48
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
23.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 483.3.f.a ✓ 48
23.b odd 2 1 inner 483.3.f.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
483.3.f.a ✓ 48 1.a even 1 1 trivial
483.3.f.a ✓ 48 23.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(483, [\chi])\).