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Properties

Label 4767.2.a.g
Level $4767$
Weight $2$
Character orbit 4767.a
Self dual yes
Analytic conductor $38.065$
Analytic rank $0$
Dimension $35$
CM no
Inner twists $1$

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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] = [4767,2,Mod(1,4767)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4767, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 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("4767.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 4767 = 3 \cdot 7 \cdot 227 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4767.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [35,7] 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: yes
Analytic conductor: \(38.0646866435\)
Analytic rank: \(0\)
Dimension: \(35\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 35 q + 7 q^{2} - 35 q^{3} + 45 q^{4} - 4 q^{5} - 7 q^{6} + 35 q^{7} + 21 q^{8} + 35 q^{9} + 11 q^{10} - 3 q^{11} - 45 q^{12} + 19 q^{13} + 7 q^{14} + 4 q^{15} + 65 q^{16} + 20 q^{17} + 7 q^{18} + 9 q^{19}+ \cdots - 3 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.63425 −1.00000 4.93925 −3.01348 2.63425 1.00000 −7.74272 1.00000 7.93824
1.2 −2.58750 −1.00000 4.69514 2.73401 2.58750 1.00000 −6.97367 1.00000 −7.07425
1.3 −2.57299 −1.00000 4.62027 0.687417 2.57299 1.00000 −6.74193 1.00000 −1.76872
1.4 −2.49137 −1.00000 4.20693 −4.21474 2.49137 1.00000 −5.49828 1.00000 10.5005
1.5 −2.15125 −1.00000 2.62788 −1.38984 2.15125 1.00000 −1.35073 1.00000 2.98990
1.6 −1.92009 −1.00000 1.68676 −0.434339 1.92009 1.00000 0.601454 1.00000 0.833972
1.7 −1.79721 −1.00000 1.22997 0.961425 1.79721 1.00000 1.38390 1.00000 −1.72789
1.8 −1.66837 −1.00000 0.783461 3.62303 1.66837 1.00000 2.02964 1.00000 −6.04455
1.9 −1.48988 −1.00000 0.219733 −3.04833 1.48988 1.00000 2.65238 1.00000 4.54163
1.10 −1.39040 −1.00000 −0.0667902 2.45696 1.39040 1.00000 2.87366 1.00000 −3.41615
1.11 −1.30454 −1.00000 −0.298164 0.639394 1.30454 1.00000 2.99806 1.00000 −0.834118
1.12 −0.858119 −1.00000 −1.26363 −3.59592 0.858119 1.00000 2.80058 1.00000 3.08573
1.13 −0.838531 −1.00000 −1.29687 2.50382 0.838531 1.00000 2.76452 1.00000 −2.09953
1.14 −0.352449 −1.00000 −1.87578 −3.67328 0.352449 1.00000 1.36602 1.00000 1.29464
1.15 −0.233639 −1.00000 −1.94541 −1.48259 0.233639 1.00000 0.921803 1.00000 0.346390
1.16 −0.168193 −1.00000 −1.97171 −2.57645 0.168193 1.00000 0.668016 1.00000 0.433342
1.17 −0.116051 −1.00000 −1.98653 3.77717 0.116051 1.00000 0.462641 1.00000 −0.438345
1.18 0.274806 −1.00000 −1.92448 0.377871 −0.274806 1.00000 −1.07847 1.00000 0.103841
1.19 0.560407 −1.00000 −1.68594 3.49665 −0.560407 1.00000 −2.06563 1.00000 1.95955
1.20 0.755262 −1.00000 −1.42958 −2.30657 −0.755262 1.00000 −2.59023 1.00000 −1.74206
See all 35 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.35
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \( +1 \)
\(7\) \( -1 \)
\(227\) \( +1 \)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4767.2.a.g ✓ 35
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4767.2.a.g ✓ 35 1.a even 1 1 trivial