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Properties

Label 820.2.u.a
Level $820$
Weight $2$
Character orbit 820.u
Analytic conductor $6.548$
Analytic rank $0$
Dimension $24$
Inner twists $2$

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Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) 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("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: \( N \) \(=\) \( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 820.u (of order \(5\), degree \(4\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(6.54773296574\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) 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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
141.1 0 −2.55771 0 −0.809017 + 0.587785i 0 0.254587 − 0.783539i 0 3.54189 0
141.2 0 −1.99261 0 −0.809017 + 0.587785i 0 −0.679183 + 2.09031i 0 0.970505 0
141.3 0 −0.595477 0 −0.809017 + 0.587785i 0 0.581775 − 1.79052i 0 −2.64541 0
141.4 0 0.753937 0 −0.809017 + 0.587785i 0 0.739823 − 2.27694i 0 −2.43158 0
141.5 0 1.34396 0 −0.809017 + 0.587785i 0 −1.10976 + 3.41550i 0 −1.19376 0
141.6 0 2.42987 0 −0.809017 + 0.587785i 0 0.903746 − 2.78144i 0 2.90425 0
201.1 0 −2.30973 0 0.309017 − 0.951057i 0 0.494995 + 0.359635i 0 2.33484 0
201.2 0 −2.12100 0 0.309017 − 0.951057i 0 −0.100704 − 0.0731654i 0 1.49863 0
201.3 0 0.124286 0 0.309017 − 0.951057i 0 2.19178 + 1.59242i 0 −2.98455 0
201.4 0 0.309639 0 0.309017 − 0.951057i 0 −1.44940 − 1.05305i 0 −2.90412 0
201.5 0 2.53712 0 0.309017 − 0.951057i 0 2.92498 + 2.12513i 0 3.43699 0
201.6 0 3.07771 0 0.309017 − 0.951057i 0 −2.25264 − 1.63664i 0 6.47232 0
221.1 0 −2.55771 0 −0.809017 − 0.587785i 0 0.254587 + 0.783539i 0 3.54189 0
221.2 0 −1.99261 0 −0.809017 − 0.587785i 0 −0.679183 − 2.09031i 0 0.970505 0
221.3 0 −0.595477 0 −0.809017 − 0.587785i 0 0.581775 + 1.79052i 0 −2.64541 0
221.4 0 0.753937 0 −0.809017 − 0.587785i 0 0.739823 + 2.27694i 0 −2.43158 0
221.5 0 1.34396 0 −0.809017 − 0.587785i 0 −1.10976 − 3.41550i 0 −1.19376 0
221.6 0 2.42987 0 −0.809017 − 0.587785i 0 0.903746 + 2.78144i 0 2.90425 0
461.1 0 −2.30973 0 0.309017 + 0.951057i 0 0.494995 − 0.359635i 0 2.33484 0
461.2 0 −2.12100 0 0.309017 + 0.951057i 0 −0.100704 + 0.0731654i 0 1.49863 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 141.6
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
41.d even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 820.2.u.a ✓ 24
41.d even 5 1 inner 820.2.u.a ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
820.2.u.a ✓ 24 1.a even 1 1 trivial
820.2.u.a ✓ 24 41.d even 5 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - T_{3}^{11} - 22 T_{3}^{10} + 17 T_{3}^{9} + 178 T_{3}^{8} - 107 T_{3}^{7} - 629 T_{3}^{6} + \cdots - 11 \) acting on \(S_{2}^{\mathrm{new}}(820, [\chi])\). Copy content Toggle raw display