Properties

Label 2916.3.c.b
Level $2916$
Weight $3$
Character orbit 2916.c
Analytic conductor $79.455$
Analytic rank $0$
Dimension $36$
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] = [2916,3,Mod(1457,2916)] 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("2916.1457"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2916, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 2916 = 2^{2} \cdot 3^{6} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 2916.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [36,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-180,0,0,0, 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,252,0,0,0,0,0,0,0,0,0,0,0,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(61)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(79.4552450875\)
Analytic rank: \(0\)
Dimension: \(36\)
Twist minimal: no (minimal twist has level 108)
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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - 180 q^{25} + 252 q^{49} + 18 q^{61} - 90 q^{67} + 126 q^{73} - 198 q^{91}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1457.1 0 0 0 − 9.50324i 0 2.36132 0 0 0
1457.2 0 0 0 − 8.78835i 0 −4.31308 0 0 0
1457.3 0 0 0 − 7.78294i 0 3.61169 0 0 0
1457.4 0 0 0 − 7.77099i 0 13.6742 0 0 0
1457.5 0 0 0 − 7.31297i 0 −9.37121 0 0 0
1457.6 0 0 0 − 7.21405i 0 −4.39191 0 0 0
1457.7 0 0 0 − 5.21679i 0 −11.6618 0 0 0
1457.8 0 0 0 − 4.83775i 0 9.71048 0 0 0
1457.9 0 0 0 − 4.39539i 0 −3.57384 0 0 0
1457.10 0 0 0 − 4.19339i 0 −11.8514 0 0 0
1457.11 0 0 0 − 4.17955i 0 5.19980 0 0 0
1457.12 0 0 0 − 3.70301i 0 −0.419343 0 0 0
1457.13 0 0 0 − 3.34301i 0 5.01893 0 0 0
1457.14 0 0 0 − 2.96937i 0 0.934448 0 0 0
1457.15 0 0 0 − 2.16582i 0 6.23376 0 0 0
1457.16 0 0 0 − 1.52502i 0 −3.44709 0 0 0
1457.17 0 0 0 − 0.464464i 0 10.8001 0 0 0
1457.18 0 0 0 − 0.200781i 0 −8.51501 0 0 0
1457.19 0 0 0 0.200781i 0 −8.51501 0 0 0
1457.20 0 0 0 0.464464i 0 10.8001 0 0 0
See all 36 embeddings
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 1457.36
Significant digits:
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Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2916.3.c.b 36
3.b odd 2 1 inner 2916.3.c.b 36
27.e even 9 1 108.3.k.a ✓ 36
27.e even 9 1 324.3.k.a 36
27.f odd 18 1 108.3.k.a ✓ 36
27.f odd 18 1 324.3.k.a 36
108.j odd 18 1 432.3.bc.b 36
108.l even 18 1 432.3.bc.b 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
108.3.k.a ✓ 36 27.e even 9 1
108.3.k.a ✓ 36 27.f odd 18 1
324.3.k.a 36 27.e even 9 1
324.3.k.a 36 27.f odd 18 1
432.3.bc.b 36 108.j odd 18 1
432.3.bc.b 36 108.l even 18 1
2916.3.c.b 36 1.a even 1 1 trivial
2916.3.c.b 36 3.b odd 2 1 inner