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Properties

Label 864.4.f.b
Level $864$
Weight $4$
Character orbit 864.f
Analytic conductor $50.978$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [864,4,Mod(431,864)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(864, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("864.431");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 864 = 2^{5} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 864.f (of order \(2\), degree \(1\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(50.9776502450\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 216)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 48 q^{19} + 600 q^{25} + 432 q^{43} - 816 q^{49} - 1632 q^{67} - 216 q^{73} - 3600 q^{91} + 2280 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
431.1 0 0 0 −21.0227 0 − 25.8057i 0 0 0
431.2 0 0 0 −21.0227 0 25.8057i 0 0 0
431.3 0 0 0 −13.3214 0 − 1.40229i 0 0 0
431.4 0 0 0 −13.3214 0 1.40229i 0 0 0
431.5 0 0 0 −12.8173 0 − 12.3152i 0 0 0
431.6 0 0 0 −12.8173 0 12.3152i 0 0 0
431.7 0 0 0 −9.32272 0 − 5.38753i 0 0 0
431.8 0 0 0 −9.32272 0 5.38753i 0 0 0
431.9 0 0 0 −5.34627 0 − 31.3735i 0 0 0
431.10 0 0 0 −5.34627 0 31.3735i 0 0 0
431.11 0 0 0 −0.898373 0 − 20.7150i 0 0 0
431.12 0 0 0 −0.898373 0 20.7150i 0 0 0
431.13 0 0 0 0.898373 0 − 20.7150i 0 0 0
431.14 0 0 0 0.898373 0 20.7150i 0 0 0
431.15 0 0 0 5.34627 0 − 31.3735i 0 0 0
431.16 0 0 0 5.34627 0 31.3735i 0 0 0
431.17 0 0 0 9.32272 0 − 5.38753i 0 0 0
431.18 0 0 0 9.32272 0 5.38753i 0 0 0
431.19 0 0 0 12.8173 0 − 12.3152i 0 0 0
431.20 0 0 0 12.8173 0 12.3152i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 431.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
8.d odd 2 1 inner
24.f even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 864.4.f.b 24
3.b odd 2 1 inner 864.4.f.b 24
4.b odd 2 1 216.4.f.b ✓ 24
8.b even 2 1 216.4.f.b ✓ 24
8.d odd 2 1 inner 864.4.f.b 24
12.b even 2 1 216.4.f.b ✓ 24
24.f even 2 1 inner 864.4.f.b 24
24.h odd 2 1 216.4.f.b ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
216.4.f.b ✓ 24 4.b odd 2 1
216.4.f.b ✓ 24 8.b even 2 1
216.4.f.b ✓ 24 12.b even 2 1
216.4.f.b ✓ 24 24.h odd 2 1
864.4.f.b 24 1.a even 1 1 trivial
864.4.f.b 24 3.b odd 2 1 inner
864.4.f.b 24 8.d odd 2 1 inner
864.4.f.b 24 24.f even 2 1 inner