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Properties

Label 2016.2.i.b
Level $2016$
Weight $2$
Character orbit 2016.i
Analytic conductor $16.098$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2016,2,Mod(881,2016)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2016, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2016.881");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2016 = 2^{5} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2016.i (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: \(16.0978410475\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 504)
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
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 72 q^{25} - 72 q^{49} - 48 q^{79}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
881.1 0 0 0 − 1.88325i 0 0.347296 + 2.62286i 0 0 0
881.2 0 0 0 1.88325i 0 0.347296 − 2.62286i 0 0 0
881.3 0 0 0 − 2.37285i 0 1.53209 − 2.15701i 0 0 0
881.4 0 0 0 2.37285i 0 1.53209 + 2.15701i 0 0 0
881.5 0 0 0 − 3.85006i 0 −1.87939 + 1.86223i 0 0 0
881.6 0 0 0 3.85006i 0 −1.87939 − 1.86223i 0 0 0
881.7 0 0 0 − 2.37285i 0 1.53209 + 2.15701i 0 0 0
881.8 0 0 0 2.37285i 0 1.53209 − 2.15701i 0 0 0
881.9 0 0 0 − 3.85006i 0 −1.87939 − 1.86223i 0 0 0
881.10 0 0 0 3.85006i 0 −1.87939 + 1.86223i 0 0 0
881.11 0 0 0 − 1.88325i 0 0.347296 + 2.62286i 0 0 0
881.12 0 0 0 1.88325i 0 0.347296 − 2.62286i 0 0 0
881.13 0 0 0 − 1.88325i 0 0.347296 − 2.62286i 0 0 0
881.14 0 0 0 1.88325i 0 0.347296 + 2.62286i 0 0 0
881.15 0 0 0 − 3.85006i 0 −1.87939 + 1.86223i 0 0 0
881.16 0 0 0 3.85006i 0 −1.87939 − 1.86223i 0 0 0
881.17 0 0 0 − 2.37285i 0 1.53209 − 2.15701i 0 0 0
881.18 0 0 0 2.37285i 0 1.53209 + 2.15701i 0 0 0
881.19 0 0 0 − 3.85006i 0 −1.87939 − 1.86223i 0 0 0
881.20 0 0 0 3.85006i 0 −1.87939 + 1.86223i 0 0 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 881.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
7.b odd 2 1 inner
8.b even 2 1 inner
21.c even 2 1 inner
24.h odd 2 1 inner
56.h odd 2 1 inner
168.i even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2016.2.i.b 24
3.b odd 2 1 inner 2016.2.i.b 24
4.b odd 2 1 504.2.i.b ✓ 24
7.b odd 2 1 inner 2016.2.i.b 24
8.b even 2 1 inner 2016.2.i.b 24
8.d odd 2 1 504.2.i.b ✓ 24
12.b even 2 1 504.2.i.b ✓ 24
21.c even 2 1 inner 2016.2.i.b 24
24.f even 2 1 504.2.i.b ✓ 24
24.h odd 2 1 inner 2016.2.i.b 24
28.d even 2 1 504.2.i.b ✓ 24
56.e even 2 1 504.2.i.b ✓ 24
56.h odd 2 1 inner 2016.2.i.b 24
84.h odd 2 1 504.2.i.b ✓ 24
168.e odd 2 1 504.2.i.b ✓ 24
168.i even 2 1 inner 2016.2.i.b 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
504.2.i.b ✓ 24 4.b odd 2 1
504.2.i.b ✓ 24 8.d odd 2 1
504.2.i.b ✓ 24 12.b even 2 1
504.2.i.b ✓ 24 24.f even 2 1
504.2.i.b ✓ 24 28.d even 2 1
504.2.i.b ✓ 24 56.e even 2 1
504.2.i.b ✓ 24 84.h odd 2 1
504.2.i.b ✓ 24 168.e odd 2 1
2016.2.i.b 24 1.a even 1 1 trivial
2016.2.i.b 24 3.b odd 2 1 inner
2016.2.i.b 24 7.b odd 2 1 inner
2016.2.i.b 24 8.b even 2 1 inner
2016.2.i.b 24 21.c even 2 1 inner
2016.2.i.b 24 24.h odd 2 1 inner
2016.2.i.b 24 56.h odd 2 1 inner
2016.2.i.b 24 168.i even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{6} + 24T_{5}^{4} + 156T_{5}^{2} + 296 \) acting on \(S_{2}^{\mathrm{new}}(2016, [\chi])\). Copy content Toggle raw display