Properties

Label 1064.2.m.b
Level $1064$
Weight $2$
Character orbit 1064.m
Analytic conductor $8.496$
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] = [1064,2,Mod(265,1064)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1064, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 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("1064.265");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.m (of order \(2\), degree \(1\), 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: \(8.49608277506\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{7} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{7} + 40 q^{9} - 36 q^{23} - 20 q^{25} - 38 q^{35} + 24 q^{39} + 20 q^{43} - 4 q^{49} - 32 q^{57} + 70 q^{63} + 102 q^{77} - 40 q^{81} + 96 q^{85} + 32 q^{93} - 36 q^{95} - 116 q^{99}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
265.1 0 −2.94661 0 1.44192i 0 −0.743572 2.53911i 0 5.68249 0
265.2 0 −2.94661 0 1.44192i 0 −0.743572 + 2.53911i 0 5.68249 0
265.3 0 −2.88400 0 0.977713i 0 2.04655 + 1.67679i 0 5.31745 0
265.4 0 −2.88400 0 0.977713i 0 2.04655 1.67679i 0 5.31745 0
265.5 0 −2.23395 0 4.18039i 0 2.56370 0.653799i 0 1.99054 0
265.6 0 −2.23395 0 4.18039i 0 2.56370 + 0.653799i 0 1.99054 0
265.7 0 −1.94588 0 1.86531i 0 1.44774 2.21451i 0 0.786449 0
265.8 0 −1.94588 0 1.86531i 0 1.44774 + 2.21451i 0 0.786449 0
265.9 0 −1.42796 0 1.88393i 0 −2.55095 0.701880i 0 −0.960935 0
265.10 0 −1.42796 0 1.88393i 0 −2.55095 + 0.701880i 0 −0.960935 0
265.11 0 −0.428956 0 2.73144i 0 −0.763462 + 2.53320i 0 −2.81600 0
265.12 0 −0.428956 0 2.73144i 0 −0.763462 2.53320i 0 −2.81600 0
265.13 0 0.428956 0 2.73144i 0 −0.763462 + 2.53320i 0 −2.81600 0
265.14 0 0.428956 0 2.73144i 0 −0.763462 2.53320i 0 −2.81600 0
265.15 0 1.42796 0 1.88393i 0 −2.55095 0.701880i 0 −0.960935 0
265.16 0 1.42796 0 1.88393i 0 −2.55095 + 0.701880i 0 −0.960935 0
265.17 0 1.94588 0 1.86531i 0 1.44774 2.21451i 0 0.786449 0
265.18 0 1.94588 0 1.86531i 0 1.44774 + 2.21451i 0 0.786449 0
265.19 0 2.23395 0 4.18039i 0 2.56370 0.653799i 0 1.99054 0
265.20 0 2.23395 0 4.18039i 0 2.56370 + 0.653799i 0 1.99054 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 265.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
19.b odd 2 1 inner
133.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1064.2.m.b 24
4.b odd 2 1 2128.2.m.h 24
7.b odd 2 1 inner 1064.2.m.b 24
19.b odd 2 1 inner 1064.2.m.b 24
28.d even 2 1 2128.2.m.h 24
76.d even 2 1 2128.2.m.h 24
133.c even 2 1 inner 1064.2.m.b 24
532.b odd 2 1 2128.2.m.h 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1064.2.m.b 24 1.a even 1 1 trivial
1064.2.m.b 24 7.b odd 2 1 inner
1064.2.m.b 24 19.b odd 2 1 inner
1064.2.m.b 24 133.c even 2 1 inner
2128.2.m.h 24 4.b odd 2 1
2128.2.m.h 24 28.d even 2 1
2128.2.m.h 24 76.d even 2 1
2128.2.m.h 24 532.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - 28T_{3}^{10} + 298T_{3}^{8} - 1499T_{3}^{6} + 3578T_{3}^{4} - 3392T_{3}^{2} + 512 \) acting on \(S_{2}^{\mathrm{new}}(1064, [\chi])\). Copy content Toggle raw display