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Properties

Label 1064.2.t.e
Level $1064$
Weight $2$
Character orbit 1064.t
Analytic conductor $8.496$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1064,2,Mod(961,1064)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1064, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1064.961");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1064.t (of order \(3\), degree \(2\), 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: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 40 q + 4 q^{3} + 2 q^{5} + q^{7} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 40 q + 4 q^{3} + 2 q^{5} + q^{7} + 32 q^{9} + 2 q^{11} - q^{13} - 2 q^{15} - 6 q^{17} - q^{19} - 8 q^{21} + 4 q^{23} - 14 q^{25} + 22 q^{27} - q^{29} - 2 q^{31} + 2 q^{35} - 11 q^{37} - 12 q^{39} - 3 q^{41} - 4 q^{43} + 34 q^{45} + 20 q^{47} + 21 q^{49} + 18 q^{51} + 8 q^{53} + 8 q^{55} + 19 q^{57} - 12 q^{59} - 18 q^{61} - 31 q^{63} + 26 q^{65} - 18 q^{67} - 36 q^{69} - 13 q^{71} - 26 q^{73} - 19 q^{75} - 20 q^{77} - 2 q^{79} + 48 q^{81} - 38 q^{83} - 9 q^{85} - q^{87} - 72 q^{89} - 46 q^{91} - 6 q^{93} + 7 q^{95} + 6 q^{97} + 30 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
961.1 0 −3.20508 0 1.01743 + 1.76225i 0 −1.44467 + 2.21651i 0 7.27254 0
961.2 0 −2.70412 0 −0.383801 − 0.664762i 0 −0.334970 − 2.62446i 0 4.31229 0
961.3 0 −2.28633 0 −1.50174 − 2.60108i 0 −1.34174 + 2.28030i 0 2.22732 0
961.4 0 −2.23181 0 1.16534 + 2.01843i 0 2.29043 + 1.32437i 0 1.98098 0
961.5 0 −1.71539 0 −0.302837 − 0.524530i 0 1.90272 − 1.83839i 0 −0.0574383 0
961.6 0 −1.58445 0 1.33698 + 2.31571i 0 2.54866 + 0.710151i 0 −0.489532 0
961.7 0 −0.910720 0 1.73355 + 3.00259i 0 −2.64545 + 0.0401300i 0 −2.17059 0
961.8 0 −0.603488 0 −0.879818 − 1.52389i 0 1.90735 + 1.83359i 0 −2.63580 0
961.9 0 −0.391112 0 0.163996 + 0.284050i 0 −2.24203 − 1.40474i 0 −2.84703 0
961.10 0 0.0187304 0 −0.746984 − 1.29381i 0 0.156989 + 2.64109i 0 −2.99965 0
961.11 0 0.392777 0 0.816491 + 1.41420i 0 −0.215670 − 2.63695i 0 −2.84573 0
961.12 0 0.440920 0 −2.20419 − 3.81776i 0 −2.34648 − 1.22231i 0 −2.80559 0
961.13 0 0.554868 0 −1.76414 − 3.05558i 0 2.29637 − 1.31403i 0 −2.69212 0
961.14 0 1.28514 0 1.27566 + 2.20951i 0 −0.755451 + 2.53561i 0 −1.34842 0
961.15 0 1.54194 0 1.38045 + 2.39101i 0 2.60594 + 0.457273i 0 −0.622416 0
961.16 0 2.14258 0 −0.442897 − 0.767120i 0 1.68009 − 2.04384i 0 1.59065 0
961.17 0 2.26665 0 −0.569866 − 0.987036i 0 −2.64563 + 0.0254846i 0 2.13772 0
961.18 0 2.85891 0 −0.564040 − 0.976945i 0 2.39970 + 1.11421i 0 5.17337 0
961.19 0 2.94031 0 −0.562983 − 0.975115i 0 −2.34154 + 1.23174i 0 5.64541 0
961.20 0 3.18968 0 2.03340 + 3.52194i 0 −0.974617 − 2.45970i 0 7.17403 0
See all 40 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 961.20
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
133.g even 3 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1064.2.t.e yes 40
7.c even 3 1 1064.2.s.e ✓ 40
19.c even 3 1 1064.2.s.e ✓ 40
133.g even 3 1 inner 1064.2.t.e yes 40
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1064.2.s.e ✓ 40 7.c even 3 1
1064.2.s.e ✓ 40 19.c even 3 1
1064.2.t.e yes 40 1.a even 1 1 trivial
1064.2.t.e yes 40 133.g even 3 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{20} - 2 T_{3}^{19} - 36 T_{3}^{18} + 67 T_{3}^{17} + 530 T_{3}^{16} - 900 T_{3}^{15} - 4138 T_{3}^{14} + \cdots - 12 \) acting on \(S_{2}^{\mathrm{new}}(1064, [\chi])\). Copy content Toggle raw display