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Properties

Label 4023.2.a.g
Level $4023$
Weight $2$
Character orbit 4023.a
Self dual yes
Analytic conductor $32.124$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4023,2,Mod(1,4023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4023, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4023 = 3^{3} \cdot 149 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4023.a (trivial)

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: yes
Analytic conductor: \(32.1238167332\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - q^{2} + 39 q^{4} + q^{5} + 13 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - q^{2} + 39 q^{4} + q^{5} + 13 q^{7} - 3 q^{8} + 7 q^{10} + 2 q^{11} + 14 q^{13} + q^{14} + 53 q^{16} + 2 q^{17} + 12 q^{19} + 9 q^{20} + 21 q^{22} - 5 q^{23} + 79 q^{25} - q^{26} + 43 q^{28} - 3 q^{29} + 14 q^{31} - 17 q^{32} + 14 q^{34} + 10 q^{35} + 57 q^{37} - 2 q^{38} + 21 q^{40} - q^{41} + 23 q^{43} - 11 q^{44} + 26 q^{46} + 85 q^{49} + 29 q^{50} + 32 q^{52} + 16 q^{53} + 19 q^{55} - 26 q^{56} + 72 q^{58} + 6 q^{59} + 33 q^{61} - 52 q^{62} + 87 q^{64} - 29 q^{65} + 51 q^{67} + 55 q^{68} + 63 q^{70} - 25 q^{71} + 91 q^{73} - 9 q^{74} + 53 q^{76} + 14 q^{77} + 29 q^{79} + 7 q^{80} + 45 q^{82} - 16 q^{83} + 68 q^{85} + 79 q^{86} + 74 q^{88} - 5 q^{89} + 32 q^{91} - 66 q^{92} + 16 q^{94} + 43 q^{95} + 94 q^{97} - 16 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.76698 0 5.65619 4.43074 0 2.54019 −10.1166 0 −12.2598
1.2 −2.71676 0 5.38079 −1.55765 0 0.787311 −9.18481 0 4.23177
1.3 −2.62241 0 4.87703 −1.94905 0 0.795246 −7.54474 0 5.11120
1.4 −2.46877 0 4.09483 −0.347405 0 4.23597 −5.17166 0 0.857663
1.5 −2.32876 0 3.42311 −3.41847 0 −3.46703 −3.31409 0 7.96079
1.6 −2.02880 0 2.11604 0.886473 0 −0.876459 −0.235432 0 −1.79848
1.7 −1.99728 0 1.98912 −3.12480 0 3.74946 0.0217292 0 6.24110
1.8 −1.65872 0 0.751365 1.19779 0 −3.56131 2.07114 0 −1.98680
1.9 −1.51359 0 0.290961 3.94832 0 −5.17999 2.58679 0 −5.97615
1.10 −1.38229 0 −0.0892743 −0.726426 0 −3.11520 2.88798 0 1.00413
1.11 −1.32250 0 −0.250993 2.66798 0 4.50418 2.97694 0 −3.52841
1.12 −1.14929 0 −0.679124 3.18229 0 4.12185 3.07910 0 −3.65739
1.13 −0.823087 0 −1.32253 −4.34017 0 −0.00772734 2.73473 0 3.57234
1.14 −0.578934 0 −1.66484 1.74954 0 −2.37565 2.12170 0 −1.01287
1.15 −0.352588 0 −1.87568 −3.98948 0 4.42393 1.36652 0 1.40664
1.16 −0.286385 0 −1.91798 −1.07189 0 1.77395 1.12205 0 0.306972
1.17 0.159782 0 −1.97447 −1.34860 0 3.76963 −0.635047 0 −0.215482
1.18 0.237818 0 −1.94344 0.506605 0 −2.14679 −0.937823 0 0.120480
1.19 0.631730 0 −1.60092 2.58556 0 0.804155 −2.27481 0 1.63338
1.20 0.678754 0 −1.53929 1.15205 0 −5.07043 −2.40231 0 0.781960
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.32
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(149\) \(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 4023.2.a.g ✓ 32
3.b odd 2 1 4023.2.a.h yes 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4023.2.a.g ✓ 32 1.a even 1 1 trivial
4023.2.a.h yes 32 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{32} + T_{2}^{31} - 51 T_{2}^{30} - 49 T_{2}^{29} + 1167 T_{2}^{28} + 1075 T_{2}^{27} + \cdots + 2943 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\). Copy content Toggle raw display