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Properties

Label 4023.2.a.f
Level $4023$
Weight $2$
Character orbit 4023.a
Self dual yes
Analytic conductor $32.124$
Analytic rank $0$
Dimension $25$
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: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q + 7 q^{2} + 27 q^{4} + 12 q^{5} - 2 q^{7} + 21 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q + 7 q^{2} + 27 q^{4} + 12 q^{5} - 2 q^{7} + 21 q^{8} - 4 q^{10} + 12 q^{11} + 10 q^{14} + 35 q^{16} + 26 q^{17} + 30 q^{20} + 8 q^{22} + 26 q^{23} + 27 q^{25} + 16 q^{26} + 4 q^{28} + 20 q^{29} - 6 q^{31} + 49 q^{32} - 14 q^{34} + 16 q^{35} - 2 q^{37} + 27 q^{38} + 2 q^{40} + 35 q^{41} + 4 q^{43} + 22 q^{44} + 6 q^{46} + 38 q^{47} + 19 q^{49} + 22 q^{50} + 4 q^{52} + 36 q^{53} + 10 q^{55} + 79 q^{56} - 22 q^{58} + 15 q^{59} + 10 q^{61} - 14 q^{62} + 41 q^{64} + 80 q^{65} - 6 q^{67} + 33 q^{68} + 8 q^{70} + 26 q^{71} - 6 q^{73} + 75 q^{74} - 10 q^{76} + 47 q^{77} - 6 q^{79} + 66 q^{80} + 12 q^{82} + 40 q^{83} - 12 q^{85} + 4 q^{86} + 12 q^{88} + 30 q^{89} + 158 q^{92} + 18 q^{94} + 22 q^{95} - 20 q^{97} + 35 q^{98}+O(q^{100}) \) 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 −2.51316 0 4.31598 1.65121 0 0.864620 −5.82042 0 −4.14975
1.2 −2.38405 0 3.68368 0.998141 0 −3.46708 −4.01398 0 −2.37961
1.3 −2.31586 0 3.36319 3.59358 0 −2.32336 −3.15696 0 −8.32222
1.4 −1.97183 0 1.88812 −0.788067 0 −2.33009 0.220613 0 1.55394
1.5 −1.77959 0 1.16693 −0.742067 0 3.55470 1.48252 0 1.32057
1.6 −1.35944 0 −0.151922 3.36242 0 2.75034 2.92541 0 −4.57100
1.7 −1.30329 0 −0.301424 −3.35120 0 −0.705123 2.99943 0 4.36761
1.8 −0.680129 0 −1.53742 −2.78190 0 −0.191226 2.40591 0 1.89205
1.9 −0.599558 0 −1.64053 −0.261228 0 −0.444015 2.18271 0 0.156622
1.10 −0.530451 0 −1.71862 3.35792 0 3.91494 1.97255 0 −1.78121
1.11 −0.365778 0 −1.86621 3.76223 0 −2.92149 1.41417 0 −1.37614
1.12 0.0533591 0 −1.99715 −0.751347 0 2.49440 −0.213285 0 −0.0400912
1.13 0.305611 0 −1.90660 −1.63568 0 −3.53407 −1.19390 0 −0.499884
1.14 0.614681 0 −1.62217 3.33074 0 3.77407 −2.22648 0 2.04734
1.15 0.964175 0 −1.07037 −0.686967 0 −3.77336 −2.96037 0 −0.662356
1.16 1.23916 0 −0.464485 −0.602488 0 1.86008 −3.05389 0 −0.746578
1.17 1.43306 0 0.0536673 2.81862 0 −4.82450 −2.78922 0 4.03925
1.18 1.51618 0 0.298802 −2.07566 0 −1.53996 −2.57932 0 −3.14707
1.19 1.79652 0 1.22747 −3.24604 0 −3.00506 −1.38786 0 −5.83156
1.20 2.16693 0 2.69559 1.04157 0 3.90919 1.50729 0 2.25701
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
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.f yes 25
3.b odd 2 1 4023.2.a.e ✓ 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4023.2.a.e ✓ 25 3.b odd 2 1
4023.2.a.f yes 25 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{25} - 7 T_{2}^{24} - 14 T_{2}^{23} + 196 T_{2}^{22} - 87 T_{2}^{21} - 2275 T_{2}^{20} + 3119 T_{2}^{19} + \cdots + 72 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\). Copy content Toggle raw display