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Properties

Label 4023.2.a.h
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 −2.69514 0 5.26380 0.0694621 0 1.23833 −8.79642 0 −0.187210
1.2 −2.59968 0 4.75836 −4.14104 0 4.25655 −7.17085 0 10.7654
1.3 −2.58179 0 4.66562 3.73605 0 −4.16546 −6.88206 0 −9.64568
1.4 −2.52747 0 4.38810 −3.05692 0 −2.06178 −6.03586 0 7.72627
1.5 −2.28378 0 3.21563 2.14810 0 4.90456 −2.77623 0 −4.90578
1.6 −2.02310 0 2.09295 −3.03365 0 2.60495 −0.188040 0 6.13738
1.7 −1.92588 0 1.70900 3.85883 0 −1.31992 0.560432 0 −7.43164
1.8 −1.77726 0 1.15865 0.250680 0 2.84115 1.49529 0 −0.445524
1.9 −1.40366 0 −0.0297260 −3.63110 0 −1.65977 2.84905 0 5.09685
1.10 −1.31596 0 −0.268244 −2.60395 0 2.74718 2.98492 0 3.42670
1.11 −1.11080 0 −0.766115 3.51523 0 −0.0270603 3.07261 0 −3.90474
1.12 −1.04454 0 −0.908927 2.32171 0 −2.06402 3.03850 0 −2.42513
1.13 −0.678754 0 −1.53929 −1.15205 0 −5.07043 2.40231 0 0.781960
1.14 −0.631730 0 −1.60092 −2.58556 0 0.804155 2.27481 0 1.63338
1.15 −0.237818 0 −1.94344 −0.506605 0 −2.14679 0.937823 0 0.120480
1.16 −0.159782 0 −1.97447 1.34860 0 3.76963 0.635047 0 −0.215482
1.17 0.286385 0 −1.91798 1.07189 0 1.77395 −1.12205 0 0.306972
1.18 0.352588 0 −1.87568 3.98948 0 4.42393 −1.36652 0 1.40664
1.19 0.578934 0 −1.66484 −1.74954 0 −2.37565 −2.12170 0 −1.01287
1.20 0.823087 0 −1.32253 4.34017 0 −0.00772734 −2.73473 0 3.57234
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.h yes 32
3.b odd 2 1 4023.2.a.g ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4023.2.a.g ✓ 32 3.b odd 2 1
4023.2.a.h yes 32 1.a even 1 1 trivial

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