↑

Properties

Label 4023.2.a.c
Level $4023$
Weight $2$
Character orbit 4023.a
Self dual yes
Analytic conductor $32.124$
Analytic rank $1$
Dimension $24$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(1\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 7 q^{2} + 25 q^{4} - 12 q^{5} - q^{7} - 21 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 7 q^{2} + 25 q^{4} - 12 q^{5} - q^{7} - 21 q^{8} + 8 q^{10} - 12 q^{11} - q^{13} - 10 q^{14} + 23 q^{16} - 26 q^{17} + 7 q^{19} - 30 q^{20} - 26 q^{23} + 20 q^{25} - 16 q^{26} - 10 q^{28} - 20 q^{29} + 6 q^{31} - 49 q^{32} + 14 q^{34} - 16 q^{35} - 9 q^{37} - 13 q^{38} + 10 q^{40} - 41 q^{41} - 8 q^{43} - 50 q^{44} - 2 q^{46} - 26 q^{47} + 17 q^{49} - 48 q^{50} + 22 q^{52} - 36 q^{53} + 6 q^{55} + 19 q^{56} + 2 q^{58} - 25 q^{59} - 9 q^{61} - 74 q^{62} + 17 q^{64} - 32 q^{65} + 5 q^{67} - 71 q^{68} - 20 q^{70} - 50 q^{71} - 7 q^{73} + 23 q^{74} - 65 q^{77} + 9 q^{79} - 66 q^{80} + 4 q^{82} - 16 q^{83} + 24 q^{85} - 60 q^{86} - 8 q^{88} - 54 q^{89} - 11 q^{91} + 2 q^{92} - 2 q^{94} - 50 q^{95} + 3 q^{97} - 63 q^{98}+O(q^{100}) \) 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 −2.65730 0 5.06126 0.532351 0 2.65721 −8.13470 0 −1.41462
1.2 −2.65423 0 5.04495 −4.31962 0 −2.76583 −8.08202 0 11.4653
1.3 −2.58309 0 4.67235 0.467469 0 −4.75978 −6.90291 0 −1.20751
1.4 −2.57985 0 4.65561 −1.47201 0 3.66706 −6.85107 0 3.79756
1.5 −2.12294 0 2.50689 0.133371 0 0.285383 −1.07609 0 −0.283139
1.6 −2.08103 0 2.33067 3.72386 0 −1.77284 −0.688126 0 −7.74944
1.7 −1.94245 0 1.77311 −4.08736 0 3.11287 0.440718 0 7.93949
1.8 −1.42489 0 0.0303005 0.280637 0 2.09782 2.80660 0 −0.399876
1.9 −1.06967 0 −0.855816 −3.10564 0 2.58911 3.05477 0 3.32199
1.10 −1.01887 0 −0.961905 −3.06877 0 −4.42586 3.01779 0 3.12668
1.11 −0.782084 0 −1.38834 1.99725 0 −0.182226 2.64997 0 −1.56202
1.12 −0.644697 0 −1.58437 3.63356 0 1.88815 2.31083 0 −2.34254
1.13 −0.581479 0 −1.66188 −1.81978 0 1.51314 2.12931 0 1.05816
1.14 0.193256 0 −1.96265 0.416886 0 −3.71235 −0.765807 0 0.0805657
1.15 0.358236 0 −1.87167 0.906963 0 5.19227 −1.38697 0 0.324907
1.16 0.427013 0 −1.81766 −3.85139 0 −1.30591 −1.63019 0 −1.64459
1.17 1.06310 0 −0.869811 −1.32308 0 −2.88846 −3.05091 0 −1.40657
1.18 1.16108 0 −0.651891 2.55585 0 −2.32357 −3.07906 0 2.96755
1.19 1.39881 0 −0.0433189 −1.19656 0 1.89806 −2.85822 0 −1.67377
1.20 1.83794 0 1.37804 2.11982 0 −1.32918 −1.14313 0 3.89611
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
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.c ✓ 24
3.b odd 2 1 4023.2.a.d yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
4023.2.a.c ✓ 24 1.a even 1 1 trivial
4023.2.a.d yes 24 3.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + 7 T_{2}^{23} - 12 T_{2}^{22} - 182 T_{2}^{21} - 105 T_{2}^{20} + 1953 T_{2}^{19} + \cdots - 375 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\). Copy content Toggle raw display