Properties

Label 8023.2.a.e
Level $8023$
Weight $2$
Character orbit 8023.a
Self dual yes
Analytic conductor $64.064$
Analytic rank $0$
Dimension $172$
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] = [8023,2,Mod(1,8023)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8023, 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("8023.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8023 = 71 \cdot 113 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8023.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: \(64.0639775417\)
Analytic rank: \(0\)
Dimension: \(172\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 172 q + 24 q^{2} + 18 q^{3} + 180 q^{4} + 28 q^{5} + 16 q^{6} + 4 q^{7} + 72 q^{8} + 198 q^{9} + 14 q^{10} + 20 q^{11} + 54 q^{12} + 36 q^{13} + 26 q^{14} + 32 q^{15} + 196 q^{16} + 123 q^{17} + 74 q^{18} + 20 q^{19} + 70 q^{20} + 37 q^{21} + 11 q^{22} + 22 q^{23} + 62 q^{24} + 210 q^{25} + 50 q^{26} + 69 q^{27} + 42 q^{28} + 58 q^{29} + 36 q^{30} + 10 q^{31} + 168 q^{32} + 124 q^{33} + 5 q^{34} + 59 q^{35} + 192 q^{36} + 40 q^{37} + 58 q^{38} + 15 q^{39} + 7 q^{40} + 155 q^{41} - 6 q^{42} + 19 q^{43} + 22 q^{44} + 76 q^{45} + q^{46} + 71 q^{47} + 144 q^{48} + 206 q^{49} + 126 q^{50} + 33 q^{51} + 71 q^{52} + 101 q^{53} + 92 q^{54} - 2 q^{55} + 57 q^{56} + 114 q^{57} + 4 q^{58} + 71 q^{59} + 38 q^{60} + 50 q^{61} + 86 q^{62} + 14 q^{63} + 240 q^{64} + 143 q^{65} + 21 q^{66} + 8 q^{67} + 192 q^{68} + 41 q^{69} - 12 q^{70} - 172 q^{71} + 156 q^{72} + 128 q^{73} + 30 q^{74} + 72 q^{75} + 74 q^{76} + 127 q^{77} + 107 q^{78} + 2 q^{79} + 50 q^{80} + 236 q^{81} + 42 q^{82} + 140 q^{83} + 71 q^{84} + 55 q^{85} + 46 q^{86} + 100 q^{87} - 31 q^{88} + 215 q^{89} - 7 q^{90} + 22 q^{91} - 15 q^{92} + 60 q^{93} + 5 q^{94} + 74 q^{95} + 182 q^{96} + 120 q^{97} + 164 q^{98} + 60 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −2.71525 −0.0977350 5.37257 1.14210 0.265375 −3.48491 −9.15737 −2.99045 −3.10108
1.2 −2.68727 1.51064 5.22143 0.313283 −4.05950 −2.80560 −8.65687 −0.717969 −0.841876
1.3 −2.68206 0.545640 5.19345 −2.53261 −1.46344 −1.66793 −8.56503 −2.70228 6.79262
1.4 −2.63836 2.01648 4.96097 1.04348 −5.32021 3.03248 −7.81211 1.06619 −2.75309
1.5 −2.61555 2.99326 4.84110 −2.84869 −7.82902 0.984788 −7.43104 5.95960 7.45089
1.6 −2.60904 −1.86481 4.80711 2.29669 4.86538 1.81523 −7.32387 0.477530 −5.99216
1.7 −2.59149 −2.64740 4.71583 −3.26554 6.86073 0.687432 −7.03805 4.00875 8.46262
1.8 −2.58451 1.24090 4.67970 4.06279 −3.20713 2.63982 −6.92572 −1.46016 −10.5003
1.9 −2.55716 −1.44904 4.53909 −0.0718207 3.70544 2.77634 −6.49287 −0.900274 0.183657
1.10 −2.47898 −2.90151 4.14536 3.57893 7.19280 −1.12807 −5.31832 5.41877 −8.87212
1.11 −2.46646 2.78762 4.08340 2.84947 −6.87554 −3.94161 −5.13862 4.77082 −7.02810
1.12 −2.44664 −2.78774 3.98604 −0.315327 6.82060 −4.26739 −4.85913 4.77151 0.771492
1.13 −2.39224 −1.88283 3.72279 −1.64189 4.50418 −4.12017 −4.12133 0.545055 3.92779
1.14 −2.39089 1.71669 3.71638 −1.13551 −4.10443 −3.27571 −4.10367 −0.0529740 2.71487
1.15 −2.38785 2.31804 3.70185 2.20960 −5.53514 3.66496 −4.06377 2.37331 −5.27621
1.16 −2.37665 −1.52236 3.64846 1.09798 3.61812 2.78247 −3.91780 −0.682408 −2.60952
1.17 −2.34076 −0.698142 3.47917 4.27326 1.63419 −0.686172 −3.46239 −2.51260 −10.0027
1.18 −2.32376 2.08372 3.39986 −3.01109 −4.84207 −1.67398 −3.25293 1.34190 6.99706
1.19 −2.31555 −0.113923 3.36176 1.48156 0.263794 4.57358 −3.15322 −2.98702 −3.43063
1.20 −2.30435 −0.933250 3.31004 −0.282102 2.15054 1.67948 −3.01880 −2.12904 0.650063
See next 80 embeddings (of 172 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.172
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(71\) \(1\)
\(113\) \(-1\)

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 8023.2.a.e 172
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8023.2.a.e 172 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{172} - 24 T_{2}^{171} + 26 T_{2}^{170} + 3928 T_{2}^{169} - 26629 T_{2}^{168} - 272224 T_{2}^{167} + 3295322 T_{2}^{166} + 8278112 T_{2}^{165} - 226770243 T_{2}^{164} + 138511518 T_{2}^{163} + \cdots + 45656199476103 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\). Copy content Toggle raw display