↑

Properties

Label 8023.2.a.b
Level $8023$
Weight $2$
Character orbit 8023.a
Self dual yes
Analytic conductor $64.064$
Analytic rank $1$
Dimension $155$
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] = [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: \(1\)
Dimension: \(155\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 155 q - 21 q^{2} - 16 q^{3} + 151 q^{4} - 26 q^{5} - 10 q^{6} - 40 q^{7} - 57 q^{8} + 135 q^{9} - 2 q^{10} - 24 q^{11} - 32 q^{12} - 62 q^{13} - 18 q^{14} - 12 q^{15} + 155 q^{16} - 129 q^{17} - 42 q^{18} - 18 q^{19} - 59 q^{20} - 45 q^{21} - 17 q^{22} - 38 q^{23} - 27 q^{24} + 129 q^{25} - 44 q^{26} - 43 q^{27} - 100 q^{28} - 52 q^{29} - 39 q^{30} - 56 q^{31} - 145 q^{32} - 126 q^{33} - q^{34} - 49 q^{35} + 131 q^{36} - 30 q^{37} - 91 q^{38} - 29 q^{39} - 5 q^{40} - 163 q^{41} - 80 q^{42} - 15 q^{43} - 118 q^{44} - 66 q^{45} + 2 q^{46} - 111 q^{47} - 89 q^{48} + 101 q^{49} - 121 q^{50} + 5 q^{51} - 111 q^{52} - 93 q^{53} - 68 q^{54} - 60 q^{55} - 27 q^{56} - 106 q^{57} + 16 q^{58} - 79 q^{59} - 103 q^{60} - 74 q^{61} - 102 q^{62} - 118 q^{63} + 175 q^{64} - 109 q^{65} + 65 q^{66} - 18 q^{67} - 346 q^{68} - 39 q^{69} + 32 q^{70} + 155 q^{71} - 203 q^{72} - 108 q^{73} - 87 q^{74} - 22 q^{75} - 16 q^{76} - 121 q^{77} - 75 q^{78} - 6 q^{79} - 136 q^{80} + 107 q^{81} - 30 q^{82} - 116 q^{83} - 5 q^{84} - 53 q^{85} + 8 q^{86} - 100 q^{87} - 43 q^{88} - 189 q^{89} - 76 q^{90} + 14 q^{91} - 99 q^{92} - 72 q^{93} + 17 q^{94} - 18 q^{95} - 50 q^{96} - 184 q^{97} - 249 q^{98} - 114 q^{99}+O(q^{100}) \) 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 −2.80015 0.646146 5.84081 1.34449 −1.80930 3.74304 −10.7548 −2.58250 −3.76478
1.2 −2.79202 −1.96792 5.79536 4.22861 5.49445 −4.72825 −10.5967 0.872693 −11.8064
1.3 −2.78061 −3.43962 5.73182 −0.171450 9.56425 −3.12589 −10.3767 8.83098 0.476736
1.4 −2.76736 2.97864 5.65827 −2.08289 −8.24297 −3.08270 −10.1238 5.87230 5.76411
1.5 −2.76547 1.71486 5.64781 −3.60382 −4.74239 −5.22895 −10.0879 −0.0592525 9.96624
1.6 −2.74054 −1.55820 5.51058 −1.15483 4.27031 −0.0750165 −9.62090 −0.572020 3.16485
1.7 −2.73747 2.98404 5.49374 −2.59125 −8.16872 4.93159 −9.56402 5.90448 7.09348
1.8 −2.68312 −1.89873 5.19916 −4.03080 5.09454 2.89742 −8.58374 0.605189 10.8151
1.9 −2.67037 −1.29029 5.13085 2.33945 3.44554 3.27756 −8.36052 −1.33516 −6.24718
1.10 −2.57631 −2.78784 4.63739 0.760791 7.18234 −2.92762 −6.79473 4.77204 −1.96004
1.11 −2.57492 1.14041 4.63023 3.61279 −2.93647 −3.17107 −6.77264 −1.69947 −9.30267
1.12 −2.57220 −0.502356 4.61621 −1.32474 1.29216 1.13423 −6.72941 −2.74764 3.40751
1.13 −2.52683 1.49048 4.38485 −0.343930 −3.76619 0.360206 −6.02610 −0.778467 0.869051
1.14 −2.48799 −3.03020 4.19010 −2.87287 7.53911 1.28027 −5.44894 6.18210 7.14768
1.15 −2.47623 2.90051 4.13171 3.57414 −7.18232 −0.249825 −5.27860 5.41293 −8.85040
1.16 −2.46916 1.70167 4.09677 −3.39881 −4.20171 3.51551 −5.17727 −0.104305 8.39223
1.17 −2.45088 1.23773 4.00682 3.46965 −3.03354 −0.238635 −4.91847 −1.46802 −8.50371
1.18 −2.44945 −0.158730 3.99982 −2.39064 0.388803 −3.35946 −4.89848 −2.97480 5.85577
1.19 −2.44920 −0.457827 3.99860 −3.52685 1.12131 −3.81804 −4.89498 −2.79039 8.63798
1.20 −2.32032 0.985491 3.38390 2.02170 −2.28666 0.848897 −3.21110 −2.02881 −4.69101
See next 80 embeddings (of 155 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.155
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.b ✓ 155
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8023.2.a.b ✓ 155 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{155} + 21 T_{2}^{154} - 10 T_{2}^{153} - 3250 T_{2}^{152} - 15745 T_{2}^{151} + 223779 T_{2}^{150} + \cdots - 4526112161 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\). Copy content Toggle raw display