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Properties

Label 8023.2.a.d
Level $8023$
Weight $2$
Character orbit 8023.a
Self dual yes
Analytic conductor $64.064$
Analytic rank $0$
Dimension $165$
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: \(165\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 165 q + 22 q^{2} + 18 q^{3} + 166 q^{4} + 28 q^{5} + 16 q^{6} + 24 q^{7} + 66 q^{8} + 177 q^{9} + 14 q^{10} + 18 q^{11} + 54 q^{12} + 44 q^{13} + 26 q^{14} + 24 q^{15} + 168 q^{16} + 143 q^{17} + 57 q^{18} + 20 q^{19} + 49 q^{20} + 39 q^{21} + 25 q^{22} + 52 q^{23} + 27 q^{24} + 175 q^{25} + 48 q^{26} + 69 q^{27} + 28 q^{28} + 58 q^{29} - 11 q^{30} + 28 q^{31} + 114 q^{32} + 110 q^{33} + 55 q^{34} + 67 q^{35} + 202 q^{36} + 44 q^{37} + 35 q^{38} + 27 q^{39} + 53 q^{40} + 141 q^{41} + 40 q^{42} + 29 q^{43} + 52 q^{44} + 54 q^{45} + 29 q^{46} + 87 q^{47} + 53 q^{48} + 143 q^{49} + 16 q^{50} + 37 q^{51} + 105 q^{52} + 101 q^{53} - 36 q^{54} + 72 q^{55} + 57 q^{56} + 82 q^{57} + 4 q^{58} + 103 q^{59} + 53 q^{60} + 16 q^{61} + 54 q^{62} + 126 q^{63} + 136 q^{64} + 159 q^{65} + 53 q^{66} + 60 q^{67} + 220 q^{68} + 81 q^{69} + 16 q^{70} + 165 q^{71} + 176 q^{72} + 124 q^{73} + 29 q^{74} + 44 q^{75} + 18 q^{76} + 127 q^{77} - 91 q^{78} + 14 q^{79} + 158 q^{80} + 213 q^{81} + 20 q^{82} + 116 q^{83} + 67 q^{84} + 59 q^{85} + 30 q^{86} + 28 q^{87} + 79 q^{88} + 195 q^{89} + 16 q^{90} - 26 q^{91} + 173 q^{92} + 116 q^{93} + 53 q^{94} + 26 q^{95} - 36 q^{96} + 88 q^{97} + 150 q^{98} + 12 q^{99}+O(q^{100}) \) 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 −2.77651 2.27500 5.70902 0.808124 −6.31657 0.0647974 −10.2981 2.17564 −2.24377
1.2 −2.72160 −0.981025 5.40712 −1.25328 2.66996 −1.09644 −9.27282 −2.03759 3.41092
1.3 −2.70370 −2.31695 5.31001 3.41961 6.26435 0.731020 −8.94928 2.36827 −9.24561
1.4 −2.64042 3.27801 4.97182 3.57654 −8.65532 2.80854 −7.84685 7.74534 −9.44356
1.5 −2.62951 0.0659678 4.91432 1.30562 −0.173463 −3.45826 −7.66322 −2.99565 −3.43314
1.6 −2.60713 −0.132138 4.79710 −1.04101 0.344501 4.69646 −7.29239 −2.98254 2.71405
1.7 −2.57888 −1.57055 4.65062 −2.72522 4.05026 −1.77487 −6.83564 −0.533376 7.02803
1.8 −2.52899 1.55552 4.39577 −1.46602 −3.93388 0.126533 −6.05887 −0.580366 3.70754
1.9 −2.51204 1.13882 4.31034 2.43582 −2.86077 −2.08264 −5.80366 −1.70308 −6.11887
1.10 −2.49309 −1.90773 4.21552 0.893200 4.75615 0.632761 −5.52349 0.639435 −2.22683
1.11 −2.44821 2.59661 3.99372 −2.59026 −6.35704 −1.59374 −4.88104 3.74237 6.34149
1.12 −2.38214 3.08941 3.67457 1.88389 −7.35940 1.49844 −3.98905 6.54446 −4.48768
1.13 −2.35257 −0.106381 3.53459 1.14622 0.250270 −0.376719 −3.61023 −2.98868 −2.69657
1.14 −2.33295 −2.77061 3.44267 −1.81617 6.46371 3.36128 −3.36567 4.67630 4.23705
1.15 −2.29416 −0.794120 3.26316 4.14537 1.82184 3.97505 −2.89789 −2.36937 −9.51013
1.16 −2.29110 0.370553 3.24912 −0.295381 −0.848972 0.894029 −2.86186 −2.86269 0.676746
1.17 −2.25574 0.317472 3.08836 −3.70971 −0.716135 −3.94071 −2.45506 −2.89921 8.36814
1.18 −2.20645 2.85395 2.86841 −2.79248 −6.29710 1.10201 −1.91611 5.14504 6.16145
1.19 −2.16974 −2.66568 2.70776 −3.38518 5.78382 −1.43929 −1.53565 4.10584 7.34496
1.20 −2.14746 −2.07357 2.61157 2.08017 4.45290 −3.04722 −1.31333 1.29970 −4.46708
See next 80 embeddings (of 165 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.165
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.d ✓ 165
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8023.2.a.d ✓ 165 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{165} - 22 T_{2}^{164} - 6 T_{2}^{163} + 3630 T_{2}^{162} - 18995 T_{2}^{161} - 265620 T_{2}^{160} + \cdots + 787040721 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8023))\). Copy content Toggle raw display