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Properties

Label 8018.2.a.k
Level $8018$
Weight $2$
Character orbit 8018.a
Self dual yes
Analytic conductor $64.024$
Analytic rank $0$
Dimension $49$
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] = [8018,2,Mod(1,8018)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8018, 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("8018.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8018.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: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(49\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 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 1.00000 −3.18331 1.00000 4.19262 −3.18331 −3.25533 1.00000 7.13346 4.19262
1.2 1.00000 −3.16496 1.00000 −1.03983 −3.16496 −1.27872 1.00000 7.01700 −1.03983
1.3 1.00000 −3.03631 1.00000 −0.470191 −3.03631 3.61227 1.00000 6.21915 −0.470191
1.4 1.00000 −3.03421 1.00000 −2.36281 −3.03421 −0.910676 1.00000 6.20641 −2.36281
1.5 1.00000 −2.78216 1.00000 3.32795 −2.78216 4.62132 1.00000 4.74040 3.32795
1.6 1.00000 −2.76297 1.00000 0.238506 −2.76297 2.08661 1.00000 4.63399 0.238506
1.7 1.00000 −2.47584 1.00000 1.97954 −2.47584 −2.02339 1.00000 3.12981 1.97954
1.8 1.00000 −2.35762 1.00000 −3.55313 −2.35762 −1.02341 1.00000 2.55835 −3.55313
1.9 1.00000 −2.16417 1.00000 3.75376 −2.16417 4.09027 1.00000 1.68362 3.75376
1.10 1.00000 −2.15958 1.00000 −0.594727 −2.15958 4.60099 1.00000 1.66376 −0.594727
1.11 1.00000 −1.57817 1.00000 −2.42122 −1.57817 −1.17267 1.00000 −0.509368 −2.42122
1.12 1.00000 −1.45260 1.00000 2.56447 −1.45260 −3.76816 1.00000 −0.889956 2.56447
1.13 1.00000 −1.41679 1.00000 −3.74277 −1.41679 3.98944 1.00000 −0.992702 −3.74277
1.14 1.00000 −1.33535 1.00000 0.425182 −1.33535 −2.10915 1.00000 −1.21683 0.425182
1.15 1.00000 −1.22925 1.00000 −2.52525 −1.22925 3.13859 1.00000 −1.48895 −2.52525
1.16 1.00000 −1.06684 1.00000 3.41038 −1.06684 −0.896941 1.00000 −1.86186 3.41038
1.17 1.00000 −0.823102 1.00000 1.30158 −0.823102 0.990463 1.00000 −2.32250 1.30158
1.18 1.00000 −0.655875 1.00000 3.82378 −0.655875 −1.10690 1.00000 −2.56983 3.82378
1.19 1.00000 −0.460040 1.00000 −0.746209 −0.460040 −4.50236 1.00000 −2.78836 −0.746209
1.20 1.00000 −0.411559 1.00000 −1.49400 −0.411559 −1.21130 1.00000 −2.83062 −1.49400
See all 49 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.49
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(19\) \(-1\)
\(211\) \(-1\)

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 8018.2.a.k ✓ 49
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8018.2.a.k ✓ 49 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{49} - 13 T_{3}^{48} - 22 T_{3}^{47} + 982 T_{3}^{46} - 2059 T_{3}^{45} - 32106 T_{3}^{44} + \cdots + 838784 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\). Copy content Toggle raw display