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Properties

Label 8018.2.a.i
Level $8018$
Weight $2$
Character orbit 8018.a
Self dual yes
Analytic conductor $64.024$
Analytic rank $0$
Dimension $43$
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: \(43\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 43 q - 43 q^{2} + 43 q^{4} + 19 q^{7} - 43 q^{8} + 53 q^{9} + 14 q^{11} + 3 q^{13} - 19 q^{14} + q^{15} + 43 q^{16} + 8 q^{17} - 53 q^{18} + 43 q^{19} - 14 q^{22} + 43 q^{23} + 97 q^{25} - 3 q^{26} + 15 q^{27} + 19 q^{28} - 25 q^{29} - q^{30} + 22 q^{31} - 43 q^{32} + 22 q^{33} - 8 q^{34} - 6 q^{35} + 53 q^{36} + 42 q^{37} - 43 q^{38} + 9 q^{39} - 40 q^{41} + 72 q^{43} + 14 q^{44} - q^{45} - 43 q^{46} + 27 q^{47} + 86 q^{49} - 97 q^{50} - 3 q^{51} + 3 q^{52} - 5 q^{53} - 15 q^{54} + 86 q^{55} - 19 q^{56} + 25 q^{58} - 43 q^{59} + q^{60} + 31 q^{61} - 22 q^{62} + 38 q^{63} + 43 q^{64} - 32 q^{65} - 22 q^{66} + 15 q^{67} + 8 q^{68} - 7 q^{69} + 6 q^{70} + 14 q^{71} - 53 q^{72} + 93 q^{73} - 42 q^{74} - 13 q^{75} + 43 q^{76} + 38 q^{77} - 9 q^{78} + 15 q^{79} + 43 q^{81} + 40 q^{82} + 34 q^{83} + 16 q^{85} - 72 q^{86} + 60 q^{87} - 14 q^{88} - 37 q^{89} + q^{90} - 3 q^{91} + 43 q^{92} + 19 q^{93} - 27 q^{94} + 27 q^{97} - 86 q^{98} - 24 q^{99}+O(q^{100}) \) 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 −3.34431 1.00000 −3.91124 3.34431 0.821669 −1.00000 8.18441 3.91124
1.2 −1.00000 −3.24783 1.00000 2.20422 3.24783 3.82287 −1.00000 7.54837 −2.20422
1.3 −1.00000 −2.91293 1.00000 2.71400 2.91293 1.04550 −1.00000 5.48515 −2.71400
1.4 −1.00000 −2.88859 1.00000 −0.162345 2.88859 −3.68356 −1.00000 5.34393 0.162345
1.5 −1.00000 −2.71486 1.00000 −0.740916 2.71486 4.34624 −1.00000 4.37046 0.740916
1.6 −1.00000 −2.54429 1.00000 −4.40933 2.54429 −2.39004 −1.00000 3.47339 4.40933
1.7 −1.00000 −2.53282 1.00000 2.86896 2.53282 3.12244 −1.00000 3.41520 −2.86896
1.8 −1.00000 −2.22097 1.00000 0.529365 2.22097 −2.58907 −1.00000 1.93269 −0.529365
1.9 −1.00000 −2.12309 1.00000 0.333090 2.12309 −1.76432 −1.00000 1.50753 −0.333090
1.10 −1.00000 −2.06580 1.00000 4.42069 2.06580 −2.80943 −1.00000 1.26754 −4.42069
1.11 −1.00000 −1.98111 1.00000 −2.70035 1.98111 2.97081 −1.00000 0.924794 2.70035
1.12 −1.00000 −1.78337 1.00000 −3.15111 1.78337 −2.13059 −1.00000 0.180410 3.15111
1.13 −1.00000 −1.49345 1.00000 1.29948 1.49345 −1.68221 −1.00000 −0.769617 −1.29948
1.14 −1.00000 −1.36513 1.00000 0.286730 1.36513 −1.35155 −1.00000 −1.13641 −0.286730
1.15 −1.00000 −1.12203 1.00000 −3.99522 1.12203 0.851275 −1.00000 −1.74104 3.99522
1.16 −1.00000 −1.11378 1.00000 4.02830 1.11378 1.02145 −1.00000 −1.75949 −4.02830
1.17 −1.00000 −1.00471 1.00000 −1.06211 1.00471 0.645369 −1.00000 −1.99055 1.06211
1.18 −1.00000 −0.978925 1.00000 −2.13476 0.978925 5.08930 −1.00000 −2.04171 2.13476
1.19 −1.00000 −0.765202 1.00000 −1.80247 0.765202 4.51708 −1.00000 −2.41447 1.80247
1.20 −1.00000 −0.649534 1.00000 3.59840 0.649534 4.54706 −1.00000 −2.57811 −3.59840
See all 43 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.43
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.i ✓ 43
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8018.2.a.i ✓ 43 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{43} - 91 T_{3}^{41} - 5 T_{3}^{40} + 3817 T_{3}^{39} + 412 T_{3}^{38} - 97975 T_{3}^{37} + \cdots + 19296472 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\). Copy content Toggle raw display