Properties

Label 8018.2.a.h
Level $8018$
Weight $2$
Character orbit 8018.a
Self dual yes
Analytic conductor $64.024$
Analytic rank $0$
Dimension $41$
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] = [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: \(41\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 41 q - 41 q^{2} + 8 q^{3} + 41 q^{4} - 9 q^{5} - 8 q^{6} + 7 q^{7} - 41 q^{8} + 43 q^{9} + 9 q^{10} - 9 q^{11} + 8 q^{12} + 13 q^{13} - 7 q^{14} + 26 q^{15} + 41 q^{16} - 16 q^{17} - 43 q^{18} - 41 q^{19} - 9 q^{20} + 2 q^{21} + 9 q^{22} + 10 q^{23} - 8 q^{24} + 60 q^{25} - 13 q^{26} + 47 q^{27} + 7 q^{28} - 14 q^{29} - 26 q^{30} + 49 q^{31} - 41 q^{32} + 12 q^{33} + 16 q^{34} - 8 q^{35} + 43 q^{36} + 54 q^{37} + 41 q^{38} + 16 q^{39} + 9 q^{40} - 18 q^{41} - 2 q^{42} + 29 q^{43} - 9 q^{44} - 13 q^{45} - 10 q^{46} - 8 q^{47} + 8 q^{48} + 44 q^{49} - 60 q^{50} - 16 q^{51} + 13 q^{52} + 7 q^{53} - 47 q^{54} + 19 q^{55} - 7 q^{56} - 8 q^{57} + 14 q^{58} - 5 q^{59} + 26 q^{60} - 6 q^{61} - 49 q^{62} + 24 q^{63} + 41 q^{64} - 26 q^{65} - 12 q^{66} + 66 q^{67} - 16 q^{68} + 12 q^{69} + 8 q^{70} + 27 q^{71} - 43 q^{72} - q^{73} - 54 q^{74} + 62 q^{75} - 41 q^{76} - 8 q^{77} - 16 q^{78} + 87 q^{79} - 9 q^{80} + 73 q^{81} + 18 q^{82} - 41 q^{83} + 2 q^{84} + 14 q^{85} - 29 q^{86} + 35 q^{87} + 9 q^{88} - 4 q^{89} + 13 q^{90} + 39 q^{91} + 10 q^{92} + 17 q^{93} + 8 q^{94} + 9 q^{95} - 8 q^{96} + 64 q^{97} - 44 q^{98} + 40 q^{99}+O(q^{100}) \) 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 −1.00000 −3.10704 1.00000 −3.25849 3.10704 4.58720 −1.00000 6.65369 3.25849
1.2 −1.00000 −2.99911 1.00000 0.291646 2.99911 −2.03701 −1.00000 5.99467 −0.291646
1.3 −1.00000 −2.94121 1.00000 −2.18985 2.94121 −0.696753 −1.00000 5.65074 2.18985
1.4 −1.00000 −2.61753 1.00000 0.199936 2.61753 0.481093 −1.00000 3.85148 −0.199936
1.5 −1.00000 −2.52494 1.00000 2.43918 2.52494 0.521147 −1.00000 3.37531 −2.43918
1.6 −1.00000 −2.15334 1.00000 −3.70592 2.15334 −3.79982 −1.00000 1.63688 3.70592
1.7 −1.00000 −2.09909 1.00000 1.36520 2.09909 4.01442 −1.00000 1.40618 −1.36520
1.8 −1.00000 −1.96501 1.00000 −1.27031 1.96501 1.60889 −1.00000 0.861269 1.27031
1.9 −1.00000 −1.82110 1.00000 −3.54712 1.82110 −2.30184 −1.00000 0.316404 3.54712
1.10 −1.00000 −1.75523 1.00000 −0.0353436 1.75523 −4.74271 −1.00000 0.0808489 0.0353436
1.11 −1.00000 −1.66216 1.00000 −4.08852 1.66216 3.79799 −1.00000 −0.237209 4.08852
1.12 −1.00000 −1.48981 1.00000 2.56048 1.48981 1.18596 −1.00000 −0.780452 −2.56048
1.13 −1.00000 −1.39030 1.00000 4.04446 1.39030 −1.52895 −1.00000 −1.06708 −4.04446
1.14 −1.00000 −1.20998 1.00000 0.0448427 1.20998 −2.73874 −1.00000 −1.53595 −0.0448427
1.15 −1.00000 −0.949118 1.00000 −3.26613 0.949118 3.22650 −1.00000 −2.09917 3.26613
1.16 −1.00000 −0.776259 1.00000 2.71672 0.776259 2.01306 −1.00000 −2.39742 −2.71672
1.17 −1.00000 −0.438243 1.00000 −0.442957 0.438243 2.11643 −1.00000 −2.80794 0.442957
1.18 −1.00000 0.0343445 1.00000 −1.14164 −0.0343445 −1.82320 −1.00000 −2.99882 1.14164
1.19 −1.00000 0.100035 1.00000 −0.345424 −0.100035 2.97223 −1.00000 −2.98999 0.345424
1.20 −1.00000 0.237080 1.00000 0.796437 −0.237080 2.80350 −1.00000 −2.94379 −0.796437
See all 41 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.41
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.h 41
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8018.2.a.h 41 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{41} - 8 T_{3}^{40} - 51 T_{3}^{39} + 547 T_{3}^{38} + 913 T_{3}^{37} - 16962 T_{3}^{36} - 1311 T_{3}^{35} + 315857 T_{3}^{34} - 235533 T_{3}^{33} - 3940756 T_{3}^{32} + 5019671 T_{3}^{31} + 34777557 T_{3}^{30} + \cdots + 65735 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\). Copy content Toggle raw display