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

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Newspace parameters

Level: \( N \) \(=\) \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8018.a (trivial)

Newform invariants

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.

\(\operatorname{Tr}(f)(q) = \) \( 41q - 41q^{2} + 8q^{3} + 41q^{4} - 9q^{5} - 8q^{6} + 7q^{7} - 41q^{8} + 43q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 41q - 41q^{2} + 8q^{3} + 41q^{4} - 9q^{5} - 8q^{6} + 7q^{7} - 41q^{8} + 43q^{9} + 9q^{10} - 9q^{11} + 8q^{12} + 13q^{13} - 7q^{14} + 26q^{15} + 41q^{16} - 16q^{17} - 43q^{18} - 41q^{19} - 9q^{20} + 2q^{21} + 9q^{22} + 10q^{23} - 8q^{24} + 60q^{25} - 13q^{26} + 47q^{27} + 7q^{28} - 14q^{29} - 26q^{30} + 49q^{31} - 41q^{32} + 12q^{33} + 16q^{34} - 8q^{35} + 43q^{36} + 54q^{37} + 41q^{38} + 16q^{39} + 9q^{40} - 18q^{41} - 2q^{42} + 29q^{43} - 9q^{44} - 13q^{45} - 10q^{46} - 8q^{47} + 8q^{48} + 44q^{49} - 60q^{50} - 16q^{51} + 13q^{52} + 7q^{53} - 47q^{54} + 19q^{55} - 7q^{56} - 8q^{57} + 14q^{58} - 5q^{59} + 26q^{60} - 6q^{61} - 49q^{62} + 24q^{63} + 41q^{64} - 26q^{65} - 12q^{66} + 66q^{67} - 16q^{68} + 12q^{69} + 8q^{70} + 27q^{71} - 43q^{72} - q^{73} - 54q^{74} + 62q^{75} - 41q^{76} - 8q^{77} - 16q^{78} + 87q^{79} - 9q^{80} + 73q^{81} + 18q^{82} - 41q^{83} + 2q^{84} + 14q^{85} - 29q^{86} + 35q^{87} + 9q^{88} - 4q^{89} + 13q^{90} + 39q^{91} + 10q^{92} + 17q^{93} + 8q^{94} + 9q^{95} - 8q^{96} + 64q^{97} - 44q^{98} + 40q^{99} + O(q^{100}) \)

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.

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:

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

Atkin-Lehner signs

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

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{3}^{41} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database