Properties

Label 8018.2.a.f
Level 8018
Weight 2
Character orbit 8018.a
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 34
CM No

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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: \(1\)
Dimension: \(34\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 34q - 34q^{2} - 10q^{3} + 34q^{4} + 7q^{5} + 10q^{6} - 6q^{7} - 34q^{8} + 38q^{9} - 7q^{10} + 4q^{11} - 10q^{12} - 5q^{13} + 6q^{14} - 17q^{15} + 34q^{16} + 8q^{17} - 38q^{18} - 34q^{19} + 7q^{20} - 4q^{22} - 24q^{23} + 10q^{24} + 5q^{25} + 5q^{26} - 31q^{27} - 6q^{28} + 24q^{29} + 17q^{30} - 28q^{31} - 34q^{32} - 16q^{33} - 8q^{34} + 2q^{35} + 38q^{36} - 36q^{37} + 34q^{38} - 9q^{39} - 7q^{40} + 9q^{41} - 24q^{43} + 4q^{44} + 22q^{45} + 24q^{46} - 29q^{47} - 10q^{48} + 22q^{49} - 5q^{50} - 21q^{51} - 5q^{52} - 9q^{53} + 31q^{54} - 28q^{55} + 6q^{56} + 10q^{57} - 24q^{58} - 28q^{59} - 17q^{60} + 23q^{61} + 28q^{62} - 27q^{63} + 34q^{64} - 6q^{65} + 16q^{66} - 51q^{67} + 8q^{68} - 17q^{69} - 2q^{70} - 31q^{71} - 38q^{72} - 26q^{73} + 36q^{74} - 109q^{75} - 34q^{76} - 28q^{77} + 9q^{78} - 36q^{79} + 7q^{80} + 6q^{81} - 9q^{82} - 10q^{83} - 32q^{85} + 24q^{86} - 8q^{87} - 4q^{88} - 34q^{89} - 22q^{90} - 41q^{91} - 24q^{92} - 33q^{93} + 29q^{94} - 7q^{95} + 10q^{96} - 56q^{97} - 22q^{98} - 28q^{99} + O(q^{100}) \)

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 −3.31570 1.00000 −0.532224 3.31570 −2.51205 −1.00000 7.99387 0.532224
1.2 −1.00000 −3.17050 1.00000 4.15425 3.17050 1.45443 −1.00000 7.05209 −4.15425
1.3 −1.00000 −3.15270 1.00000 −2.25930 3.15270 −1.49908 −1.00000 6.93949 2.25930
1.4 −1.00000 −3.08799 1.00000 2.62819 3.08799 −3.66609 −1.00000 6.53566 −2.62819
1.5 −1.00000 −2.56521 1.00000 3.62382 2.56521 4.81473 −1.00000 3.58031 −3.62382
1.6 −1.00000 −2.52151 1.00000 −1.30481 2.52151 0.799571 −1.00000 3.35801 1.30481
1.7 −1.00000 −2.46365 1.00000 −0.0638040 2.46365 3.24244 −1.00000 3.06956 0.0638040
1.8 −1.00000 −2.15742 1.00000 −2.78011 2.15742 −1.33229 −1.00000 1.65446 2.78011
1.9 −1.00000 −2.09965 1.00000 1.88296 2.09965 −4.81740 −1.00000 1.40851 −1.88296
1.10 −1.00000 −2.04582 1.00000 −4.09434 2.04582 1.49846 −1.00000 1.18539 4.09434
1.11 −1.00000 −1.91986 1.00000 0.472260 1.91986 4.62137 −1.00000 0.685870 −0.472260
1.12 −1.00000 −1.71717 1.00000 1.96614 1.71717 0.664883 −1.00000 −0.0513372 −1.96614
1.13 −1.00000 −1.39250 1.00000 3.35741 1.39250 −0.849778 −1.00000 −1.06096 −3.35741
1.14 −1.00000 −1.11253 1.00000 −2.63739 1.11253 −4.04134 −1.00000 −1.76228 2.63739
1.15 −1.00000 −0.916646 1.00000 −1.80395 0.916646 −2.30047 −1.00000 −2.15976 1.80395
1.16 −1.00000 −0.860547 1.00000 2.52015 0.860547 −0.0296623 −1.00000 −2.25946 −2.52015
1.17 −1.00000 −0.656283 1.00000 −1.22883 0.656283 2.46640 −1.00000 −2.56929 1.22883
1.18 −1.00000 −0.358038 1.00000 3.12453 0.358038 −3.38298 −1.00000 −2.87181 −3.12453
1.19 −1.00000 −0.350444 1.00000 −0.178230 0.350444 −3.90849 −1.00000 −2.87719 0.178230
1.20 −1.00000 0.100558 1.00000 2.02652 −0.100558 1.91249 −1.00000 −2.98989 −2.02652
See all 34 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.34
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

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

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{3}^{34} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).