Properties

Label 8018.2.a.j
Level 8018
Weight 2
Character orbit 8018.a
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
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: \(0\)
Dimension: \(47\)
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.

\(\operatorname{Tr}(f)(q) = \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.22214 1.00000 3.63661 −3.22214 −0.166372 1.00000 7.38220 3.63661
1.2 1.00000 −3.13813 1.00000 2.17673 −3.13813 2.94096 1.00000 6.84787 2.17673
1.3 1.00000 −3.07943 1.00000 −3.30634 −3.07943 −2.62160 1.00000 6.48290 −3.30634
1.4 1.00000 −2.90959 1.00000 −4.15278 −2.90959 3.02073 1.00000 5.46571 −4.15278
1.5 1.00000 −2.83191 1.00000 1.28371 −2.83191 −4.11947 1.00000 5.01973 1.28371
1.6 1.00000 −2.78985 1.00000 −2.51493 −2.78985 −0.381461 1.00000 4.78329 −2.51493
1.7 1.00000 −2.41559 1.00000 0.828405 −2.41559 0.635145 1.00000 2.83509 0.828405
1.8 1.00000 −2.28341 1.00000 4.33431 −2.28341 −0.955796 1.00000 2.21398 4.33431
1.9 1.00000 −2.19254 1.00000 1.33631 −2.19254 −4.99100 1.00000 1.80723 1.33631
1.10 1.00000 −2.00763 1.00000 −1.79399 −2.00763 −2.43862 1.00000 1.03060 −1.79399
1.11 1.00000 −1.99735 1.00000 −0.291796 −1.99735 −0.492820 1.00000 0.989407 −0.291796
1.12 1.00000 −1.51480 1.00000 −1.33044 −1.51480 −3.41282 1.00000 −0.705394 −1.33044
1.13 1.00000 −1.46195 1.00000 2.14418 −1.46195 2.84565 1.00000 −0.862709 2.14418
1.14 1.00000 −1.39823 1.00000 0.539425 −1.39823 5.05784 1.00000 −1.04494 0.539425
1.15 1.00000 −1.14813 1.00000 2.89240 −1.14813 3.60462 1.00000 −1.68179 2.89240
1.16 1.00000 −1.10999 1.00000 3.90024 −1.10999 −4.77719 1.00000 −1.76791 3.90024
1.17 1.00000 −1.03614 1.00000 0.118794 −1.03614 2.13406 1.00000 −1.92642 0.118794
1.18 1.00000 −0.833135 1.00000 −3.18557 −0.833135 0.455061 1.00000 −2.30589 −3.18557
1.19 1.00000 −0.764189 1.00000 −0.445775 −0.764189 −0.938446 1.00000 −2.41602 −0.445775
1.20 1.00000 −0.316697 1.00000 −0.633871 −0.316697 1.30218 1.00000 −2.89970 −0.633871
See all 47 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.47
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 \(T_{3}^{47} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).