Properties

Label 8018.2.a.d
Level 8018
Weight 2
Character orbit 8018.a
Self dual Yes
Analytic conductor 64.024
Analytic rank 1
Dimension 30
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: \(30\)
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.

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

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 −3.23056 1.00000 −3.65226 −3.23056 2.39039 1.00000 7.43653 −3.65226
1.2 1.00000 −3.09428 1.00000 2.68879 −3.09428 2.69798 1.00000 6.57455 2.68879
1.3 1.00000 −2.74076 1.00000 0.116951 −2.74076 −0.997196 1.00000 4.51179 0.116951
1.4 1.00000 −2.56870 1.00000 −1.11955 −2.56870 −1.44974 1.00000 3.59821 −1.11955
1.5 1.00000 −2.47683 1.00000 −0.567392 −2.47683 −4.82108 1.00000 3.13468 −0.567392
1.6 1.00000 −2.43818 1.00000 3.21483 −2.43818 −0.555600 1.00000 2.94471 3.21483
1.7 1.00000 −2.39570 1.00000 −3.46674 −2.39570 −3.11450 1.00000 2.73936 −3.46674
1.8 1.00000 −2.02842 1.00000 2.47134 −2.02842 1.41486 1.00000 1.11447 2.47134
1.9 1.00000 −1.51420 1.00000 −2.91196 −1.51420 −3.75064 1.00000 −0.707195 −2.91196
1.10 1.00000 −1.46114 1.00000 1.82408 −1.46114 −2.77663 1.00000 −0.865063 1.82408
1.11 1.00000 −1.44219 1.00000 −1.29569 −1.44219 1.46621 1.00000 −0.920075 −1.29569
1.12 1.00000 −1.14046 1.00000 1.90163 −1.14046 2.39414 1.00000 −1.69934 1.90163
1.13 1.00000 −0.894762 1.00000 −0.0669598 −0.894762 1.42997 1.00000 −2.19940 −0.0669598
1.14 1.00000 −0.851234 1.00000 −2.73591 −0.851234 0.590237 1.00000 −2.27540 −2.73591
1.15 1.00000 −0.785531 1.00000 −1.33472 −0.785531 4.52537 1.00000 −2.38294 −1.33472
1.16 1.00000 −0.219326 1.00000 2.27443 −0.219326 −3.32577 1.00000 −2.95190 2.27443
1.17 1.00000 0.180143 1.00000 0.229721 0.180143 −1.11361 1.00000 −2.96755 0.229721
1.18 1.00000 0.460726 1.00000 0.645126 0.460726 1.69833 1.00000 −2.78773 0.645126
1.19 1.00000 0.677734 1.00000 −4.37664 0.677734 −1.03965 1.00000 −2.54068 −4.37664
1.20 1.00000 0.846820 1.00000 2.51574 0.846820 −3.73115 1.00000 −2.28290 2.51574
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.30
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 \(T_{3}^{30} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8018))\).