Properties

Label 8026.2.a.a
Level 8026
Weight 2
Character orbit 8026.a
Self dual Yes
Analytic conductor 64.088
Analytic rank 1
Dimension 71
CM No

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Newspace parameters

Level: \( N \) = \( 8026 = 2 \cdot 4013 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8026.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0879326623\)
Analytic rank: \(1\)
Dimension: \(71\)
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.

\(\operatorname{Tr}(f)(q) = \) \(71q \) \(\mathstrut +\mathstrut 71q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 71q^{4} \) \(\mathstrut -\mathstrut 34q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 71q^{8} \) \(\mathstrut +\mathstrut 34q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(71q \) \(\mathstrut +\mathstrut 71q^{2} \) \(\mathstrut -\mathstrut 9q^{3} \) \(\mathstrut +\mathstrut 71q^{4} \) \(\mathstrut -\mathstrut 34q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 71q^{8} \) \(\mathstrut +\mathstrut 34q^{9} \) \(\mathstrut -\mathstrut 34q^{10} \) \(\mathstrut -\mathstrut 37q^{11} \) \(\mathstrut -\mathstrut 9q^{12} \) \(\mathstrut -\mathstrut 62q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut -\mathstrut 29q^{15} \) \(\mathstrut +\mathstrut 71q^{16} \) \(\mathstrut -\mathstrut 52q^{17} \) \(\mathstrut +\mathstrut 34q^{18} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 34q^{20} \) \(\mathstrut -\mathstrut 51q^{21} \) \(\mathstrut -\mathstrut 37q^{22} \) \(\mathstrut -\mathstrut 45q^{23} \) \(\mathstrut -\mathstrut 9q^{24} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut -\mathstrut 62q^{26} \) \(\mathstrut -\mathstrut 27q^{27} \) \(\mathstrut -\mathstrut 19q^{28} \) \(\mathstrut -\mathstrut 55q^{29} \) \(\mathstrut -\mathstrut 29q^{30} \) \(\mathstrut -\mathstrut 61q^{31} \) \(\mathstrut +\mathstrut 71q^{32} \) \(\mathstrut -\mathstrut 73q^{33} \) \(\mathstrut -\mathstrut 52q^{34} \) \(\mathstrut -\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 34q^{36} \) \(\mathstrut -\mathstrut 43q^{37} \) \(\mathstrut -\mathstrut 30q^{38} \) \(\mathstrut -\mathstrut 40q^{39} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut -\mathstrut 87q^{41} \) \(\mathstrut -\mathstrut 51q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 37q^{44} \) \(\mathstrut -\mathstrut 81q^{45} \) \(\mathstrut -\mathstrut 45q^{46} \) \(\mathstrut -\mathstrut 89q^{47} \) \(\mathstrut -\mathstrut 9q^{48} \) \(\mathstrut -\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut 27q^{50} \) \(\mathstrut -\mathstrut 19q^{51} \) \(\mathstrut -\mathstrut 62q^{52} \) \(\mathstrut -\mathstrut 50q^{53} \) \(\mathstrut -\mathstrut 27q^{54} \) \(\mathstrut -\mathstrut 66q^{55} \) \(\mathstrut -\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 45q^{57} \) \(\mathstrut -\mathstrut 55q^{58} \) \(\mathstrut -\mathstrut 118q^{59} \) \(\mathstrut -\mathstrut 29q^{60} \) \(\mathstrut -\mathstrut 92q^{61} \) \(\mathstrut -\mathstrut 61q^{62} \) \(\mathstrut -\mathstrut 54q^{63} \) \(\mathstrut +\mathstrut 71q^{64} \) \(\mathstrut -\mathstrut 51q^{65} \) \(\mathstrut -\mathstrut 73q^{66} \) \(\mathstrut -\mathstrut 17q^{67} \) \(\mathstrut -\mathstrut 52q^{68} \) \(\mathstrut -\mathstrut 89q^{69} \) \(\mathstrut -\mathstrut 33q^{70} \) \(\mathstrut -\mathstrut 95q^{71} \) \(\mathstrut +\mathstrut 34q^{72} \) \(\mathstrut -\mathstrut 114q^{73} \) \(\mathstrut -\mathstrut 43q^{74} \) \(\mathstrut -\mathstrut 38q^{75} \) \(\mathstrut -\mathstrut 30q^{76} \) \(\mathstrut -\mathstrut 73q^{77} \) \(\mathstrut -\mathstrut 40q^{78} \) \(\mathstrut -\mathstrut 47q^{79} \) \(\mathstrut -\mathstrut 34q^{80} \) \(\mathstrut -\mathstrut 57q^{81} \) \(\mathstrut -\mathstrut 87q^{82} \) \(\mathstrut -\mathstrut 68q^{83} \) \(\mathstrut -\mathstrut 51q^{84} \) \(\mathstrut -\mathstrut 67q^{85} \) \(\mathstrut -\mathstrut 4q^{86} \) \(\mathstrut -\mathstrut 55q^{87} \) \(\mathstrut -\mathstrut 37q^{88} \) \(\mathstrut -\mathstrut 150q^{89} \) \(\mathstrut -\mathstrut 81q^{90} \) \(\mathstrut -\mathstrut 23q^{91} \) \(\mathstrut -\mathstrut 45q^{92} \) \(\mathstrut -\mathstrut 59q^{93} \) \(\mathstrut -\mathstrut 89q^{94} \) \(\mathstrut -\mathstrut 47q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut -\mathstrut 97q^{97} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut -\mathstrut 57q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.33028 1.00000 −2.81719 −3.33028 2.39962 1.00000 8.09075 −2.81719
1.2 1.00000 −3.18837 1.00000 1.76077 −3.18837 −1.56118 1.00000 7.16572 1.76077
1.3 1.00000 −3.08324 1.00000 −2.29351 −3.08324 −1.56272 1.00000 6.50635 −2.29351
1.4 1.00000 −3.00113 1.00000 2.08729 −3.00113 1.33710 1.00000 6.00675 2.08729
1.5 1.00000 −2.91430 1.00000 −0.167675 −2.91430 0.471775 1.00000 5.49314 −0.167675
1.6 1.00000 −2.72893 1.00000 0.723438 −2.72893 −3.46721 1.00000 4.44707 0.723438
1.7 1.00000 −2.59864 1.00000 −3.30872 −2.59864 −3.09209 1.00000 3.75294 −3.30872
1.8 1.00000 −2.57686 1.00000 −0.429942 −2.57686 3.15501 1.00000 3.64023 −0.429942
1.9 1.00000 −2.52707 1.00000 −2.67563 −2.52707 −1.45299 1.00000 3.38607 −2.67563
1.10 1.00000 −2.46200 1.00000 −1.19890 −2.46200 2.88631 1.00000 3.06146 −1.19890
1.11 1.00000 −2.45931 1.00000 3.45635 −2.45931 3.30103 1.00000 3.04822 3.45635
1.12 1.00000 −2.11692 1.00000 −3.74472 −2.11692 4.88608 1.00000 1.48134 −3.74472
1.13 1.00000 −2.05160 1.00000 2.89935 −2.05160 −3.15492 1.00000 1.20907 2.89935
1.14 1.00000 −2.02406 1.00000 1.61352 −2.02406 −3.12008 1.00000 1.09682 1.61352
1.15 1.00000 −2.02372 1.00000 3.74567 −2.02372 1.02525 1.00000 1.09543 3.74567
1.16 1.00000 −1.97637 1.00000 −0.168031 −1.97637 −1.30361 1.00000 0.906032 −0.168031
1.17 1.00000 −1.95374 1.00000 0.792660 −1.95374 2.85182 1.00000 0.817104 0.792660
1.18 1.00000 −1.89918 1.00000 −0.474376 −1.89918 1.52174 1.00000 0.606869 −0.474376
1.19 1.00000 −1.72230 1.00000 −4.08988 −1.72230 −0.697853 1.00000 −0.0336847 −4.08988
1.20 1.00000 −1.70684 1.00000 −2.82175 −1.70684 3.08724 1.00000 −0.0867059 −2.82175
See all 71 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.71
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(4013\) \(-1\)