Properties

Label 8026.2.a.c
Level 8026
Weight 2
Character orbit 8026.a
Self dual Yes
Analytic conductor 64.088
Analytic rank 0
Dimension 86
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: \(0\)
Dimension: \(86\)
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.

\(\operatorname{Tr}(f)(q) = \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut +\mathstrut 25q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 105q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(86q \) \(\mathstrut -\mathstrut 86q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 86q^{4} \) \(\mathstrut +\mathstrut 25q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 3q^{7} \) \(\mathstrut -\mathstrut 86q^{8} \) \(\mathstrut +\mathstrut 105q^{9} \) \(\mathstrut -\mathstrut 25q^{10} \) \(\mathstrut +\mathstrut 44q^{11} \) \(\mathstrut +\mathstrut 11q^{12} \) \(\mathstrut -\mathstrut 36q^{13} \) \(\mathstrut +\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 19q^{15} \) \(\mathstrut +\mathstrut 86q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 105q^{18} \) \(\mathstrut +\mathstrut 35q^{19} \) \(\mathstrut +\mathstrut 25q^{20} \) \(\mathstrut +\mathstrut 23q^{21} \) \(\mathstrut -\mathstrut 44q^{22} \) \(\mathstrut +\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut +\mathstrut 85q^{25} \) \(\mathstrut +\mathstrut 36q^{26} \) \(\mathstrut +\mathstrut 47q^{27} \) \(\mathstrut -\mathstrut 3q^{28} \) \(\mathstrut +\mathstrut 30q^{29} \) \(\mathstrut -\mathstrut 19q^{30} \) \(\mathstrut +\mathstrut 23q^{31} \) \(\mathstrut -\mathstrut 86q^{32} \) \(\mathstrut +\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 21q^{34} \) \(\mathstrut +\mathstrut 59q^{35} \) \(\mathstrut +\mathstrut 105q^{36} \) \(\mathstrut -\mathstrut 20q^{37} \) \(\mathstrut -\mathstrut 35q^{38} \) \(\mathstrut +\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 25q^{40} \) \(\mathstrut +\mathstrut 64q^{41} \) \(\mathstrut -\mathstrut 23q^{42} \) \(\mathstrut +\mathstrut 23q^{43} \) \(\mathstrut +\mathstrut 44q^{44} \) \(\mathstrut +\mathstrut 60q^{45} \) \(\mathstrut -\mathstrut 38q^{46} \) \(\mathstrut +\mathstrut 77q^{47} \) \(\mathstrut +\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut 109q^{49} \) \(\mathstrut -\mathstrut 85q^{50} \) \(\mathstrut +\mathstrut 47q^{51} \) \(\mathstrut -\mathstrut 36q^{52} \) \(\mathstrut +\mathstrut 22q^{53} \) \(\mathstrut -\mathstrut 47q^{54} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut +\mathstrut 3q^{56} \) \(\mathstrut -\mathstrut 9q^{57} \) \(\mathstrut -\mathstrut 30q^{58} \) \(\mathstrut +\mathstrut 145q^{59} \) \(\mathstrut +\mathstrut 19q^{60} \) \(\mathstrut -\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut 23q^{62} \) \(\mathstrut +\mathstrut 6q^{63} \) \(\mathstrut +\mathstrut 86q^{64} \) \(\mathstrut +\mathstrut 37q^{65} \) \(\mathstrut -\mathstrut 5q^{66} \) \(\mathstrut +\mathstrut 44q^{67} \) \(\mathstrut +\mathstrut 21q^{68} \) \(\mathstrut +\mathstrut 25q^{69} \) \(\mathstrut -\mathstrut 59q^{70} \) \(\mathstrut +\mathstrut 107q^{71} \) \(\mathstrut -\mathstrut 105q^{72} \) \(\mathstrut -\mathstrut 55q^{73} \) \(\mathstrut +\mathstrut 20q^{74} \) \(\mathstrut +\mathstrut 86q^{75} \) \(\mathstrut +\mathstrut 35q^{76} \) \(\mathstrut +\mathstrut 25q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 2q^{79} \) \(\mathstrut +\mathstrut 25q^{80} \) \(\mathstrut +\mathstrut 170q^{81} \) \(\mathstrut -\mathstrut 64q^{82} \) \(\mathstrut +\mathstrut 109q^{83} \) \(\mathstrut +\mathstrut 23q^{84} \) \(\mathstrut -\mathstrut 13q^{85} \) \(\mathstrut -\mathstrut 23q^{86} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut -\mathstrut 44q^{88} \) \(\mathstrut +\mathstrut 121q^{89} \) \(\mathstrut -\mathstrut 60q^{90} \) \(\mathstrut +\mathstrut 81q^{91} \) \(\mathstrut +\mathstrut 38q^{92} \) \(\mathstrut +\mathstrut 27q^{93} \) \(\mathstrut -\mathstrut 77q^{94} \) \(\mathstrut +\mathstrut 49q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 109q^{98} \) \(\mathstrut +\mathstrut 158q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.25486 1.00000 3.01406 3.25486 −0.942473 −1.00000 7.59411 −3.01406
1.2 −1.00000 −3.25191 1.00000 −1.61920 3.25191 −4.93737 −1.00000 7.57490 1.61920
1.3 −1.00000 −3.20966 1.00000 0.782750 3.20966 3.68309 −1.00000 7.30189 −0.782750
1.4 −1.00000 −3.19050 1.00000 −0.434778 3.19050 2.23469 −1.00000 7.17932 0.434778
1.5 −1.00000 −3.14403 1.00000 0.849411 3.14403 0.337791 −1.00000 6.88495 −0.849411
1.6 −1.00000 −3.04565 1.00000 −0.405483 3.04565 −0.211812 −1.00000 6.27596 0.405483
1.7 −1.00000 −2.97454 1.00000 −1.53544 2.97454 2.95859 −1.00000 5.84792 1.53544
1.8 −1.00000 −2.68740 1.00000 3.50149 2.68740 −3.96925 −1.00000 4.22214 −3.50149
1.9 −1.00000 −2.64301 1.00000 −0.786430 2.64301 −4.08167 −1.00000 3.98548 0.786430
1.10 −1.00000 −2.62565 1.00000 −4.13736 2.62565 −3.98462 −1.00000 3.89402 4.13736
1.11 −1.00000 −2.61892 1.00000 3.93925 2.61892 4.49129 −1.00000 3.85875 −3.93925
1.12 −1.00000 −2.55894 1.00000 −3.60377 2.55894 −1.20803 −1.00000 3.54817 3.60377
1.13 −1.00000 −2.34399 1.00000 1.04947 2.34399 −2.18495 −1.00000 2.49429 −1.04947
1.14 −1.00000 −2.31833 1.00000 1.68969 2.31833 −0.814652 −1.00000 2.37465 −1.68969
1.15 −1.00000 −2.09967 1.00000 3.00804 2.09967 1.34654 −1.00000 1.40862 −3.00804
1.16 −1.00000 −2.07592 1.00000 1.44155 2.07592 −4.11205 −1.00000 1.30942 −1.44155
1.17 −1.00000 −2.06398 1.00000 −1.63652 2.06398 0.580095 −1.00000 1.26000 1.63652
1.18 −1.00000 −1.90629 1.00000 −3.44864 1.90629 0.576337 −1.00000 0.633932 3.44864
1.19 −1.00000 −1.83924 1.00000 4.20278 1.83924 −0.870895 −1.00000 0.382816 −4.20278
1.20 −1.00000 −1.77113 1.00000 −2.88416 1.77113 −2.34784 −1.00000 0.136917 2.88416
See all 86 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.86
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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