Properties

Label 8006.2.a.d
Level 8006
Weight 2
Character orbit 8006.a
Self dual Yes
Analytic conductor 63.928
Analytic rank 0
Dimension 98
CM No

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Newspace parameters

Level: \( N \) = \( 8006 = 2 \cdot 4003 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8006.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9282318582\)
Analytic rank: \(0\)
Dimension: \(98\)
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.

\(\operatorname{Tr}(f)(q) = \) \(98q \) \(\mathstrut +\mathstrut 98q^{2} \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 29q^{7} \) \(\mathstrut +\mathstrut 98q^{8} \) \(\mathstrut +\mathstrut 130q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(98q \) \(\mathstrut +\mathstrut 98q^{2} \) \(\mathstrut +\mathstrut 16q^{3} \) \(\mathstrut +\mathstrut 98q^{4} \) \(\mathstrut +\mathstrut 4q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 29q^{7} \) \(\mathstrut +\mathstrut 98q^{8} \) \(\mathstrut +\mathstrut 130q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 16q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 29q^{14} \) \(\mathstrut +\mathstrut 57q^{15} \) \(\mathstrut +\mathstrut 98q^{16} \) \(\mathstrut +\mathstrut 35q^{17} \) \(\mathstrut +\mathstrut 130q^{18} \) \(\mathstrut +\mathstrut 77q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 46q^{21} \) \(\mathstrut +\mathstrut 51q^{22} \) \(\mathstrut +\mathstrut 73q^{23} \) \(\mathstrut +\mathstrut 16q^{24} \) \(\mathstrut +\mathstrut 150q^{25} \) \(\mathstrut +\mathstrut 31q^{26} \) \(\mathstrut +\mathstrut 52q^{27} \) \(\mathstrut +\mathstrut 29q^{28} \) \(\mathstrut +\mathstrut 20q^{29} \) \(\mathstrut +\mathstrut 57q^{30} \) \(\mathstrut +\mathstrut 59q^{31} \) \(\mathstrut +\mathstrut 98q^{32} \) \(\mathstrut +\mathstrut 27q^{33} \) \(\mathstrut +\mathstrut 35q^{34} \) \(\mathstrut +\mathstrut 48q^{35} \) \(\mathstrut +\mathstrut 130q^{36} \) \(\mathstrut +\mathstrut 41q^{37} \) \(\mathstrut +\mathstrut 77q^{38} \) \(\mathstrut +\mathstrut 64q^{39} \) \(\mathstrut +\mathstrut 4q^{40} \) \(\mathstrut +\mathstrut 29q^{41} \) \(\mathstrut +\mathstrut 46q^{42} \) \(\mathstrut +\mathstrut 94q^{43} \) \(\mathstrut +\mathstrut 51q^{44} \) \(\mathstrut -\mathstrut 3q^{45} \) \(\mathstrut +\mathstrut 73q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 149q^{49} \) \(\mathstrut +\mathstrut 150q^{50} \) \(\mathstrut +\mathstrut 58q^{51} \) \(\mathstrut +\mathstrut 31q^{52} \) \(\mathstrut -\mathstrut 11q^{53} \) \(\mathstrut +\mathstrut 52q^{54} \) \(\mathstrut +\mathstrut 56q^{55} \) \(\mathstrut +\mathstrut 29q^{56} \) \(\mathstrut +\mathstrut 64q^{57} \) \(\mathstrut +\mathstrut 20q^{58} \) \(\mathstrut +\mathstrut 45q^{59} \) \(\mathstrut +\mathstrut 57q^{60} \) \(\mathstrut +\mathstrut 73q^{61} \) \(\mathstrut +\mathstrut 59q^{62} \) \(\mathstrut +\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 98q^{64} \) \(\mathstrut +\mathstrut 39q^{65} \) \(\mathstrut +\mathstrut 27q^{66} \) \(\mathstrut +\mathstrut 133q^{67} \) \(\mathstrut +\mathstrut 35q^{68} \) \(\mathstrut +\mathstrut 13q^{69} \) \(\mathstrut +\mathstrut 48q^{70} \) \(\mathstrut +\mathstrut 67q^{71} \) \(\mathstrut +\mathstrut 130q^{72} \) \(\mathstrut +\mathstrut 42q^{73} \) \(\mathstrut +\mathstrut 41q^{74} \) \(\mathstrut +\mathstrut 36q^{75} \) \(\mathstrut +\mathstrut 77q^{76} \) \(\mathstrut -\mathstrut 25q^{77} \) \(\mathstrut +\mathstrut 64q^{78} \) \(\mathstrut +\mathstrut 154q^{79} \) \(\mathstrut +\mathstrut 4q^{80} \) \(\mathstrut +\mathstrut 198q^{81} \) \(\mathstrut +\mathstrut 29q^{82} \) \(\mathstrut +\mathstrut 69q^{83} \) \(\mathstrut +\mathstrut 46q^{84} \) \(\mathstrut +\mathstrut 81q^{85} \) \(\mathstrut +\mathstrut 94q^{86} \) \(\mathstrut +\mathstrut 25q^{87} \) \(\mathstrut +\mathstrut 51q^{88} \) \(\mathstrut +\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 3q^{90} \) \(\mathstrut +\mathstrut 95q^{91} \) \(\mathstrut +\mathstrut 73q^{92} \) \(\mathstrut -\mathstrut 23q^{93} \) \(\mathstrut +\mathstrut 58q^{94} \) \(\mathstrut +\mathstrut 50q^{95} \) \(\mathstrut +\mathstrut 16q^{96} \) \(\mathstrut +\mathstrut 76q^{97} \) \(\mathstrut +\mathstrut 149q^{98} \) \(\mathstrut +\mathstrut 149q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.34117 1.00000 −2.63189 −3.34117 −3.23365 1.00000 8.16344 −2.63189
1.2 1.00000 −3.30357 1.00000 −2.71504 −3.30357 0.802195 1.00000 7.91355 −2.71504
1.3 1.00000 −3.23335 1.00000 1.72220 −3.23335 4.52664 1.00000 7.45455 1.72220
1.4 1.00000 −3.15680 1.00000 −2.35136 −3.15680 −0.0333758 1.00000 6.96536 −2.35136
1.5 1.00000 −3.07582 1.00000 1.83927 −3.07582 −1.83961 1.00000 6.46070 1.83927
1.6 1.00000 −3.05574 1.00000 2.27846 −3.05574 −0.374830 1.00000 6.33757 2.27846
1.7 1.00000 −3.04444 1.00000 −4.16552 −3.04444 −3.08322 1.00000 6.26861 −4.16552
1.8 1.00000 −2.80568 1.00000 1.82812 −2.80568 4.55893 1.00000 4.87183 1.82812
1.9 1.00000 −2.77826 1.00000 −3.83157 −2.77826 3.52049 1.00000 4.71872 −3.83157
1.10 1.00000 −2.73443 1.00000 −0.0905939 −2.73443 −4.21224 1.00000 4.47709 −0.0905939
1.11 1.00000 −2.69452 1.00000 −4.09763 −2.69452 4.00132 1.00000 4.26044 −4.09763
1.12 1.00000 −2.67018 1.00000 0.0387933 −2.67018 −0.245209 1.00000 4.12985 0.0387933
1.13 1.00000 −2.57565 1.00000 −1.28503 −2.57565 −4.37657 1.00000 3.63399 −1.28503
1.14 1.00000 −2.52562 1.00000 3.79609 −2.52562 −3.83950 1.00000 3.37877 3.79609
1.15 1.00000 −2.49687 1.00000 3.81192 −2.49687 2.89844 1.00000 3.23436 3.81192
1.16 1.00000 −2.29904 1.00000 −0.379667 −2.29904 −2.21994 1.00000 2.28559 −0.379667
1.17 1.00000 −2.28004 1.00000 0.593845 −2.28004 −0.744586 1.00000 2.19860 0.593845
1.18 1.00000 −2.25105 1.00000 −0.876874 −2.25105 −0.763073 1.00000 2.06722 −0.876874
1.19 1.00000 −2.20795 1.00000 −3.75545 −2.20795 −1.87926 1.00000 1.87502 −3.75545
1.20 1.00000 −2.20682 1.00000 0.892162 −2.20682 −0.549139 1.00000 1.87006 0.892162
See all 98 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.98
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(4003\) \(1\)