Properties

Label 8029.2.a.h
Level 8029
Weight 2
Character orbit 8029.a
Self dual Yes
Analytic conductor 64.112
Analytic rank 0
Dimension 71
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8029 = 7 \cdot 31 \cdot 37 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8029.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1118877829\)
Analytic rank: \(0\)
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.

\(\operatorname{Tr}(f)(q) = \) \(71q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 78q^{4} \) \(\mathstrut +\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut 71q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 87q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(71q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 78q^{4} \) \(\mathstrut +\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut 71q^{7} \) \(\mathstrut +\mathstrut 18q^{8} \) \(\mathstrut +\mathstrut 87q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 57q^{11} \) \(\mathstrut +\mathstrut 21q^{12} \) \(\mathstrut -\mathstrut 20q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 22q^{15} \) \(\mathstrut +\mathstrut 88q^{16} \) \(\mathstrut -\mathstrut 19q^{17} \) \(\mathstrut +\mathstrut q^{18} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut +\mathstrut 25q^{20} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut +\mathstrut 18q^{22} \) \(\mathstrut +\mathstrut 34q^{23} \) \(\mathstrut +\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 81q^{25} \) \(\mathstrut -\mathstrut 13q^{26} \) \(\mathstrut +\mathstrut 20q^{27} \) \(\mathstrut -\mathstrut 78q^{28} \) \(\mathstrut +\mathstrut 16q^{29} \) \(\mathstrut +\mathstrut 6q^{30} \) \(\mathstrut -\mathstrut 71q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut -\mathstrut 16q^{33} \) \(\mathstrut +\mathstrut 32q^{34} \) \(\mathstrut +\mathstrut 125q^{36} \) \(\mathstrut +\mathstrut 71q^{37} \) \(\mathstrut +\mathstrut 13q^{38} \) \(\mathstrut +\mathstrut 30q^{39} \) \(\mathstrut +\mathstrut 31q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut -\mathstrut 5q^{42} \) \(\mathstrut +\mathstrut 38q^{43} \) \(\mathstrut +\mathstrut 80q^{44} \) \(\mathstrut -\mathstrut q^{45} \) \(\mathstrut +\mathstrut 26q^{46} \) \(\mathstrut +\mathstrut 32q^{47} \) \(\mathstrut +\mathstrut 61q^{48} \) \(\mathstrut +\mathstrut 71q^{49} \) \(\mathstrut +\mathstrut 47q^{50} \) \(\mathstrut +\mathstrut 73q^{51} \) \(\mathstrut -\mathstrut 23q^{52} \) \(\mathstrut +\mathstrut 31q^{53} \) \(\mathstrut +\mathstrut 47q^{54} \) \(\mathstrut +\mathstrut 11q^{55} \) \(\mathstrut -\mathstrut 18q^{56} \) \(\mathstrut +\mathstrut 17q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 97q^{59} \) \(\mathstrut +\mathstrut 103q^{60} \) \(\mathstrut -\mathstrut q^{61} \) \(\mathstrut -\mathstrut 6q^{62} \) \(\mathstrut -\mathstrut 87q^{63} \) \(\mathstrut +\mathstrut 100q^{64} \) \(\mathstrut +\mathstrut 46q^{65} \) \(\mathstrut +\mathstrut 43q^{66} \) \(\mathstrut +\mathstrut 75q^{67} \) \(\mathstrut -\mathstrut 43q^{68} \) \(\mathstrut +\mathstrut 10q^{69} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 131q^{71} \) \(\mathstrut -\mathstrut 11q^{72} \) \(\mathstrut -\mathstrut 15q^{73} \) \(\mathstrut +\mathstrut 6q^{74} \) \(\mathstrut +\mathstrut 76q^{75} \) \(\mathstrut +\mathstrut 41q^{76} \) \(\mathstrut -\mathstrut 57q^{77} \) \(\mathstrut +\mathstrut 89q^{78} \) \(\mathstrut +\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 171q^{81} \) \(\mathstrut +\mathstrut 14q^{82} \) \(\mathstrut +\mathstrut 18q^{83} \) \(\mathstrut -\mathstrut 21q^{84} \) \(\mathstrut +\mathstrut 47q^{85} \) \(\mathstrut +\mathstrut 90q^{86} \) \(\mathstrut -\mathstrut 59q^{87} \) \(\mathstrut +\mathstrut 13q^{88} \) \(\mathstrut +\mathstrut 18q^{89} \) \(\mathstrut +\mathstrut 69q^{90} \) \(\mathstrut +\mathstrut 20q^{91} \) \(\mathstrut +\mathstrut 110q^{92} \) \(\mathstrut -\mathstrut 8q^{93} \) \(\mathstrut +\mathstrut 39q^{94} \) \(\mathstrut +\mathstrut 72q^{95} \) \(\mathstrut +\mathstrut 100q^{96} \) \(\mathstrut +\mathstrut 23q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut 168q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.78017 2.03796 5.72934 0.445141 −5.66588 −1.00000 −10.3682 1.15330 −1.23757
1.2 −2.69431 0.251057 5.25931 0.178464 −0.676426 −1.00000 −8.78160 −2.93697 −0.480839
1.3 −2.64917 −3.09220 5.01811 0.332247 8.19178 −1.00000 −7.99549 6.56173 −0.880180
1.4 −2.63529 −1.71677 4.94476 −3.15507 4.52418 −1.00000 −7.76032 −0.0527133 8.31452
1.5 −2.40369 2.90614 3.77774 −0.715086 −6.98547 −1.00000 −4.27315 5.44566 1.71885
1.6 −2.38302 3.20550 3.67879 −2.71243 −7.63877 −1.00000 −4.00058 7.27524 6.46378
1.7 −2.31484 −2.30235 3.35848 0.0649698 5.32957 −1.00000 −3.14465 2.30082 −0.150395
1.8 −2.30726 1.92904 3.32347 4.29364 −4.45079 −1.00000 −3.05358 0.721177 −9.90655
1.9 −2.28647 −0.837618 3.22797 2.08578 1.91519 −1.00000 −2.80772 −2.29840 −4.76908
1.10 −2.10847 1.17312 2.44565 1.33093 −2.47348 −1.00000 −0.939631 −1.62379 −2.80623
1.11 −2.07728 −3.28410 2.31510 0.477215 6.82201 −1.00000 −0.654560 7.78532 −0.991310
1.12 −2.06856 3.20449 2.27895 4.21324 −6.62868 −1.00000 −0.577029 7.26874 −8.71536
1.13 −2.02141 0.0362870 2.08609 −2.43486 −0.0733508 −1.00000 −0.174025 −2.99868 4.92185
1.14 −2.02044 −0.0586839 2.08218 2.29077 0.118567 −1.00000 −0.166030 −2.99656 −4.62836
1.15 −1.95127 1.43500 1.80747 −4.32832 −2.80008 −1.00000 0.375685 −0.940772 8.44573
1.16 −1.86191 −1.06463 1.46672 −1.77871 1.98225 −1.00000 0.992917 −1.86656 3.31181
1.17 −1.56268 −3.23783 0.441960 −3.23512 5.05968 −1.00000 2.43471 7.48352 5.05544
1.18 −1.50294 0.107359 0.258826 3.46915 −0.161355 −1.00000 2.61688 −2.98847 −5.21392
1.19 −1.49331 −1.98225 0.229971 2.93836 2.96012 −1.00000 2.64320 0.929333 −4.38788
1.20 −1.38552 1.91783 −0.0803442 −0.654097 −2.65719 −1.00000 2.88235 0.678074 0.906262
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
\(7\) \(1\)
\(31\) \(1\)
\(37\) \(-1\)