Properties

Label 8029.2.a.g
Level 8029
Weight 2
Character orbit 8029.a
Self dual Yes
Analytic conductor 64.112
Analytic rank 0
Dimension 70
CM No

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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: \(70\)
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.

\(\operatorname{Tr}(f)(q) = \) \(70q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 22q^{3} \) \(\mathstrut +\mathstrut 71q^{4} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 70q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 78q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(70q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 22q^{3} \) \(\mathstrut +\mathstrut 71q^{4} \) \(\mathstrut +\mathstrut 24q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 70q^{7} \) \(\mathstrut +\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 78q^{9} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 61q^{11} \) \(\mathstrut +\mathstrut 49q^{12} \) \(\mathstrut +\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 5q^{14} \) \(\mathstrut +\mathstrut 22q^{15} \) \(\mathstrut +\mathstrut 73q^{16} \) \(\mathstrut +\mathstrut 37q^{17} \) \(\mathstrut +\mathstrut 8q^{18} \) \(\mathstrut +\mathstrut 23q^{19} \) \(\mathstrut +\mathstrut 45q^{20} \) \(\mathstrut +\mathstrut 22q^{21} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 26q^{23} \) \(\mathstrut +\mathstrut 3q^{24} \) \(\mathstrut +\mathstrut 66q^{25} \) \(\mathstrut +\mathstrut 57q^{26} \) \(\mathstrut +\mathstrut 76q^{27} \) \(\mathstrut +\mathstrut 71q^{28} \) \(\mathstrut +\mathstrut 38q^{29} \) \(\mathstrut -\mathstrut 14q^{30} \) \(\mathstrut +\mathstrut 70q^{31} \) \(\mathstrut -\mathstrut 2q^{32} \) \(\mathstrut +\mathstrut 44q^{33} \) \(\mathstrut +\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 46q^{36} \) \(\mathstrut +\mathstrut 70q^{37} \) \(\mathstrut +\mathstrut 21q^{38} \) \(\mathstrut +\mathstrut 10q^{39} \) \(\mathstrut +\mathstrut 13q^{40} \) \(\mathstrut +\mathstrut 71q^{41} \) \(\mathstrut +\mathstrut 9q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 108q^{44} \) \(\mathstrut +\mathstrut 13q^{45} \) \(\mathstrut -\mathstrut 14q^{46} \) \(\mathstrut +\mathstrut 78q^{47} \) \(\mathstrut +\mathstrut 85q^{48} \) \(\mathstrut +\mathstrut 70q^{49} \) \(\mathstrut -\mathstrut 12q^{50} \) \(\mathstrut +\mathstrut 21q^{51} \) \(\mathstrut +\mathstrut 23q^{52} \) \(\mathstrut +\mathstrut 47q^{53} \) \(\mathstrut +\mathstrut 17q^{54} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut +\mathstrut 9q^{56} \) \(\mathstrut +\mathstrut 9q^{57} \) \(\mathstrut +\mathstrut 8q^{58} \) \(\mathstrut +\mathstrut 109q^{59} \) \(\mathstrut -\mathstrut q^{60} \) \(\mathstrut +\mathstrut 41q^{61} \) \(\mathstrut +\mathstrut 5q^{62} \) \(\mathstrut +\mathstrut 78q^{63} \) \(\mathstrut +\mathstrut 29q^{64} \) \(\mathstrut +\mathstrut 36q^{65} \) \(\mathstrut +\mathstrut 5q^{66} \) \(\mathstrut +\mathstrut 23q^{67} \) \(\mathstrut +\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 99q^{71} \) \(\mathstrut +\mathstrut 8q^{72} \) \(\mathstrut +\mathstrut 33q^{73} \) \(\mathstrut +\mathstrut 5q^{74} \) \(\mathstrut +\mathstrut 94q^{75} \) \(\mathstrut -\mathstrut 19q^{76} \) \(\mathstrut +\mathstrut 61q^{77} \) \(\mathstrut +\mathstrut 37q^{78} \) \(\mathstrut +\mathstrut 52q^{79} \) \(\mathstrut +\mathstrut 78q^{80} \) \(\mathstrut +\mathstrut 102q^{81} \) \(\mathstrut +\mathstrut 118q^{83} \) \(\mathstrut +\mathstrut 49q^{84} \) \(\mathstrut -\mathstrut 21q^{85} \) \(\mathstrut +\mathstrut 74q^{86} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 21q^{88} \) \(\mathstrut +\mathstrut 86q^{89} \) \(\mathstrut -\mathstrut 7q^{90} \) \(\mathstrut +\mathstrut 28q^{91} \) \(\mathstrut +\mathstrut 14q^{92} \) \(\mathstrut +\mathstrut 22q^{93} \) \(\mathstrut +\mathstrut 35q^{94} \) \(\mathstrut +\mathstrut 24q^{95} \) \(\mathstrut -\mathstrut 40q^{96} \) \(\mathstrut +\mathstrut 9q^{97} \) \(\mathstrut +\mathstrut 5q^{98} \) \(\mathstrut +\mathstrut 92q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.75348 −0.719252 5.58165 0.633986 1.98045 1.00000 −9.86202 −2.48268 −1.74567
1.2 −2.70672 2.12991 5.32631 −2.23028 −5.76507 1.00000 −9.00339 1.53652 6.03675
1.3 −2.69962 2.88270 5.28797 3.78908 −7.78221 1.00000 −8.87628 5.30996 −10.2291
1.4 −2.54550 −1.20009 4.47956 2.75807 3.05483 1.00000 −6.31172 −1.55978 −7.02066
1.5 −2.49220 −0.243085 4.21105 3.85659 0.605816 1.00000 −5.51038 −2.94091 −9.61139
1.6 −2.46404 −1.44903 4.07148 −2.15186 3.57045 1.00000 −5.10420 −0.900323 5.30226
1.7 −2.35192 3.14960 3.53152 −3.21971 −7.40760 1.00000 −3.60200 6.91997 7.57250
1.8 −2.30530 0.494804 3.31440 1.43730 −1.14067 1.00000 −3.03008 −2.75517 −3.31341
1.9 −2.19859 1.85317 2.83381 −0.955285 −4.07436 1.00000 −1.83320 0.434225 2.10028
1.10 −2.18873 2.37642 2.79052 1.52040 −5.20134 1.00000 −1.73024 2.64738 −3.32774
1.11 −2.01064 −3.19206 2.04266 −1.79732 6.41808 1.00000 −0.0857692 7.18928 3.61376
1.12 −2.00414 −1.87169 2.01657 −1.61289 3.75112 1.00000 −0.0331998 0.503210 3.23245
1.13 −1.96118 1.44792 1.84625 −1.74883 −2.83964 1.00000 0.301540 −0.903529 3.42978
1.14 −1.91642 −2.33665 1.67267 3.67008 4.47800 1.00000 0.627304 2.45993 −7.03342
1.15 −1.91066 −1.87934 1.65063 −2.89304 3.59078 1.00000 0.667519 0.531906 5.52763
1.16 −1.74189 1.96861 1.03416 1.87277 −3.42909 1.00000 1.68238 0.875422 −3.26215
1.17 −1.48293 −0.919958 0.199089 1.22196 1.36424 1.00000 2.67063 −2.15368 −1.81208
1.18 −1.43732 3.17240 0.0658921 3.13251 −4.55975 1.00000 2.77993 7.06410 −4.50243
1.19 −1.39384 1.56439 −0.0572072 4.02287 −2.18052 1.00000 2.86742 −0.552671 −5.60723
1.20 −1.35296 0.0580579 −0.169502 −2.28030 −0.0785499 1.00000 2.93525 −2.99663 3.08516
See all 70 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.70
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(7\) \(-1\)
\(31\) \(-1\)
\(37\) \(-1\)