Properties

Label 8031.2.a.a
Level 8031
Weight 2
Character orbit 8031.a
Self dual Yes
Analytic conductor 64.128
Analytic rank 1
Dimension 92
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8031 = 3 \cdot 2677 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8031.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1278578633\)
Analytic rank: \(1\)
Dimension: \(92\)
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.

\(\operatorname{Tr}(f)(q) = \) \(92q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 92q^{3} \) \(\mathstrut +\mathstrut 70q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 42q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 92q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(92q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 92q^{3} \) \(\mathstrut +\mathstrut 70q^{4} \) \(\mathstrut -\mathstrut 18q^{5} \) \(\mathstrut -\mathstrut 6q^{6} \) \(\mathstrut -\mathstrut 42q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 92q^{9} \) \(\mathstrut -\mathstrut 44q^{10} \) \(\mathstrut -\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 70q^{12} \) \(\mathstrut -\mathstrut 48q^{13} \) \(\mathstrut -\mathstrut 29q^{14} \) \(\mathstrut -\mathstrut 18q^{15} \) \(\mathstrut +\mathstrut 26q^{16} \) \(\mathstrut -\mathstrut 69q^{17} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 74q^{19} \) \(\mathstrut -\mathstrut 42q^{20} \) \(\mathstrut -\mathstrut 42q^{21} \) \(\mathstrut -\mathstrut 62q^{22} \) \(\mathstrut -\mathstrut 19q^{23} \) \(\mathstrut -\mathstrut 15q^{24} \) \(\mathstrut +\mathstrut 16q^{25} \) \(\mathstrut -\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 92q^{27} \) \(\mathstrut -\mathstrut 101q^{28} \) \(\mathstrut -\mathstrut 54q^{29} \) \(\mathstrut -\mathstrut 44q^{30} \) \(\mathstrut -\mathstrut 67q^{31} \) \(\mathstrut -\mathstrut 36q^{32} \) \(\mathstrut -\mathstrut 24q^{33} \) \(\mathstrut -\mathstrut 63q^{34} \) \(\mathstrut -\mathstrut 31q^{35} \) \(\mathstrut +\mathstrut 70q^{36} \) \(\mathstrut -\mathstrut 70q^{37} \) \(\mathstrut -\mathstrut 18q^{38} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 125q^{40} \) \(\mathstrut -\mathstrut 98q^{41} \) \(\mathstrut -\mathstrut 29q^{42} \) \(\mathstrut -\mathstrut 159q^{43} \) \(\mathstrut -\mathstrut 52q^{44} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 68q^{46} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 26q^{48} \) \(\mathstrut -\mathstrut 28q^{49} \) \(\mathstrut -\mathstrut 7q^{50} \) \(\mathstrut -\mathstrut 69q^{51} \) \(\mathstrut -\mathstrut 98q^{52} \) \(\mathstrut -\mathstrut 23q^{53} \) \(\mathstrut -\mathstrut 6q^{54} \) \(\mathstrut -\mathstrut 93q^{55} \) \(\mathstrut -\mathstrut 48q^{56} \) \(\mathstrut -\mathstrut 74q^{57} \) \(\mathstrut -\mathstrut 37q^{58} \) \(\mathstrut -\mathstrut 36q^{59} \) \(\mathstrut -\mathstrut 42q^{60} \) \(\mathstrut -\mathstrut 172q^{61} \) \(\mathstrut -\mathstrut 26q^{62} \) \(\mathstrut -\mathstrut 42q^{63} \) \(\mathstrut -\mathstrut 23q^{64} \) \(\mathstrut -\mathstrut 66q^{65} \) \(\mathstrut -\mathstrut 62q^{66} \) \(\mathstrut -\mathstrut 143q^{67} \) \(\mathstrut -\mathstrut 74q^{68} \) \(\mathstrut -\mathstrut 19q^{69} \) \(\mathstrut -\mathstrut 30q^{70} \) \(\mathstrut -\mathstrut 9q^{71} \) \(\mathstrut -\mathstrut 15q^{72} \) \(\mathstrut -\mathstrut 134q^{73} \) \(\mathstrut -\mathstrut 19q^{74} \) \(\mathstrut +\mathstrut 16q^{75} \) \(\mathstrut -\mathstrut 157q^{76} \) \(\mathstrut -\mathstrut 25q^{77} \) \(\mathstrut -\mathstrut 27q^{78} \) \(\mathstrut -\mathstrut 138q^{79} \) \(\mathstrut -\mathstrut 29q^{80} \) \(\mathstrut +\mathstrut 92q^{81} \) \(\mathstrut -\mathstrut 61q^{82} \) \(\mathstrut -\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 101q^{84} \) \(\mathstrut -\mathstrut 84q^{85} \) \(\mathstrut +\mathstrut 14q^{86} \) \(\mathstrut -\mathstrut 54q^{87} \) \(\mathstrut -\mathstrut 140q^{88} \) \(\mathstrut -\mathstrut 148q^{89} \) \(\mathstrut -\mathstrut 44q^{90} \) \(\mathstrut -\mathstrut 115q^{91} \) \(\mathstrut -\mathstrut 12q^{92} \) \(\mathstrut -\mathstrut 67q^{93} \) \(\mathstrut -\mathstrut 79q^{94} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 36q^{96} \) \(\mathstrut -\mathstrut 165q^{97} \) \(\mathstrut +\mathstrut 36q^{98} \) \(\mathstrut -\mathstrut 24q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.68500 1.00000 5.20922 −2.40260 −2.68500 −1.66915 −8.61677 1.00000 6.45098
1.2 −2.67330 1.00000 5.14651 3.81418 −2.67330 −0.936528 −8.41154 1.00000 −10.1964
1.3 −2.66818 1.00000 5.11918 2.50193 −2.66818 2.17887 −8.32253 1.00000 −6.67559
1.4 −2.62702 1.00000 4.90122 1.25106 −2.62702 −3.99448 −7.62155 1.00000 −3.28657
1.5 −2.55172 1.00000 4.51128 1.01019 −2.55172 1.76064 −6.40810 1.00000 −2.57772
1.6 −2.49908 1.00000 4.24541 −0.718338 −2.49908 −1.10283 −5.61146 1.00000 1.79519
1.7 −2.48341 1.00000 4.16735 1.79948 −2.48341 −1.15988 −5.38242 1.00000 −4.46885
1.8 −2.42805 1.00000 3.89545 −1.43452 −2.42805 −1.67888 −4.60225 1.00000 3.48309
1.9 −2.38249 1.00000 3.67627 −1.60383 −2.38249 −3.97189 −3.99371 1.00000 3.82111
1.10 −2.36612 1.00000 3.59855 −2.41373 −2.36612 −0.423916 −3.78236 1.00000 5.71118
1.11 −2.23528 1.00000 2.99648 3.03614 −2.23528 −1.46620 −2.22741 1.00000 −6.78662
1.12 −2.18167 1.00000 2.75970 −1.98716 −2.18167 3.32615 −1.65742 1.00000 4.33533
1.13 −2.14091 1.00000 2.58350 1.26139 −2.14091 1.10366 −1.24922 1.00000 −2.70053
1.14 −2.07850 1.00000 2.32016 −0.257221 −2.07850 4.13615 −0.665460 1.00000 0.534635
1.15 −2.04285 1.00000 2.17322 −1.55350 −2.04285 −3.43191 −0.353867 1.00000 3.17355
1.16 −1.98646 1.00000 1.94604 −2.53807 −1.98646 2.04373 0.107184 1.00000 5.04179
1.17 −1.94029 1.00000 1.76473 1.85416 −1.94029 2.13881 0.456483 1.00000 −3.59761
1.18 −1.93878 1.00000 1.75885 3.19668 −1.93878 −4.95854 0.467527 1.00000 −6.19764
1.19 −1.91510 1.00000 1.66760 −3.82966 −1.91510 0.699529 0.636574 1.00000 7.33417
1.20 −1.77964 1.00000 1.16710 2.79221 −1.77964 0.728008 1.48226 1.00000 −4.96911
See all 92 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.92
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(2677\) \(-1\)