Properties

Label 8042.2.a.d
Level 8042
Weight 2
Character orbit 8042.a
Self dual Yes
Analytic conductor 64.216
Analytic rank 0
Dimension 101
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8042 = 2 \cdot 4021 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8042.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2156933055\)
Analytic rank: \(0\)
Dimension: \(101\)
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.

\(\operatorname{Tr}(f)(q) = \) \(101q \) \(\mathstrut +\mathstrut 101q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 101q^{4} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 42q^{7} \) \(\mathstrut +\mathstrut 101q^{8} \) \(\mathstrut +\mathstrut 147q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(101q \) \(\mathstrut +\mathstrut 101q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 101q^{4} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 42q^{7} \) \(\mathstrut +\mathstrut 101q^{8} \) \(\mathstrut +\mathstrut 147q^{9} \) \(\mathstrut +\mathstrut 19q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 58q^{13} \) \(\mathstrut +\mathstrut 42q^{14} \) \(\mathstrut +\mathstrut 27q^{15} \) \(\mathstrut +\mathstrut 101q^{16} \) \(\mathstrut +\mathstrut 34q^{17} \) \(\mathstrut +\mathstrut 147q^{18} \) \(\mathstrut +\mathstrut 36q^{19} \) \(\mathstrut +\mathstrut 19q^{20} \) \(\mathstrut +\mathstrut 45q^{21} \) \(\mathstrut +\mathstrut 4q^{22} \) \(\mathstrut +\mathstrut 47q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 174q^{25} \) \(\mathstrut +\mathstrut 58q^{26} \) \(\mathstrut +\mathstrut 31q^{27} \) \(\mathstrut +\mathstrut 42q^{28} \) \(\mathstrut +\mathstrut 62q^{29} \) \(\mathstrut +\mathstrut 27q^{30} \) \(\mathstrut +\mathstrut 47q^{31} \) \(\mathstrut +\mathstrut 101q^{32} \) \(\mathstrut +\mathstrut 55q^{33} \) \(\mathstrut +\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut +\mathstrut 147q^{36} \) \(\mathstrut +\mathstrut 90q^{37} \) \(\mathstrut +\mathstrut 36q^{38} \) \(\mathstrut +\mathstrut 50q^{39} \) \(\mathstrut +\mathstrut 19q^{40} \) \(\mathstrut +\mathstrut 54q^{41} \) \(\mathstrut +\mathstrut 45q^{42} \) \(\mathstrut +\mathstrut 65q^{43} \) \(\mathstrut +\mathstrut 4q^{44} \) \(\mathstrut +\mathstrut 47q^{45} \) \(\mathstrut +\mathstrut 47q^{46} \) \(\mathstrut +\mathstrut 54q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 189q^{49} \) \(\mathstrut +\mathstrut 174q^{50} \) \(\mathstrut +\mathstrut 36q^{51} \) \(\mathstrut +\mathstrut 58q^{52} \) \(\mathstrut +\mathstrut 94q^{53} \) \(\mathstrut +\mathstrut 31q^{54} \) \(\mathstrut +\mathstrut 68q^{55} \) \(\mathstrut +\mathstrut 42q^{56} \) \(\mathstrut +\mathstrut 79q^{57} \) \(\mathstrut +\mathstrut 62q^{58} \) \(\mathstrut -\mathstrut 6q^{59} \) \(\mathstrut +\mathstrut 27q^{60} \) \(\mathstrut +\mathstrut 58q^{61} \) \(\mathstrut +\mathstrut 47q^{62} \) \(\mathstrut +\mathstrut 117q^{63} \) \(\mathstrut +\mathstrut 101q^{64} \) \(\mathstrut +\mathstrut 89q^{65} \) \(\mathstrut +\mathstrut 55q^{66} \) \(\mathstrut +\mathstrut 127q^{67} \) \(\mathstrut +\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 45q^{69} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut +\mathstrut 87q^{71} \) \(\mathstrut +\mathstrut 147q^{72} \) \(\mathstrut +\mathstrut 83q^{73} \) \(\mathstrut +\mathstrut 90q^{74} \) \(\mathstrut -\mathstrut 4q^{75} \) \(\mathstrut +\mathstrut 36q^{76} \) \(\mathstrut +\mathstrut 53q^{77} \) \(\mathstrut +\mathstrut 50q^{78} \) \(\mathstrut +\mathstrut 74q^{79} \) \(\mathstrut +\mathstrut 19q^{80} \) \(\mathstrut +\mathstrut 241q^{81} \) \(\mathstrut +\mathstrut 54q^{82} \) \(\mathstrut +\mathstrut 11q^{83} \) \(\mathstrut +\mathstrut 45q^{84} \) \(\mathstrut +\mathstrut 120q^{85} \) \(\mathstrut +\mathstrut 65q^{86} \) \(\mathstrut +\mathstrut 37q^{87} \) \(\mathstrut +\mathstrut 4q^{88} \) \(\mathstrut +\mathstrut 89q^{89} \) \(\mathstrut +\mathstrut 47q^{90} \) \(\mathstrut +\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 47q^{92} \) \(\mathstrut +\mathstrut 123q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut +\mathstrut 61q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 85q^{97} \) \(\mathstrut +\mathstrut 189q^{98} \) \(\mathstrut -\mathstrut 55q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.43699 1.00000 −1.87422 −3.43699 −3.00439 1.00000 8.81289 −1.87422
1.2 1.00000 −3.38233 1.00000 3.47698 −3.38233 4.68177 1.00000 8.44012 3.47698
1.3 1.00000 −3.33232 1.00000 −1.78644 −3.33232 −0.0456798 1.00000 8.10435 −1.78644
1.4 1.00000 −3.21463 1.00000 −0.910313 −3.21463 2.06915 1.00000 7.33384 −0.910313
1.5 1.00000 −3.07090 1.00000 3.36444 −3.07090 2.10143 1.00000 6.43042 3.36444
1.6 1.00000 −3.06519 1.00000 −3.42202 −3.06519 2.44027 1.00000 6.39539 −3.42202
1.7 1.00000 −3.05772 1.00000 1.21871 −3.05772 −4.97978 1.00000 6.34964 1.21871
1.8 1.00000 −3.03040 1.00000 −4.23996 −3.03040 3.85031 1.00000 6.18334 −4.23996
1.9 1.00000 −3.00872 1.00000 1.27297 −3.00872 −1.78578 1.00000 6.05237 1.27297
1.10 1.00000 −2.92582 1.00000 4.30943 −2.92582 −1.07433 1.00000 5.56042 4.30943
1.11 1.00000 −2.78808 1.00000 1.68662 −2.78808 −0.478055 1.00000 4.77338 1.68662
1.12 1.00000 −2.74700 1.00000 1.34490 −2.74700 3.95509 1.00000 4.54602 1.34490
1.13 1.00000 −2.72397 1.00000 −3.81508 −2.72397 −1.37701 1.00000 4.42003 −3.81508
1.14 1.00000 −2.64364 1.00000 4.09219 −2.64364 −2.76746 1.00000 3.98881 4.09219
1.15 1.00000 −2.58579 1.00000 −4.00078 −2.58579 −2.06018 1.00000 3.68634 −4.00078
1.16 1.00000 −2.42928 1.00000 2.55543 −2.42928 4.80532 1.00000 2.90141 2.55543
1.17 1.00000 −2.42720 1.00000 2.10259 −2.42720 2.07633 1.00000 2.89131 2.10259
1.18 1.00000 −2.39327 1.00000 3.11355 −2.39327 −5.17926 1.00000 2.72774 3.11355
1.19 1.00000 −2.31266 1.00000 −2.37478 −2.31266 −3.49882 1.00000 2.34838 −2.37478
1.20 1.00000 −2.18140 1.00000 −1.90416 −2.18140 1.71599 1.00000 1.75849 −1.90416
See next 80 embeddings (of 101 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.101
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(4021\) \(1\)