Properties

Label 8019.2.a.k
Level 8019
Weight 2
Character orbit 8019.a
Self dual Yes
Analytic conductor 64.032
Analytic rank 0
Dimension 51
CM No

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Newspace parameters

Level: \( N \) = \( 8019 = 3^{6} \cdot 11 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8019.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0320373809\)
Analytic rank: \(0\)
Dimension: \(51\)
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.

\(\operatorname{Tr}(f)(q) = \) \(51q \) \(\mathstrut +\mathstrut 60q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(51q \) \(\mathstrut +\mathstrut 60q^{4} \) \(\mathstrut -\mathstrut 6q^{5} \) \(\mathstrut +\mathstrut 12q^{7} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut -\mathstrut 51q^{11} \) \(\mathstrut +\mathstrut 30q^{13} \) \(\mathstrut -\mathstrut 12q^{14} \) \(\mathstrut +\mathstrut 78q^{16} \) \(\mathstrut +\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 18q^{20} \) \(\mathstrut -\mathstrut 3q^{23} \) \(\mathstrut +\mathstrut 75q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 36q^{28} \) \(\mathstrut +\mathstrut 42q^{31} \) \(\mathstrut +\mathstrut 15q^{32} \) \(\mathstrut +\mathstrut 42q^{34} \) \(\mathstrut +\mathstrut 9q^{35} \) \(\mathstrut +\mathstrut 48q^{37} \) \(\mathstrut +\mathstrut 3q^{38} \) \(\mathstrut +\mathstrut 54q^{40} \) \(\mathstrut +\mathstrut 18q^{43} \) \(\mathstrut -\mathstrut 60q^{44} \) \(\mathstrut +\mathstrut 42q^{46} \) \(\mathstrut -\mathstrut 30q^{47} \) \(\mathstrut +\mathstrut 99q^{49} \) \(\mathstrut +\mathstrut 30q^{50} \) \(\mathstrut +\mathstrut 60q^{52} \) \(\mathstrut -\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 30q^{58} \) \(\mathstrut -\mathstrut 24q^{59} \) \(\mathstrut +\mathstrut 99q^{61} \) \(\mathstrut +\mathstrut 114q^{64} \) \(\mathstrut +\mathstrut 15q^{65} \) \(\mathstrut +\mathstrut 39q^{67} \) \(\mathstrut +\mathstrut 39q^{68} \) \(\mathstrut +\mathstrut 48q^{70} \) \(\mathstrut -\mathstrut 30q^{71} \) \(\mathstrut +\mathstrut 69q^{73} \) \(\mathstrut +\mathstrut 90q^{76} \) \(\mathstrut -\mathstrut 12q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut -\mathstrut 42q^{80} \) \(\mathstrut +\mathstrut 42q^{82} \) \(\mathstrut +\mathstrut 21q^{83} \) \(\mathstrut +\mathstrut 84q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut -\mathstrut 15q^{89} \) \(\mathstrut +\mathstrut 69q^{91} \) \(\mathstrut +\mathstrut 66q^{92} \) \(\mathstrut +\mathstrut 66q^{94} \) \(\mathstrut +\mathstrut 12q^{95} \) \(\mathstrut +\mathstrut 72q^{97} \) \(\mathstrut +\mathstrut 57q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.76871 0 5.66575 −0.801804 0 −0.629042 −10.1494 0 2.21996
1.2 −2.67622 0 5.16217 −0.731731 0 −3.74848 −8.46268 0 1.95828
1.3 −2.62878 0 4.91050 −2.26452 0 3.85414 −7.65109 0 5.95293
1.4 −2.61712 0 4.84933 −2.95330 0 3.35710 −7.45704 0 7.72914
1.5 −2.47541 0 4.12764 0.628090 0 1.20891 −5.26679 0 −1.55478
1.6 −2.45230 0 4.01379 3.72780 0 2.27663 −4.93843 0 −9.14169
1.7 −2.41800 0 3.84673 −3.72510 0 1.45693 −4.46540 0 9.00729
1.8 −2.23281 0 2.98545 2.49621 0 3.71630 −2.20033 0 −5.57356
1.9 −2.15387 0 2.63914 −3.34557 0 −4.79440 −1.37662 0 7.20590
1.10 −1.88963 0 1.57069 3.05305 0 −3.76670 0.811240 0 −5.76913
1.11 −1.76094 0 1.10089 3.93345 0 0.464070 1.58327 0 −6.92656
1.12 −1.75810 0 1.09093 −0.0727216 0 −2.24688 1.59824 0 0.127852
1.13 −1.74381 0 1.04089 −1.65090 0 3.26657 1.67251 0 2.87887
1.14 −1.70504 0 0.907156 −0.871790 0 5.05699 1.86334 0 1.48644
1.15 −1.31194 0 −0.278801 0.542226 0 −2.66849 2.98966 0 −0.711370
1.16 −1.28722 0 −0.343067 −0.396824 0 −0.0201110 3.01604 0 0.510800
1.17 −1.25801 0 −0.417404 −4.24212 0 −1.43200 3.04112 0 5.33665
1.18 −1.22452 0 −0.500542 −2.64802 0 2.83927 3.06197 0 3.24257
1.19 −1.05352 0 −0.890100 0.294863 0 −2.16091 3.04477 0 −0.310644
1.20 −1.01035 0 −0.979187 3.04931 0 0.331635 3.01003 0 −3.08088
See all 51 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.51
Significant digits:
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Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(11\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{51} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8019))\).