Properties

Label 8019.2.a.l
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 −2.79071 0 5.78806 −3.06614 0 −1.43628 −10.5714 0 8.55671
1.2 −2.71465 0 5.36931 3.09118 0 4.07222 −9.14647 0 −8.39147
1.3 −2.66034 0 5.07742 3.00650 0 −4.51333 −8.18698 0 −7.99831
1.4 −2.65065 0 5.02592 −0.556977 0 3.79141 −8.02065 0 1.47635
1.5 −2.49410 0 4.22054 −0.845382 0 2.75453 −5.53826 0 2.10847
1.6 −2.41765 0 3.84501 −4.26448 0 −1.48558 −4.46059 0 10.3100
1.7 −2.35184 0 3.53116 1.70161 0 −2.57467 −3.60105 0 −4.00192
1.8 −2.30721 0 3.32320 −3.68924 0 2.72959 −3.05291 0 8.51183
1.9 −1.98291 0 1.93194 0.594867 0 −1.24839 0.134957 0 −1.17957
1.10 −1.89185 0 1.57908 −1.88472 0 1.84735 0.796313 0 3.56560
1.11 −1.83739 0 1.37599 3.72662 0 0.891460 1.14655 0 −6.84725
1.12 −1.79315 0 1.21539 3.19791 0 −3.70301 1.40692 0 −5.73435
1.13 −1.65054 0 0.724279 1.45553 0 −4.69391 2.10563 0 −2.40240
1.14 −1.64539 0 0.707320 −1.78224 0 −2.05789 2.12697 0 2.93248
1.15 −1.44992 0 0.102274 1.93239 0 2.99081 2.75156 0 −2.80182
1.16 −1.44748 0 0.0951963 −3.47143 0 5.22882 2.75716 0 5.02482
1.17 −1.18428 0 −0.597486 2.95374 0 3.03845 3.07615 0 −3.49805
1.18 −1.08097 0 −0.831507 −2.81118 0 −2.10385 3.06077 0 3.03880
1.19 −0.933308 0 −1.12894 1.97519 0 5.04438 2.92026 0 −1.84346
1.20 −0.763545 0 −1.41700 −2.20032 0 −4.85667 2.60903 0 1.68004
See all 51 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.51
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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

Hecke kernels

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