Properties

Label 4023.2.a.f
Level 4023
Weight 2
Character orbit 4023.a
Self dual Yes
Analytic conductor 32.124
Analytic rank 0
Dimension 25
CM No

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Newspace parameters

Level: \( N \) = \( 4023 = 3^{3} \cdot 149 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4023.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1238167332\)
Analytic rank: \(0\)
Dimension: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \(25q \) \(\mathstrut +\mathstrut 7q^{2} \) \(\mathstrut +\mathstrut 27q^{4} \) \(\mathstrut +\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(25q \) \(\mathstrut +\mathstrut 7q^{2} \) \(\mathstrut +\mathstrut 27q^{4} \) \(\mathstrut +\mathstrut 12q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 12q^{11} \) \(\mathstrut +\mathstrut 10q^{14} \) \(\mathstrut +\mathstrut 35q^{16} \) \(\mathstrut +\mathstrut 26q^{17} \) \(\mathstrut +\mathstrut 30q^{20} \) \(\mathstrut +\mathstrut 8q^{22} \) \(\mathstrut +\mathstrut 26q^{23} \) \(\mathstrut +\mathstrut 27q^{25} \) \(\mathstrut +\mathstrut 16q^{26} \) \(\mathstrut +\mathstrut 4q^{28} \) \(\mathstrut +\mathstrut 20q^{29} \) \(\mathstrut -\mathstrut 6q^{31} \) \(\mathstrut +\mathstrut 49q^{32} \) \(\mathstrut -\mathstrut 14q^{34} \) \(\mathstrut +\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 27q^{38} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut +\mathstrut 35q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut +\mathstrut 22q^{44} \) \(\mathstrut +\mathstrut 6q^{46} \) \(\mathstrut +\mathstrut 38q^{47} \) \(\mathstrut +\mathstrut 19q^{49} \) \(\mathstrut +\mathstrut 22q^{50} \) \(\mathstrut +\mathstrut 4q^{52} \) \(\mathstrut +\mathstrut 36q^{53} \) \(\mathstrut +\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 79q^{56} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 10q^{61} \) \(\mathstrut -\mathstrut 14q^{62} \) \(\mathstrut +\mathstrut 41q^{64} \) \(\mathstrut +\mathstrut 80q^{65} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 33q^{68} \) \(\mathstrut +\mathstrut 8q^{70} \) \(\mathstrut +\mathstrut 26q^{71} \) \(\mathstrut -\mathstrut 6q^{73} \) \(\mathstrut +\mathstrut 75q^{74} \) \(\mathstrut -\mathstrut 10q^{76} \) \(\mathstrut +\mathstrut 47q^{77} \) \(\mathstrut -\mathstrut 6q^{79} \) \(\mathstrut +\mathstrut 66q^{80} \) \(\mathstrut +\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 40q^{83} \) \(\mathstrut -\mathstrut 12q^{85} \) \(\mathstrut +\mathstrut 4q^{86} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 30q^{89} \) \(\mathstrut +\mathstrut 158q^{92} \) \(\mathstrut +\mathstrut 18q^{94} \) \(\mathstrut +\mathstrut 22q^{95} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 35q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.51316 0 4.31598 1.65121 0 0.864620 −5.82042 0 −4.14975
1.2 −2.38405 0 3.68368 0.998141 0 −3.46708 −4.01398 0 −2.37961
1.3 −2.31586 0 3.36319 3.59358 0 −2.32336 −3.15696 0 −8.32222
1.4 −1.97183 0 1.88812 −0.788067 0 −2.33009 0.220613 0 1.55394
1.5 −1.77959 0 1.16693 −0.742067 0 3.55470 1.48252 0 1.32057
1.6 −1.35944 0 −0.151922 3.36242 0 2.75034 2.92541 0 −4.57100
1.7 −1.30329 0 −0.301424 −3.35120 0 −0.705123 2.99943 0 4.36761
1.8 −0.680129 0 −1.53742 −2.78190 0 −0.191226 2.40591 0 1.89205
1.9 −0.599558 0 −1.64053 −0.261228 0 −0.444015 2.18271 0 0.156622
1.10 −0.530451 0 −1.71862 3.35792 0 3.91494 1.97255 0 −1.78121
1.11 −0.365778 0 −1.86621 3.76223 0 −2.92149 1.41417 0 −1.37614
1.12 0.0533591 0 −1.99715 −0.751347 0 2.49440 −0.213285 0 −0.0400912
1.13 0.305611 0 −1.90660 −1.63568 0 −3.53407 −1.19390 0 −0.499884
1.14 0.614681 0 −1.62217 3.33074 0 3.77407 −2.22648 0 2.04734
1.15 0.964175 0 −1.07037 −0.686967 0 −3.77336 −2.96037 0 −0.662356
1.16 1.23916 0 −0.464485 −0.602488 0 1.86008 −3.05389 0 −0.746578
1.17 1.43306 0 0.0536673 2.81862 0 −4.82450 −2.78922 0 4.03925
1.18 1.51618 0 0.298802 −2.07566 0 −1.53996 −2.57932 0 −3.14707
1.19 1.79652 0 1.22747 −3.24604 0 −3.00506 −1.38786 0 −5.83156
1.20 2.16693 0 2.69559 1.04157 0 3.90919 1.50729 0 2.25701
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(3\) \(1\)
\(149\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{25} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4023))\).