Properties

Label 8001.2.a.y
Level 8001
Weight 2
Character orbit 8001.a
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \(28q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(28q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 28q^{7} \) \(\mathstrut +\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 8q^{13} \) \(\mathstrut +\mathstrut 42q^{16} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 14q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut +\mathstrut 56q^{31} \) \(\mathstrut -\mathstrut 6q^{37} \) \(\mathstrut +\mathstrut 38q^{40} \) \(\mathstrut +\mathstrut 18q^{43} \) \(\mathstrut +\mathstrut 16q^{46} \) \(\mathstrut +\mathstrut 28q^{49} \) \(\mathstrut +\mathstrut 18q^{52} \) \(\mathstrut +\mathstrut 48q^{55} \) \(\mathstrut +\mathstrut 2q^{58} \) \(\mathstrut +\mathstrut 36q^{61} \) \(\mathstrut +\mathstrut 76q^{64} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 50q^{73} \) \(\mathstrut +\mathstrut 132q^{76} \) \(\mathstrut +\mathstrut 66q^{79} \) \(\mathstrut -\mathstrut 36q^{82} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 6q^{88} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.72816 0 5.44285 0.297532 0 −1.00000 −9.39264 0 −0.811714
1.2 −2.71687 0 5.38141 −1.23671 0 −1.00000 −9.18686 0 3.35997
1.3 −2.47474 0 4.12433 −3.91787 0 −1.00000 −5.25716 0 9.69570
1.4 −2.27499 0 3.17556 3.81133 0 −1.00000 −2.67439 0 −8.67073
1.5 −2.02489 0 2.10018 2.65037 0 −1.00000 −0.202857 0 −5.36671
1.6 −1.99802 0 1.99208 −1.55092 0 −1.00000 0.0158280 0 3.09877
1.7 −1.55816 0 0.427866 −3.44623 0 −1.00000 2.44964 0 5.36979
1.8 −1.42730 0 0.0371861 2.54057 0 −1.00000 2.80152 0 −3.62615
1.9 −1.34710 0 −0.185322 0.124848 0 −1.00000 2.94385 0 −0.168183
1.10 −1.24740 0 −0.443996 1.34151 0 −1.00000 3.04864 0 −1.67339
1.11 −0.662421 0 −1.56120 −3.26980 0 −1.00000 2.35901 0 2.16599
1.12 −0.512239 0 −1.73761 1.76990 0 −1.00000 1.91455 0 −0.906610
1.13 −0.487315 0 −1.76252 0.708639 0 −1.00000 1.83353 0 −0.345330
1.14 −0.0958522 0 −1.99081 1.26637 0 −1.00000 0.382528 0 −0.121384
1.15 0.0958522 0 −1.99081 −1.26637 0 −1.00000 −0.382528 0 −0.121384
1.16 0.487315 0 −1.76252 −0.708639 0 −1.00000 −1.83353 0 −0.345330
1.17 0.512239 0 −1.73761 −1.76990 0 −1.00000 −1.91455 0 −0.906610
1.18 0.662421 0 −1.56120 3.26980 0 −1.00000 −2.35901 0 2.16599
1.19 1.24740 0 −0.443996 −1.34151 0 −1.00000 −3.04864 0 −1.67339
1.20 1.34710 0 −0.185322 −0.124848 0 −1.00000 −2.94385 0 −0.168183
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
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
\(3\) \(1\)
\(7\) \(1\)
\(127\) \(-1\)

Hecke kernels

This newform can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8001))\):

\(T_{2}^{28} - \cdots\)
\(T_{5}^{28} - \cdots\)