Properties

Label 8044.2.a.a
Level 8044
Weight 2
Character orbit 8044.a
Self dual yes
Analytic conductor 64.232
Analytic rank 1
Dimension 80
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8044 = 2^{2} \cdot 2011 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8044.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.2316633859\)
Analytic rank: \(1\)
Dimension: \(80\)
Coefficient ring index: multiple of None
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 80q - 13q^{3} - 2q^{5} - 12q^{7} + 63q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 80q - 13q^{3} - 2q^{5} - 12q^{7} + 63q^{9} - 34q^{11} - q^{13} - 24q^{15} - 35q^{17} - 31q^{19} - 3q^{21} - 43q^{23} + 58q^{25} - 49q^{27} - 5q^{29} - 56q^{31} - 23q^{33} - 72q^{35} - 11q^{37} - 74q^{39} - 81q^{41} - 34q^{43} - 14q^{45} - 64q^{47} + 40q^{49} - 59q^{51} + 3q^{53} - 53q^{55} - 34q^{57} - 116q^{59} - 13q^{61} - 61q^{63} - 55q^{65} - 22q^{67} - 10q^{69} - 86q^{71} - 32q^{73} - 85q^{75} + 4q^{77} - 88q^{79} + 12q^{81} - 83q^{83} - 2q^{85} - 87q^{87} - 72q^{89} - 49q^{91} - 102q^{95} - 34q^{97} - 103q^{99} + O(q^{100}) \)

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 0 −3.40275 0 −1.72550 0 −2.88747 0 8.57873 0
1.2 0 −3.30826 0 0.889537 0 −1.31364 0 7.94459 0
1.3 0 −3.15920 0 −3.92220 0 2.93790 0 6.98053 0
1.4 0 −3.15577 0 3.07374 0 −1.51261 0 6.95887 0
1.5 0 −3.13382 0 2.56113 0 −0.308664 0 6.82084 0
1.6 0 −3.01017 0 −0.450076 0 4.39052 0 6.06114 0
1.7 0 −2.88063 0 4.02746 0 2.18923 0 5.29800 0
1.8 0 −2.78192 0 1.93177 0 −4.05350 0 4.73908 0
1.9 0 −2.69065 0 −1.88521 0 −0.388125 0 4.23960 0
1.10 0 −2.64514 0 −1.03664 0 1.03871 0 3.99678 0
1.11 0 −2.64034 0 1.50045 0 0.628661 0 3.97141 0
1.12 0 −2.57629 0 −1.13453 0 −4.92532 0 3.63726 0
1.13 0 −2.57058 0 3.02835 0 −3.19846 0 3.60789 0
1.14 0 −2.56684 0 −2.59165 0 1.04792 0 3.58865 0
1.15 0 −2.41417 0 −0.367373 0 2.85158 0 2.82820 0
1.16 0 −2.27117 0 −3.46385 0 −0.730522 0 2.15820 0
1.17 0 −2.04584 0 −1.96310 0 −5.24497 0 1.18544 0
1.18 0 −1.94593 0 4.46459 0 −3.96440 0 0.786636 0
1.19 0 −1.93385 0 −1.81561 0 3.06905 0 0.739771 0
1.20 0 −1.85715 0 0.680485 0 2.30245 0 0.448994 0
See all 80 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.80
Significant digits:
Format:

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 8044.2.a.a 80
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8044.2.a.a 80 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(2011\) \(-1\)