Properties

Label 8002.2.a.g
Level 8002
Weight 2
Character orbit 8002.a
Self dual yes
Analytic conductor 63.896
Analytic rank 0
Dimension 95
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8002.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.8962916974\)
Analytic rank: \(0\)
Dimension: \(95\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 95q + 95q^{2} + 24q^{3} + 95q^{4} + 36q^{5} + 24q^{6} + 21q^{7} + 95q^{8} + 121q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 95q + 95q^{2} + 24q^{3} + 95q^{4} + 36q^{5} + 24q^{6} + 21q^{7} + 95q^{8} + 121q^{9} + 36q^{10} + 40q^{11} + 24q^{12} + 52q^{13} + 21q^{14} + 15q^{15} + 95q^{16} + 84q^{17} + 121q^{18} + 37q^{19} + 36q^{20} + 36q^{21} + 40q^{22} + 37q^{23} + 24q^{24} + 133q^{25} + 52q^{26} + 93q^{27} + 21q^{28} + 66q^{29} + 15q^{30} + 10q^{31} + 95q^{32} + 63q^{33} + 84q^{34} + 55q^{35} + 121q^{36} + 49q^{37} + 37q^{38} + 14q^{39} + 36q^{40} + 98q^{41} + 36q^{42} + 37q^{43} + 40q^{44} + 97q^{45} + 37q^{46} + 91q^{47} + 24q^{48} + 170q^{49} + 133q^{50} + 22q^{51} + 52q^{52} + 70q^{53} + 93q^{54} - q^{55} + 21q^{56} + 50q^{57} + 66q^{58} + 72q^{59} + 15q^{60} + 97q^{61} + 10q^{62} + 75q^{63} + 95q^{64} + 75q^{65} + 63q^{66} + 39q^{67} + 84q^{68} + 65q^{69} + 55q^{70} + 28q^{71} + 121q^{72} + 117q^{73} + 49q^{74} + 62q^{75} + 37q^{76} + 92q^{77} + 14q^{78} + q^{79} + 36q^{80} + 155q^{81} + 98q^{82} + 117q^{83} + 36q^{84} + 81q^{85} + 37q^{86} + 46q^{87} + 40q^{88} + 90q^{89} + 97q^{90} + 65q^{91} + 37q^{92} + 36q^{93} + 91q^{94} + 38q^{95} + 24q^{96} + 111q^{97} + 170q^{98} + 97q^{99} + O(q^{100}) \)

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 1.00000 −3.41089 1.00000 2.42267 −3.41089 3.23449 1.00000 8.63416 2.42267
1.2 1.00000 −3.18851 1.00000 0.351128 −3.18851 −0.0577605 1.00000 7.16662 0.351128
1.3 1.00000 −3.08942 1.00000 −3.01572 −3.08942 −0.515913 1.00000 6.54453 −3.01572
1.4 1.00000 −2.96030 1.00000 3.24617 −2.96030 −2.38509 1.00000 5.76337 3.24617
1.5 1.00000 −2.82799 1.00000 4.14459 −2.82799 4.30276 1.00000 4.99754 4.14459
1.6 1.00000 −2.80236 1.00000 1.73987 −2.80236 −0.386891 1.00000 4.85324 1.73987
1.7 1.00000 −2.78398 1.00000 3.98298 −2.78398 −2.83528 1.00000 4.75054 3.98298
1.8 1.00000 −2.76392 1.00000 −0.367238 −2.76392 3.23477 1.00000 4.63923 −0.367238
1.9 1.00000 −2.73826 1.00000 −2.29649 −2.73826 −2.81204 1.00000 4.49807 −2.29649
1.10 1.00000 −2.72633 1.00000 0.195975 −2.72633 −4.75513 1.00000 4.43286 0.195975
1.11 1.00000 −2.68330 1.00000 −1.68032 −2.68330 0.225636 1.00000 4.20011 −1.68032
1.12 1.00000 −2.66813 1.00000 2.32067 −2.66813 −4.26871 1.00000 4.11889 2.32067
1.13 1.00000 −2.37543 1.00000 −2.94724 −2.37543 −3.40112 1.00000 2.64268 −2.94724
1.14 1.00000 −2.24343 1.00000 −3.17394 −2.24343 1.39363 1.00000 2.03297 −3.17394
1.15 1.00000 −2.22371 1.00000 3.47056 −2.22371 3.09791 1.00000 1.94489 3.47056
1.16 1.00000 −2.22303 1.00000 −1.84239 −2.22303 1.24832 1.00000 1.94184 −1.84239
1.17 1.00000 −2.18707 1.00000 −0.511085 −2.18707 4.44664 1.00000 1.78325 −0.511085
1.18 1.00000 −2.11368 1.00000 1.91949 −2.11368 3.49294 1.00000 1.46764 1.91949
1.19 1.00000 −1.94136 1.00000 −0.368072 −1.94136 −3.56861 1.00000 0.768897 −0.368072
1.20 1.00000 −1.87090 1.00000 4.22840 −1.87090 −1.96654 1.00000 0.500276 4.22840
See all 95 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.95
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 8002.2.a.g 95
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8002.2.a.g 95 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(4001\) \(1\)

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{3}^{95} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8002))\).

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database