Properties

Label 8003.2.a.b
Level 8003
Weight 2
Character orbit 8003.a
Self dual yes
Analytic conductor 63.904
Analytic rank 1
Dimension 153
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) \(=\) \( 8003 = 53 \cdot 151 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8003.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(63.9042767376\)
Analytic rank: \(1\)
Dimension: \(153\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 153q - 9q^{2} - 17q^{3} + 137q^{4} - 31q^{5} - 10q^{6} - 17q^{7} - 30q^{8} + 136q^{9} - 34q^{10} - q^{11} - 60q^{12} - 101q^{13} - 16q^{14} - 14q^{15} + 97q^{16} - 12q^{17} - 45q^{18} - 45q^{19} - 52q^{20} - 76q^{21} - 46q^{22} - 28q^{23} - 30q^{24} + 84q^{25} - 22q^{26} - 68q^{27} - 64q^{28} - 14q^{29} - q^{30} - 70q^{31} - 54q^{32} - 85q^{33} - 59q^{34} - 16q^{35} + 87q^{36} - 167q^{37} - 48q^{38} - 28q^{39} - 68q^{40} - 38q^{41} + 2q^{42} - 71q^{43} - 10q^{44} - 151q^{45} - 37q^{46} - 37q^{47} - 166q^{48} + 74q^{49} - 3q^{50} - 11q^{51} - 183q^{52} - 153q^{53} - 40q^{54} - 88q^{55} - 69q^{56} - 26q^{57} - 43q^{58} - 34q^{59} - 12q^{60} - 90q^{61} - 37q^{62} - 36q^{63} + 58q^{64} - 19q^{65} + 52q^{66} - 86q^{67} - 22q^{68} - 81q^{69} - 144q^{70} - 50q^{71} - 190q^{72} - 171q^{73} - 14q^{74} - 69q^{75} - 88q^{76} - 72q^{77} - 61q^{78} - 13q^{79} - 84q^{80} + 117q^{81} - 124q^{82} - 72q^{83} - 106q^{84} - 193q^{85} - 44q^{86} - 65q^{87} - 89q^{88} - 10q^{89} - 152q^{90} - 67q^{91} - 29q^{92} - 129q^{93} - 43q^{94} - 29q^{95} - 106q^{96} - 177q^{97} - 69q^{98} - 11q^{99} + O(q^{100}) \)

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 −2.82377 0.0811365 5.97367 1.22528 −0.229111 1.93678 −11.2207 −2.99342 −3.45990
1.2 −2.76122 −1.93941 5.62432 −0.205414 5.35515 −1.99038 −10.0076 0.761331 0.567192
1.3 −2.72579 2.89515 5.42994 −2.27822 −7.89157 −3.84210 −9.34930 5.38188 6.20996
1.4 −2.71996 −3.40952 5.39818 0.859174 9.27375 3.37109 −9.24292 8.62480 −2.33692
1.5 −2.64082 1.90424 4.97394 2.87158 −5.02877 0.865912 −7.85365 0.626146 −7.58334
1.6 −2.62408 −2.48215 4.88578 −3.25865 6.51336 0.610888 −7.57250 3.16108 8.55094
1.7 −2.55787 −0.498344 4.54269 3.86602 1.27470 −1.47646 −6.50388 −2.75165 −9.88878
1.8 −2.55291 −0.169380 4.51736 −0.762748 0.432413 0.998481 −6.42660 −2.97131 1.94723
1.9 −2.54449 −2.75216 4.47442 −0.0821866 7.00285 −2.51361 −6.29612 4.57441 0.209123
1.10 −2.53517 1.42230 4.42707 −0.780530 −3.60576 3.78955 −6.15303 −0.977076 1.97877
1.11 −2.49383 −0.270355 4.21918 −2.99495 0.674220 −3.80387 −5.53426 −2.92691 7.46890
1.12 −2.46809 2.55539 4.09144 0.103837 −6.30691 0.172456 −5.16186 3.53000 −0.256278
1.13 −2.45028 −2.96227 4.00387 −1.96635 7.25838 −3.26353 −4.91003 5.77502 4.81810
1.14 −2.41716 −1.38399 3.84266 1.63498 3.34533 −3.98295 −4.45401 −1.08457 −3.95202
1.15 −2.40368 2.42213 3.77770 1.57847 −5.82205 −3.75128 −4.27303 2.86673 −3.79414
1.16 −2.36991 −1.12262 3.61648 0.983312 2.66051 2.71051 −3.83091 −1.73972 −2.33036
1.17 −2.35186 2.82673 3.53125 2.18646 −6.64808 0.649269 −3.60130 4.99041 −5.14224
1.18 −2.34979 −2.55203 3.52153 3.27958 5.99675 4.82178 −3.57528 3.51287 −7.70633
1.19 −2.34552 3.15214 3.50145 −3.97132 −7.39341 −1.04283 −3.52168 6.93601 9.31479
1.20 −2.32654 −0.105675 3.41278 −1.05522 0.245856 0.945293 −3.28688 −2.98883 2.45502
See next 80 embeddings (of 153 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.153
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 8003.2.a.b 153
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8003.2.a.b 153 1.a even 1 1 trivial

Atkin-Lehner signs

\( p \) Sign
\(53\) \(1\)
\(151\) \(1\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database