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:

Atkin-Lehner signs

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

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

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database