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

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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: \(153\)
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.

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

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 −2.82377 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 have CM; other inner twists have not been computed.

Atkin-Lehner signs

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