Properties

Label 8003.2.a.a
Level 8003
Weight 2
Character orbit 8003.a
Self dual Yes
Analytic conductor 63.904
Analytic rank 1
Dimension 147
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: \(147\)
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.

\(\operatorname{Tr}(f)(q) = \) \(147q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 130q^{4} \) \(\mathstrut -\mathstrut 25q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 33q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 114q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(147q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 23q^{3} \) \(\mathstrut +\mathstrut 130q^{4} \) \(\mathstrut -\mathstrut 25q^{5} \) \(\mathstrut -\mathstrut 18q^{6} \) \(\mathstrut -\mathstrut 33q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 114q^{9} \) \(\mathstrut -\mathstrut 24q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut -\mathstrut 52q^{12} \) \(\mathstrut -\mathstrut 119q^{13} \) \(\mathstrut -\mathstrut 6q^{14} \) \(\mathstrut -\mathstrut 22q^{15} \) \(\mathstrut +\mathstrut 100q^{16} \) \(\mathstrut -\mathstrut 42q^{17} \) \(\mathstrut -\mathstrut 6q^{18} \) \(\mathstrut -\mathstrut 31q^{19} \) \(\mathstrut -\mathstrut 50q^{20} \) \(\mathstrut -\mathstrut 44q^{21} \) \(\mathstrut -\mathstrut 38q^{22} \) \(\mathstrut -\mathstrut 16q^{23} \) \(\mathstrut -\mathstrut 30q^{24} \) \(\mathstrut +\mathstrut 80q^{25} \) \(\mathstrut -\mathstrut 18q^{26} \) \(\mathstrut -\mathstrut 68q^{27} \) \(\mathstrut -\mathstrut 72q^{28} \) \(\mathstrut -\mathstrut 40q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut -\mathstrut 44q^{31} \) \(\mathstrut -\mathstrut 41q^{32} \) \(\mathstrut -\mathstrut 71q^{33} \) \(\mathstrut -\mathstrut 55q^{34} \) \(\mathstrut -\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 108q^{36} \) \(\mathstrut -\mathstrut 145q^{37} \) \(\mathstrut -\mathstrut 39q^{38} \) \(\mathstrut +\mathstrut 28q^{39} \) \(\mathstrut -\mathstrut 81q^{40} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 54q^{42} \) \(\mathstrut -\mathstrut 47q^{43} \) \(\mathstrut -\mathstrut 33q^{44} \) \(\mathstrut -\mathstrut 89q^{45} \) \(\mathstrut -\mathstrut 43q^{46} \) \(\mathstrut -\mathstrut 65q^{47} \) \(\mathstrut -\mathstrut 82q^{48} \) \(\mathstrut +\mathstrut 52q^{49} \) \(\mathstrut -\mathstrut 43q^{50} \) \(\mathstrut +\mathstrut 7q^{51} \) \(\mathstrut -\mathstrut 215q^{52} \) \(\mathstrut +\mathstrut 147q^{53} \) \(\mathstrut -\mathstrut 88q^{54} \) \(\mathstrut -\mathstrut 48q^{55} \) \(\mathstrut +\mathstrut 19q^{56} \) \(\mathstrut -\mathstrut 66q^{57} \) \(\mathstrut -\mathstrut 110q^{58} \) \(\mathstrut -\mathstrut 66q^{59} \) \(\mathstrut -\mathstrut 118q^{60} \) \(\mathstrut -\mathstrut 80q^{61} \) \(\mathstrut -\mathstrut 41q^{62} \) \(\mathstrut -\mathstrut 52q^{63} \) \(\mathstrut +\mathstrut 33q^{64} \) \(\mathstrut -\mathstrut 17q^{65} \) \(\mathstrut -\mathstrut 86q^{66} \) \(\mathstrut -\mathstrut 114q^{67} \) \(\mathstrut -\mathstrut 77q^{68} \) \(\mathstrut -\mathstrut 49q^{69} \) \(\mathstrut -\mathstrut 56q^{70} \) \(\mathstrut +\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 5q^{72} \) \(\mathstrut -\mathstrut 143q^{73} \) \(\mathstrut -\mathstrut 30q^{74} \) \(\mathstrut -\mathstrut 97q^{75} \) \(\mathstrut -\mathstrut 104q^{76} \) \(\mathstrut -\mathstrut 116q^{77} \) \(\mathstrut -\mathstrut 33q^{78} \) \(\mathstrut -\mathstrut 31q^{79} \) \(\mathstrut -\mathstrut 83q^{80} \) \(\mathstrut -\mathstrut q^{81} \) \(\mathstrut -\mathstrut 72q^{82} \) \(\mathstrut -\mathstrut 70q^{83} \) \(\mathstrut -\mathstrut 64q^{84} \) \(\mathstrut -\mathstrut 85q^{85} \) \(\mathstrut -\mathstrut 43q^{87} \) \(\mathstrut -\mathstrut 149q^{88} \) \(\mathstrut -\mathstrut 130q^{89} \) \(\mathstrut +\mathstrut 42q^{90} \) \(\mathstrut -\mathstrut 35q^{91} \) \(\mathstrut -\mathstrut 31q^{92} \) \(\mathstrut -\mathstrut 149q^{93} \) \(\mathstrut -\mathstrut 94q^{94} \) \(\mathstrut -\mathstrut 9q^{95} \) \(\mathstrut +\mathstrut 6q^{96} \) \(\mathstrut -\mathstrut 211q^{97} \) \(\mathstrut -\mathstrut 18q^{98} \) \(\mathstrut -\mathstrut 19q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.76716 −2.20267 5.65717 0.836026 6.09513 −1.25752 −10.1200 1.85174 −2.31342
1.2 −2.74141 2.30375 5.51534 −1.31886 −6.31554 1.25952 −9.63701 2.30728 3.61554
1.3 −2.73133 −0.575375 5.46014 −2.64139 1.57154 −4.90025 −9.45076 −2.66894 7.21448
1.4 −2.69892 1.36364 5.28418 3.25523 −3.68037 0.105698 −8.86375 −1.14047 −8.78561
1.5 −2.69176 −2.97285 5.24555 2.64194 8.00219 −3.02993 −8.73623 5.83784 −7.11145
1.6 −2.68460 −1.10941 5.20709 3.69885 2.97832 2.40865 −8.60976 −1.76921 −9.92993
1.7 −2.63479 0.411921 4.94210 −2.62173 −1.08532 0.446803 −7.75181 −2.83032 6.90770
1.8 −2.57093 1.68353 4.60966 0.0447393 −4.32822 −3.24015 −6.70923 −0.165740 −0.115021
1.9 −2.46705 3.03255 4.08634 −1.27620 −7.48147 0.505683 −5.14712 6.19639 3.14846
1.10 −2.46471 −1.16892 4.07480 −2.61176 2.88105 −0.765646 −5.11379 −1.63363 6.43723
1.11 −2.45879 −0.163481 4.04563 2.51114 0.401964 −0.639591 −5.02975 −2.97327 −6.17435
1.12 −2.44772 −0.651188 3.99131 −1.37302 1.59392 0.683234 −4.87416 −2.57595 3.36077
1.13 −2.41146 1.80060 3.81513 0.537438 −4.34207 4.37842 −4.37711 0.242159 −1.29601
1.14 −2.40138 1.08484 3.76663 −1.87801 −2.60511 −2.74065 −4.24236 −1.82313 4.50981
1.15 −2.37028 −0.677898 3.61822 2.58676 1.60681 −3.88263 −3.83563 −2.54045 −6.13133
1.16 −2.33017 −2.83003 3.42967 −2.62223 6.59443 3.30505 −3.33137 5.00905 6.11023
1.17 −2.31195 2.01743 3.34512 −2.72339 −4.66419 −3.92860 −3.10985 1.07001 6.29634
1.18 −2.30251 −2.68436 3.30157 −0.273715 6.18077 3.09928 −2.99689 4.20577 0.630233
1.19 −2.28070 −3.18519 3.20158 −4.19393 7.26446 −3.02488 −2.74045 7.14546 9.56509
1.20 −2.26111 −1.67317 3.11264 0.0442572 3.78322 2.69750 −2.51581 −0.200518 −0.100071
See next 80 embeddings (of 147 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.147
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

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