Properties

Label 8003.2.a.d
Level 8003
Weight 2
Character orbit 8003.a
Self dual yes
Analytic conductor 63.904
Analytic rank 0
Dimension 179
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: \(0\)
Dimension: \(179\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 179q + 8q^{2} + 15q^{3} + 202q^{4} + 27q^{5} + 18q^{6} + 23q^{7} + 21q^{8} + 214q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 179q + 8q^{2} + 15q^{3} + 202q^{4} + 27q^{5} + 18q^{6} + 23q^{7} + 21q^{8} + 214q^{9} + 28q^{10} + 21q^{11} + 46q^{12} + 113q^{13} - 2q^{14} + 30q^{15} + 240q^{16} + 48q^{17} + 40q^{18} + 35q^{19} + 24q^{20} + 56q^{21} + 22q^{22} + 16q^{23} + 54q^{24} + 266q^{25} + 60q^{27} + 64q^{28} + 34q^{29} - 19q^{30} + 60q^{31} + 15q^{32} + 65q^{33} + 31q^{34} - 20q^{35} + 282q^{36} + 169q^{37} + 52q^{38} + 20q^{39} + 74q^{40} + 20q^{41} + 34q^{42} + 43q^{43} + 56q^{44} + 139q^{45} + 13q^{46} + 73q^{47} + 88q^{48} + 292q^{49} + 12q^{50} + 8q^{51} + 225q^{52} + 179q^{53} - 16q^{54} + 72q^{55} - 17q^{56} + 62q^{57} + 125q^{58} + 68q^{59} + 116q^{60} + 96q^{61} + 71q^{62} + 52q^{63} + 309q^{64} - 5q^{65} + 90q^{67} + 122q^{68} + 111q^{69} + 72q^{70} + 26q^{71} + 65q^{72} + 139q^{73} - 82q^{74} + 55q^{75} + 146q^{76} + 76q^{77} - 9q^{78} + 29q^{79} + 68q^{80} + 231q^{81} + 84q^{82} + 8q^{83} - 24q^{84} + 115q^{85} - 20q^{86} + 47q^{87} + 143q^{88} + 150q^{89} + 34q^{90} + 113q^{91} - 31q^{92} + 195q^{93} + 131q^{94} + 55q^{95} + 90q^{96} + 235q^{97} + 84q^{98} + 7q^{99} + O(q^{100}) \)

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 −2.81186 −1.67550 5.90655 −2.52541 4.71126 3.13505 −10.9847 −0.192706 7.10109
1.2 −2.76280 0.0815042 5.63307 2.29049 −0.225180 −4.47769 −10.0374 −2.99336 −6.32817
1.3 −2.76009 2.82654 5.61808 3.76331 −7.80149 −3.62929 −9.98623 4.98931 −10.3871
1.4 −2.73492 −2.66806 5.47977 3.59226 7.29692 3.26568 −9.51690 4.11853 −9.82454
1.5 −2.72330 1.38182 5.41638 0.695892 −3.76310 2.22178 −9.30382 −1.09059 −1.89512
1.6 −2.69327 −0.453777 5.25372 −2.96502 1.22215 4.09118 −8.76316 −2.79409 7.98562
1.7 −2.68916 1.31955 5.23156 0.565625 −3.54848 −3.46548 −8.69016 −1.25878 −1.52105
1.8 −2.63717 2.57307 4.95467 −2.90004 −6.78562 1.48673 −7.79198 3.62067 7.64791
1.9 −2.62553 −3.09813 4.89340 −2.94807 8.13422 1.83284 −7.59671 6.59839 7.74024
1.10 −2.59548 −2.23952 4.73650 −0.915423 5.81261 −1.92878 −7.10252 2.01543 2.37596
1.11 −2.59447 −1.57672 4.73128 2.96648 4.09075 0.648960 −7.08623 −0.513957 −7.69644
1.12 −2.59279 0.176343 4.72258 −4.20399 −0.457220 0.364097 −7.05909 −2.96890 10.9001
1.13 −2.58313 −0.944028 4.67256 2.39597 2.43855 2.66460 −6.90357 −2.10881 −6.18909
1.14 −2.56401 2.69258 4.57412 −0.262266 −6.90379 3.89440 −6.60007 4.24998 0.672451
1.15 −2.52781 2.99330 4.38982 1.15266 −7.56649 −2.64816 −6.04101 5.95984 −2.91370
1.16 −2.48629 −1.57430 4.18165 −3.66584 3.91418 −5.15105 −5.42422 −0.521566 9.11435
1.17 −2.47698 3.33984 4.13542 −4.25899 −8.27272 3.67754 −5.28940 8.15455 10.5494
1.18 −2.47596 −1.58949 4.13039 −0.715359 3.93552 −0.683204 −5.27477 −0.473513 1.77120
1.19 −2.36148 1.10160 3.57657 1.64504 −2.60141 0.267733 −3.72302 −1.78647 −3.88472
1.20 −2.33610 −3.21364 3.45737 1.58018 7.50740 0.0419320 −3.40456 7.32750 −3.69146
See next 80 embeddings (of 179 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.179
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.d 179
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8003.2.a.d 179 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