Properties

Label 8027.2.a.e
Level 8027
Weight 2
Character orbit 8027.a
Self dual Yes
Analytic conductor 64.096
Analytic rank 0
Dimension 169
CM No

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Newspace parameters

Level: \( N \) = \( 8027 = 23 \cdot 349 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(169\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 169q + 6q^{2} + 2q^{3} + 186q^{4} + 28q^{5} + 5q^{6} + 38q^{7} + 18q^{8} + 185q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 169q + 6q^{2} + 2q^{3} + 186q^{4} + 28q^{5} + 5q^{6} + 38q^{7} + 18q^{8} + 185q^{9} + 28q^{10} + 17q^{11} + 10q^{12} + 91q^{13} + 20q^{14} + 29q^{15} + 200q^{16} + 16q^{17} + 31q^{18} + 30q^{19} + 45q^{20} + 49q^{21} + 76q^{22} - 169q^{23} + 3q^{24} + 241q^{25} - 15q^{26} + 14q^{27} + 118q^{28} + 23q^{29} + 52q^{30} + 45q^{31} + 42q^{32} + 62q^{33} + 65q^{34} - 16q^{35} + 199q^{36} + 226q^{37} + 49q^{38} + 17q^{39} + 95q^{40} + 19q^{41} + 32q^{42} + 71q^{43} + 46q^{44} + 127q^{45} - 6q^{46} + 27q^{47} + 5q^{48} + 239q^{49} + 24q^{50} + 39q^{51} + 154q^{52} + 111q^{53} + 22q^{54} + 47q^{55} + 39q^{56} + 122q^{57} + 146q^{58} - 73q^{59} + 109q^{60} + 125q^{61} + 14q^{62} + 109q^{63} + 260q^{64} + 73q^{65} + 26q^{66} + 152q^{67} + 40q^{68} - 2q^{69} + 76q^{70} - 79q^{71} + 126q^{72} + 106q^{73} + 23q^{74} + 12q^{75} + 122q^{76} + 63q^{77} + 101q^{78} + 82q^{79} + 134q^{80} + 225q^{81} + 125q^{82} + 28q^{83} + 73q^{84} + 197q^{85} + 97q^{86} + 18q^{87} + 183q^{88} + 54q^{89} + 52q^{90} + 106q^{91} - 186q^{92} + 194q^{93} + q^{94} + 18q^{95} - 39q^{96} + 239q^{97} + 5q^{98} + 85q^{99} + O(q^{100}) \)

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 −2.75446 1.69224 5.58704 1.99190 −4.66119 −2.92850 −9.88036 −0.136337 −5.48661
1.2 −2.75254 −1.96907 5.57647 −0.0473576 5.41994 2.07710 −9.84438 0.877234 0.130354
1.3 −2.71035 −1.96664 5.34597 2.92225 5.33028 3.98832 −9.06874 0.867686 −7.92031
1.4 −2.70848 3.38397 5.33587 −0.801714 −9.16542 2.62162 −9.03513 8.45127 2.17143
1.5 −2.70691 1.62616 5.32735 −1.60888 −4.40186 −2.81542 −9.00682 −0.355610 4.35510
1.6 −2.69664 −0.711836 5.27186 2.29086 1.91957 3.32005 −8.82303 −2.49329 −6.17762
1.7 −2.69608 1.22457 5.26883 −1.75306 −3.30153 4.29034 −8.81301 −1.50043 4.72638
1.8 −2.66018 0.0465626 5.07657 −3.78943 −0.123865 2.50882 −8.18425 −2.99783 10.0806
1.9 −2.60952 −0.136825 4.80961 −0.260304 0.357049 −0.298256 −7.33174 −2.98128 0.679270
1.10 −2.60584 −2.87607 4.79042 −4.02377 7.49460 0.529095 −7.27140 5.27181 10.4853
1.11 −2.57271 0.131094 4.61881 4.05012 −0.337267 −4.42802 −6.73744 −2.98281 −10.4198
1.12 −2.50053 2.23425 4.25264 −3.72100 −5.58681 −1.83421 −5.63280 1.99189 9.30447
1.13 −2.48779 −1.56706 4.18912 −0.470974 3.89852 −0.335999 −5.44607 −0.544327 1.17169
1.14 −2.47925 −2.94109 4.14669 −0.477027 7.29170 −3.55930 −5.32218 5.65002 1.18267
1.15 −2.47225 −1.54593 4.11203 3.04029 3.82192 −2.57940 −5.22147 −0.610108 −7.51637
1.16 −2.43156 2.09261 3.91247 2.37281 −5.08829 3.03145 −4.65029 1.37900 −5.76963
1.17 −2.35712 0.851105 3.55600 1.53859 −2.00615 0.407410 −3.66768 −2.27562 −3.62663
1.18 −2.35439 −0.664496 3.54317 −2.57609 1.56449 5.27951 −3.63324 −2.55844 6.06514
1.19 −2.32136 −1.73102 3.38869 −3.82853 4.01832 −3.14873 −3.22365 −0.00355516 8.88737
1.20 −2.31715 2.98534 3.36921 4.10060 −6.91750 4.34971 −3.17266 5.91228 −9.50172
See next 80 embeddings (of 169 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.169
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(23\) \(1\)
\(349\) \(-1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{169} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).