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.

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

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 −2.75446 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).