Properties

Label 8027.2.a.d
Level 8027
Weight 2
Character orbit 8027.a
Self dual Yes
Analytic conductor 64.096
Analytic rank 1
Dimension 149
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: \(1\)
Dimension: \(149\)
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.

\(\operatorname{Tr}(f)(q) = \) \(149q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 135q^{4} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut 33q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 134q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(149q \) \(\mathstrut -\mathstrut 5q^{2} \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 135q^{4} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 5q^{6} \) \(\mathstrut -\mathstrut 33q^{7} \) \(\mathstrut -\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 134q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut -\mathstrut 20q^{11} \) \(\mathstrut -\mathstrut 32q^{12} \) \(\mathstrut -\mathstrut 73q^{13} \) \(\mathstrut -\mathstrut 18q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 99q^{16} \) \(\mathstrut -\mathstrut 32q^{17} \) \(\mathstrut -\mathstrut 50q^{18} \) \(\mathstrut -\mathstrut 32q^{19} \) \(\mathstrut -\mathstrut 67q^{20} \) \(\mathstrut -\mathstrut 36q^{21} \) \(\mathstrut -\mathstrut 78q^{22} \) \(\mathstrut -\mathstrut 149q^{23} \) \(\mathstrut -\mathstrut 27q^{24} \) \(\mathstrut +\mathstrut 75q^{25} \) \(\mathstrut +\mathstrut 7q^{26} \) \(\mathstrut -\mathstrut 23q^{27} \) \(\mathstrut -\mathstrut 90q^{28} \) \(\mathstrut -\mathstrut 20q^{29} \) \(\mathstrut -\mathstrut 12q^{30} \) \(\mathstrut -\mathstrut 34q^{31} \) \(\mathstrut -\mathstrut 35q^{32} \) \(\mathstrut -\mathstrut 63q^{33} \) \(\mathstrut -\mathstrut 43q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 98q^{36} \) \(\mathstrut -\mathstrut 228q^{37} \) \(\mathstrut -\mathstrut 25q^{38} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 79q^{40} \) \(\mathstrut -\mathstrut 4q^{41} \) \(\mathstrut -\mathstrut 88q^{42} \) \(\mathstrut -\mathstrut 70q^{43} \) \(\mathstrut -\mathstrut 80q^{44} \) \(\mathstrut -\mathstrut 153q^{45} \) \(\mathstrut +\mathstrut 5q^{46} \) \(\mathstrut -\mathstrut 3q^{47} \) \(\mathstrut -\mathstrut 95q^{48} \) \(\mathstrut +\mathstrut 86q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 57q^{51} \) \(\mathstrut -\mathstrut 146q^{52} \) \(\mathstrut -\mathstrut 110q^{53} \) \(\mathstrut -\mathstrut 18q^{54} \) \(\mathstrut -\mathstrut 33q^{55} \) \(\mathstrut -\mathstrut 75q^{56} \) \(\mathstrut -\mathstrut 132q^{57} \) \(\mathstrut -\mathstrut 92q^{58} \) \(\mathstrut +\mathstrut 41q^{59} \) \(\mathstrut -\mathstrut 107q^{60} \) \(\mathstrut -\mathstrut 82q^{61} \) \(\mathstrut -\mathstrut 34q^{62} \) \(\mathstrut -\mathstrut 99q^{63} \) \(\mathstrut +\mathstrut 35q^{64} \) \(\mathstrut -\mathstrut 47q^{65} \) \(\mathstrut -\mathstrut 58q^{66} \) \(\mathstrut -\mathstrut 162q^{67} \) \(\mathstrut -\mathstrut 80q^{68} \) \(\mathstrut +\mathstrut 5q^{69} \) \(\mathstrut -\mathstrut 88q^{70} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut 117q^{72} \) \(\mathstrut -\mathstrut 124q^{73} \) \(\mathstrut -\mathstrut 51q^{74} \) \(\mathstrut -\mathstrut q^{75} \) \(\mathstrut -\mathstrut 74q^{76} \) \(\mathstrut -\mathstrut 56q^{77} \) \(\mathstrut -\mathstrut 95q^{78} \) \(\mathstrut -\mathstrut 89q^{79} \) \(\mathstrut -\mathstrut 90q^{80} \) \(\mathstrut +\mathstrut 93q^{81} \) \(\mathstrut -\mathstrut 91q^{82} \) \(\mathstrut -\mathstrut 64q^{83} \) \(\mathstrut -\mathstrut 93q^{84} \) \(\mathstrut -\mathstrut 155q^{85} \) \(\mathstrut -\mathstrut 21q^{86} \) \(\mathstrut -\mathstrut 49q^{87} \) \(\mathstrut -\mathstrut 263q^{88} \) \(\mathstrut -\mathstrut 60q^{89} \) \(\mathstrut -\mathstrut 122q^{90} \) \(\mathstrut -\mathstrut 130q^{91} \) \(\mathstrut -\mathstrut 135q^{92} \) \(\mathstrut -\mathstrut 179q^{93} \) \(\mathstrut -\mathstrut 21q^{94} \) \(\mathstrut +\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 17q^{96} \) \(\mathstrut -\mathstrut 199q^{97} \) \(\mathstrut -\mathstrut 72q^{98} \) \(\mathstrut -\mathstrut 91q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.77862 1.96044 5.72072 −1.21161 −5.44733 1.22758 −10.3385 0.843341 3.36659
1.2 −2.75811 −1.16707 5.60719 −1.99614 3.21892 −2.42048 −9.94903 −1.63794 5.50558
1.3 −2.74408 1.08258 5.52999 4.29779 −2.97068 1.02479 −9.68658 −1.82803 −11.7935
1.4 −2.74361 −3.40606 5.52740 −0.590422 9.34489 −1.99716 −9.67782 8.60122 1.61989
1.5 −2.63043 0.0298964 4.91916 −2.77768 −0.0786403 −4.82248 −7.67864 −2.99911 7.30650
1.6 −2.60291 2.78039 4.77512 −1.36371 −7.23709 −4.03414 −7.22339 4.73056 3.54962
1.7 −2.59099 −0.493919 4.71322 1.04082 1.27974 −3.08433 −7.02991 −2.75604 −2.69675
1.8 −2.57108 2.45924 4.61046 0.658521 −6.32291 1.43884 −6.71170 3.04787 −1.69311
1.9 −2.55845 −2.16736 4.54566 2.09071 5.54507 −1.08828 −6.51294 1.69743 −5.34897
1.10 −2.55473 −3.25140 4.52663 2.74770 8.30644 1.12543 −6.45485 7.57160 −7.01962
1.11 −2.54629 −1.60651 4.48361 −2.62778 4.09064 1.52719 −6.32399 −0.419134 6.69110
1.12 −2.37150 0.0708005 3.62401 3.28290 −0.167903 −0.427363 −3.85135 −2.99499 −7.78539
1.13 −2.34386 0.672591 3.49366 0.169027 −1.57646 4.26981 −3.50093 −2.54762 −0.396175
1.14 −2.34025 −2.24282 3.47677 1.33607 5.24876 2.78387 −3.45602 2.03023 −3.12673
1.15 −2.33451 2.56074 3.44993 1.12501 −5.97807 −4.54116 −3.38489 3.55739 −2.62635
1.16 −2.31791 −1.39322 3.37270 −1.41282 3.22936 3.95674 −3.18178 −1.05893 3.27480
1.17 −2.27388 0.787573 3.17053 −4.28008 −1.79085 1.25028 −2.66164 −2.37973 9.73239
1.18 −2.26494 1.60784 3.12995 −1.10184 −3.64166 0.234772 −2.55928 −0.414855 2.49560
1.19 −2.21508 0.0631249 2.90657 −0.959004 −0.139827 −0.280080 −2.00812 −2.99602 2.12427
1.20 −2.20146 −2.87956 2.84641 0.0712627 6.33923 3.68192 −1.86333 5.29189 −0.156882
See next 80 embeddings (of 149 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.149
Significant digits:
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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 \(T_{2}^{149} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).