Properties

Label 8027.2.a.c
Level 8027
Weight 2
Character orbit 8027.a
Self dual Yes
Analytic conductor 64.096
Analytic rank 1
Dimension 143
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: \(143\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 143q - 17q^{2} - 17q^{3} + 121q^{4} - 22q^{5} - 11q^{6} - 33q^{7} - 45q^{8} + 104q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 143q - 17q^{2} - 17q^{3} + 121q^{4} - 22q^{5} - 11q^{6} - 33q^{7} - 45q^{8} + 104q^{9} - 22q^{10} - 14q^{11} - 36q^{12} - 87q^{13} - 18q^{14} - 19q^{15} + 81q^{16} - 14q^{17} - 60q^{18} - 18q^{19} - 25q^{20} - 26q^{21} - 62q^{22} + 143q^{23} - 21q^{24} + 67q^{25} - 5q^{26} - 47q^{27} - 76q^{28} - 54q^{29} - 22q^{30} - 62q^{31} - 117q^{32} - 59q^{33} - 35q^{34} - 52q^{35} + 52q^{36} - 190q^{37} - 19q^{38} - 43q^{39} - 41q^{40} - 50q^{41} + 8q^{42} - 50q^{43} - 18q^{44} - 75q^{45} - 17q^{46} - 63q^{47} - 35q^{48} + 74q^{49} - 53q^{50} - 33q^{51} - 124q^{52} - 100q^{53} - 46q^{54} - 61q^{55} - 3q^{56} - 80q^{57} - 112q^{58} - 109q^{59} - 55q^{60} - 76q^{61} - 6q^{62} - 93q^{63} + 57q^{64} - 17q^{65} + 50q^{66} - 120q^{67} + 26q^{68} - 17q^{69} - 109q^{71} - 153q^{72} - 94q^{73} + 35q^{74} - 105q^{75} - 16q^{76} - 52q^{77} - 59q^{78} - 29q^{79} - 30q^{80} + 39q^{81} - 65q^{82} + 8q^{83} + 11q^{84} - 155q^{85} - 15q^{86} - 25q^{87} - 139q^{88} + 6q^{89} + 82q^{90} - 34q^{91} + 121q^{92} - 151q^{93} - 3q^{94} - 70q^{95} - 23q^{96} - 203q^{97} - 18q^{98} - 49q^{99} + O(q^{100}) \)

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 −2.81318 −2.25224 5.91397 2.72187 6.33595 −2.92129 −11.0107 2.07257 −7.65711
1.2 −2.73897 −2.10858 5.50198 −1.32967 5.77534 4.16128 −9.59184 1.44610 3.64193
1.3 −2.72223 2.61290 5.41054 −3.36664 −7.11292 −3.38304 −9.28427 3.82726 9.16478
1.4 −2.70535 −0.945977 5.31892 2.14258 2.55920 −0.218411 −8.97883 −2.10513 −5.79642
1.5 −2.66984 −0.755713 5.12803 0.937284 2.01763 2.29767 −8.35133 −2.42890 −2.50240
1.6 −2.65785 2.82218 5.06415 0.881121 −7.50092 1.80840 −8.14403 4.96471 −2.34188
1.7 −2.62887 1.58844 4.91095 0.705653 −4.17581 −0.559393 −7.65249 −0.476845 −1.85507
1.8 −2.59213 0.439138 4.71916 1.76571 −1.13830 3.87571 −7.04843 −2.80716 −4.57697
1.9 −2.56363 3.26823 4.57221 −1.87479 −8.37854 −1.87590 −6.59421 7.68132 4.80627
1.10 −2.54714 −2.88541 4.48790 −0.694174 7.34952 −2.36870 −6.33703 5.32557 1.76816
1.11 −2.53949 −2.72406 4.44903 −2.80223 6.91773 −4.07042 −6.21931 4.42048 7.11625
1.12 −2.53769 0.0556295 4.43986 2.89276 −0.141170 −5.18186 −6.19160 −2.99691 −7.34093
1.13 −2.48946 −0.455224 4.19741 −1.13104 1.13326 −1.16006 −5.47036 −2.79277 2.81568
1.14 −2.42374 0.415987 3.87452 −3.49995 −1.00824 −1.51919 −4.54334 −2.82696 8.48296
1.15 −2.40779 2.53147 3.79745 0.438044 −6.09525 1.85360 −4.32788 3.40834 −1.05472
1.16 −2.40357 1.04878 3.77713 −2.29703 −2.52082 −0.387376 −4.27144 −1.90005 5.52106
1.17 −2.32772 −2.91674 3.41827 2.71745 6.78934 4.37081 −3.30132 5.50736 −6.32547
1.18 −2.31697 −3.13483 3.36836 −3.69960 7.26332 1.63548 −3.17044 6.82718 8.57187
1.19 −2.31347 1.92997 3.35213 3.01701 −4.46493 −2.82894 −3.12810 0.724803 −6.97976
1.20 −2.30190 0.450462 3.29874 −0.676454 −1.03692 2.59801 −2.98957 −2.79708 1.55713
See next 80 embeddings (of 143 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.143
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 \(T_{2}^{143} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\).