Properties

Label 4027.2.a.b
Level 4027
Weight 2
Character orbit 4027.a
Self dual Yes
Analytic conductor 32.156
Analytic rank 1
Dimension 159
CM No

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Newspace parameters

Level: \( N \) = \( 4027 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4027.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.155756894\)
Analytic rank: \(1\)
Dimension: \(159\)
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.

\(\operatorname{Tr}(f)(q) = \) \(159q \) \(\mathstrut -\mathstrut 22q^{2} \) \(\mathstrut -\mathstrut 19q^{3} \) \(\mathstrut +\mathstrut 148q^{4} \) \(\mathstrut -\mathstrut 70q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 66q^{8} \) \(\mathstrut +\mathstrut 126q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(159q \) \(\mathstrut -\mathstrut 22q^{2} \) \(\mathstrut -\mathstrut 19q^{3} \) \(\mathstrut +\mathstrut 148q^{4} \) \(\mathstrut -\mathstrut 70q^{5} \) \(\mathstrut -\mathstrut 23q^{6} \) \(\mathstrut -\mathstrut 19q^{7} \) \(\mathstrut -\mathstrut 66q^{8} \) \(\mathstrut +\mathstrut 126q^{9} \) \(\mathstrut -\mathstrut 23q^{10} \) \(\mathstrut -\mathstrut 33q^{11} \) \(\mathstrut -\mathstrut 57q^{12} \) \(\mathstrut -\mathstrut 90q^{13} \) \(\mathstrut -\mathstrut 28q^{14} \) \(\mathstrut -\mathstrut 22q^{15} \) \(\mathstrut +\mathstrut 130q^{16} \) \(\mathstrut -\mathstrut 145q^{17} \) \(\mathstrut -\mathstrut 50q^{18} \) \(\mathstrut -\mathstrut 28q^{19} \) \(\mathstrut -\mathstrut 121q^{20} \) \(\mathstrut -\mathstrut 69q^{21} \) \(\mathstrut -\mathstrut 26q^{22} \) \(\mathstrut -\mathstrut 79q^{23} \) \(\mathstrut -\mathstrut 62q^{24} \) \(\mathstrut +\mathstrut 123q^{25} \) \(\mathstrut -\mathstrut 40q^{26} \) \(\mathstrut -\mathstrut 70q^{27} \) \(\mathstrut -\mathstrut 43q^{28} \) \(\mathstrut -\mathstrut 109q^{29} \) \(\mathstrut -\mathstrut 43q^{30} \) \(\mathstrut -\mathstrut 21q^{31} \) \(\mathstrut -\mathstrut 139q^{32} \) \(\mathstrut -\mathstrut 83q^{33} \) \(\mathstrut -\mathstrut 93q^{35} \) \(\mathstrut +\mathstrut 75q^{36} \) \(\mathstrut -\mathstrut 65q^{37} \) \(\mathstrut -\mathstrut 122q^{38} \) \(\mathstrut -\mathstrut 18q^{39} \) \(\mathstrut -\mathstrut 43q^{40} \) \(\mathstrut -\mathstrut 71q^{41} \) \(\mathstrut -\mathstrut 88q^{42} \) \(\mathstrut -\mathstrut 72q^{43} \) \(\mathstrut -\mathstrut 79q^{44} \) \(\mathstrut -\mathstrut 181q^{45} \) \(\mathstrut -\mathstrut 11q^{46} \) \(\mathstrut -\mathstrut 114q^{47} \) \(\mathstrut -\mathstrut 118q^{48} \) \(\mathstrut +\mathstrut 118q^{49} \) \(\mathstrut -\mathstrut 77q^{50} \) \(\mathstrut -\mathstrut 29q^{51} \) \(\mathstrut -\mathstrut 169q^{52} \) \(\mathstrut -\mathstrut 220q^{53} \) \(\mathstrut -\mathstrut 80q^{54} \) \(\mathstrut -\mathstrut 37q^{55} \) \(\mathstrut -\mathstrut 72q^{56} \) \(\mathstrut -\mathstrut 90q^{57} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 60q^{59} \) \(\mathstrut -\mathstrut 42q^{60} \) \(\mathstrut -\mathstrut 108q^{61} \) \(\mathstrut -\mathstrut 152q^{62} \) \(\mathstrut -\mathstrut 65q^{63} \) \(\mathstrut +\mathstrut 114q^{64} \) \(\mathstrut -\mathstrut 81q^{65} \) \(\mathstrut -\mathstrut 40q^{66} \) \(\mathstrut -\mathstrut 50q^{67} \) \(\mathstrut -\mathstrut 319q^{68} \) \(\mathstrut -\mathstrut 103q^{69} \) \(\mathstrut +\mathstrut 4q^{70} \) \(\mathstrut -\mathstrut 7q^{71} \) \(\mathstrut -\mathstrut 129q^{72} \) \(\mathstrut -\mathstrut 94q^{73} \) \(\mathstrut -\mathstrut 79q^{74} \) \(\mathstrut -\mathstrut 59q^{75} \) \(\mathstrut -\mathstrut 46q^{76} \) \(\mathstrut -\mathstrut 329q^{77} \) \(\mathstrut +\mathstrut 8q^{78} \) \(\mathstrut -\mathstrut 18q^{79} \) \(\mathstrut -\mathstrut 190q^{80} \) \(\mathstrut +\mathstrut 59q^{81} \) \(\mathstrut -\mathstrut 56q^{82} \) \(\mathstrut -\mathstrut 201q^{83} \) \(\mathstrut -\mathstrut 71q^{84} \) \(\mathstrut -\mathstrut 26q^{85} \) \(\mathstrut -\mathstrut 52q^{86} \) \(\mathstrut -\mathstrut 126q^{87} \) \(\mathstrut -\mathstrut 66q^{88} \) \(\mathstrut -\mathstrut 114q^{89} \) \(\mathstrut -\mathstrut 33q^{90} \) \(\mathstrut -\mathstrut 30q^{91} \) \(\mathstrut -\mathstrut 204q^{92} \) \(\mathstrut -\mathstrut 125q^{93} \) \(\mathstrut +\mathstrut 9q^{94} \) \(\mathstrut -\mathstrut 84q^{95} \) \(\mathstrut -\mathstrut 88q^{96} \) \(\mathstrut -\mathstrut 56q^{97} \) \(\mathstrut -\mathstrut 110q^{98} \) \(\mathstrut -\mathstrut 46q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.82139 1.96833 5.96026 2.22438 −5.55342 0.144940 −11.1735 0.874306 −6.27587
1.2 −2.78842 −1.28715 5.77530 −4.20295 3.58911 −2.09011 −10.5271 −1.34326 11.7196
1.3 −2.73932 −1.57093 5.50386 0.430202 4.30328 4.35305 −9.59817 −0.532177 −1.17846
1.4 −2.73389 −3.04946 5.47414 −1.23983 8.33688 −1.91443 −9.49790 6.29922 3.38954
1.5 −2.72666 0.318995 5.43469 −1.22389 −0.869792 −4.59347 −9.36524 −2.89824 3.33713
1.6 −2.70494 2.29108 5.31668 −3.64034 −6.19723 2.95034 −8.97141 2.24905 9.84688
1.7 −2.69495 1.90961 5.26276 −0.957907 −5.14631 0.102731 −8.79297 0.646618 2.58151
1.8 −2.64324 2.50355 4.98674 1.52675 −6.61749 −4.42325 −7.89468 3.26775 −4.03556
1.9 −2.63499 −1.76075 4.94319 1.57936 4.63957 3.18044 −7.75529 0.100248 −4.16161
1.10 −2.59596 −2.97309 4.73903 −2.99704 7.71803 3.05793 −7.11041 5.83925 7.78021
1.11 −2.59401 −2.55671 4.72888 1.35267 6.63213 −3.48116 −7.07874 3.53677 −3.50885
1.12 −2.58046 0.749522 4.65878 −1.56103 −1.93411 3.58823 −6.86087 −2.43822 4.02819
1.13 −2.57109 −0.605717 4.61051 3.41025 1.55735 −4.02437 −6.71185 −2.63311 −8.76807
1.14 −2.54982 3.26459 4.50158 −1.30834 −8.32411 3.58480 −6.37858 7.65753 3.33603
1.15 −2.50942 −0.724063 4.29717 −3.46864 1.81698 2.45320 −5.76455 −2.47573 8.70427
1.16 −2.48250 −1.21941 4.16279 0.264971 3.02717 −2.37151 −5.36913 −1.51305 −0.657790
1.17 −2.46215 −2.74752 4.06218 4.08202 6.76481 −0.414263 −5.07738 4.54887 −10.0505
1.18 −2.44784 0.695688 3.99191 2.35878 −1.70293 2.06757 −4.87586 −2.51602 −5.77391
1.19 −2.37585 0.673958 3.64466 −1.12762 −1.60122 1.18808 −3.90747 −2.54578 2.67904
1.20 −2.29049 2.02403 3.24633 −4.01248 −4.63602 1.58118 −2.85471 1.09671 9.19054
See next 80 embeddings (of 159 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.159
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(4027\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{159} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(4027))\).