Properties

Label 8033.2.a.b
Level 8033
Weight 2
Character orbit 8033.a
Self dual Yes
Analytic conductor 64.144
Analytic rank 1
Dimension 153
CM No

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Newspace parameters

Level: \( N \) = \( 8033 = 29 \cdot 277 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8033.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.1438279437\)
Analytic rank: \(1\)
Dimension: \(153\)
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.

\(\operatorname{Tr}(f)(q) = \) \(153q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 135q^{4} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 76q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 133q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(153q \) \(\mathstrut -\mathstrut 3q^{2} \) \(\mathstrut -\mathstrut 12q^{3} \) \(\mathstrut +\mathstrut 135q^{4} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 17q^{6} \) \(\mathstrut -\mathstrut 76q^{7} \) \(\mathstrut -\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 133q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 39q^{12} \) \(\mathstrut -\mathstrut 65q^{13} \) \(\mathstrut +\mathstrut q^{14} \) \(\mathstrut -\mathstrut 26q^{15} \) \(\mathstrut +\mathstrut 107q^{16} \) \(\mathstrut -\mathstrut 20q^{17} \) \(\mathstrut -\mathstrut 21q^{18} \) \(\mathstrut -\mathstrut 65q^{19} \) \(\mathstrut -\mathstrut 23q^{20} \) \(\mathstrut -\mathstrut 24q^{21} \) \(\mathstrut -\mathstrut 59q^{22} \) \(\mathstrut -\mathstrut 62q^{23} \) \(\mathstrut -\mathstrut 59q^{24} \) \(\mathstrut +\mathstrut 102q^{25} \) \(\mathstrut -\mathstrut 18q^{26} \) \(\mathstrut -\mathstrut 57q^{27} \) \(\mathstrut -\mathstrut 155q^{28} \) \(\mathstrut -\mathstrut 153q^{29} \) \(\mathstrut -\mathstrut 82q^{30} \) \(\mathstrut -\mathstrut 49q^{31} \) \(\mathstrut -\mathstrut 17q^{32} \) \(\mathstrut -\mathstrut 59q^{33} \) \(\mathstrut -\mathstrut 68q^{34} \) \(\mathstrut -\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 74q^{36} \) \(\mathstrut -\mathstrut 30q^{37} \) \(\mathstrut -\mathstrut 67q^{38} \) \(\mathstrut -\mathstrut 47q^{39} \) \(\mathstrut -\mathstrut 108q^{40} \) \(\mathstrut -\mathstrut 9q^{41} \) \(\mathstrut -\mathstrut 62q^{42} \) \(\mathstrut -\mathstrut 90q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut -\mathstrut 56q^{45} \) \(\mathstrut -\mathstrut 52q^{46} \) \(\mathstrut -\mathstrut 54q^{47} \) \(\mathstrut -\mathstrut 76q^{48} \) \(\mathstrut +\mathstrut 101q^{49} \) \(\mathstrut -\mathstrut 36q^{50} \) \(\mathstrut -\mathstrut 60q^{51} \) \(\mathstrut -\mathstrut 191q^{52} \) \(\mathstrut -\mathstrut 38q^{53} \) \(\mathstrut -\mathstrut 82q^{54} \) \(\mathstrut -\mathstrut 215q^{55} \) \(\mathstrut +\mathstrut 24q^{56} \) \(\mathstrut -\mathstrut 52q^{57} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut -\mathstrut 55q^{59} \) \(\mathstrut -\mathstrut 60q^{60} \) \(\mathstrut -\mathstrut 90q^{61} \) \(\mathstrut -\mathstrut 66q^{62} \) \(\mathstrut -\mathstrut 229q^{63} \) \(\mathstrut +\mathstrut 52q^{64} \) \(\mathstrut -\mathstrut 67q^{65} \) \(\mathstrut -\mathstrut 29q^{66} \) \(\mathstrut -\mathstrut 114q^{67} \) \(\mathstrut -\mathstrut 78q^{68} \) \(\mathstrut -\mathstrut 68q^{69} \) \(\mathstrut -\mathstrut 61q^{70} \) \(\mathstrut -\mathstrut 52q^{71} \) \(\mathstrut -\mathstrut 47q^{72} \) \(\mathstrut -\mathstrut 83q^{73} \) \(\mathstrut -\mathstrut 21q^{74} \) \(\mathstrut -\mathstrut 47q^{75} \) \(\mathstrut -\mathstrut 100q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 17q^{78} \) \(\mathstrut -\mathstrut 151q^{79} \) \(\mathstrut -\mathstrut 24q^{80} \) \(\mathstrut +\mathstrut 81q^{81} \) \(\mathstrut -\mathstrut 151q^{82} \) \(\mathstrut -\mathstrut 94q^{83} \) \(\mathstrut -\mathstrut 84q^{84} \) \(\mathstrut -\mathstrut 77q^{85} \) \(\mathstrut -\mathstrut 43q^{86} \) \(\mathstrut +\mathstrut 12q^{87} \) \(\mathstrut -\mathstrut 121q^{88} \) \(\mathstrut +\mathstrut 11q^{89} \) \(\mathstrut -\mathstrut 14q^{90} \) \(\mathstrut -\mathstrut 66q^{91} \) \(\mathstrut -\mathstrut 156q^{92} \) \(\mathstrut -\mathstrut 66q^{93} \) \(\mathstrut -\mathstrut 22q^{94} \) \(\mathstrut -\mathstrut 67q^{95} \) \(\mathstrut -\mathstrut 131q^{96} \) \(\mathstrut -\mathstrut 78q^{97} \) \(\mathstrut -\mathstrut 67q^{98} \) \(\mathstrut -\mathstrut 41q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.80428 −1.04470 5.86401 3.49231 2.92963 −4.86354 −10.8358 −1.90861 −9.79343
1.2 −2.66806 0.0181973 5.11854 3.52830 −0.0485515 0.996923 −8.32043 −2.99967 −9.41371
1.3 −2.65443 −2.20662 5.04598 0.185737 5.85731 −3.52416 −8.08534 1.86917 −0.493026
1.4 −2.63089 0.747844 4.92157 1.13408 −1.96749 1.55238 −7.68633 −2.44073 −2.98365
1.5 −2.62862 3.02798 4.90963 2.24361 −7.95940 −3.55148 −7.64830 6.16867 −5.89760
1.6 −2.62733 2.34750 4.90284 −3.13713 −6.16764 −4.86517 −7.62672 2.51073 8.24227
1.7 −2.61377 −0.423851 4.83180 −1.13525 1.10785 −2.59527 −7.40168 −2.82035 2.96728
1.8 −2.59993 −1.45421 4.75963 −1.16680 3.78083 3.18169 −7.17483 −0.885282 3.03360
1.9 −2.59547 1.19515 4.73648 −3.51521 −3.10198 1.20876 −7.10244 −1.57161 9.12363
1.10 −2.57712 −3.09746 4.64157 −1.30860 7.98254 0.204481 −6.80764 6.59427 3.37243
1.11 −2.56362 2.58113 4.57213 0.513446 −6.61703 0.254616 −6.59395 3.66224 −1.31628
1.12 −2.54311 2.35643 4.46742 −1.04349 −5.99266 0.854661 −6.27493 2.55275 2.65370
1.13 −2.47232 −2.46852 4.11238 2.27915 6.10297 −3.16815 −5.22247 3.09358 −5.63478
1.14 −2.31211 −1.42285 3.34587 1.74031 3.28979 1.79626 −3.11180 −0.975501 −4.02380
1.15 −2.31178 −3.06195 3.34432 1.34142 7.07855 1.68714 −3.10776 6.37553 −3.10106
1.16 −2.27026 −0.124315 3.15409 1.98639 0.282227 3.17086 −2.62008 −2.98455 −4.50963
1.17 −2.25257 −2.81760 3.07408 −4.05860 6.34684 −4.96798 −2.41944 4.93885 9.14228
1.18 −2.25207 0.273415 3.07181 −3.19262 −0.615750 −2.20872 −2.41378 −2.92524 7.19000
1.19 −2.24392 1.38924 3.03516 −1.50344 −3.11734 0.570287 −2.32282 −1.07002 3.37359
1.20 −2.22882 1.59395 2.96765 3.65354 −3.55262 −2.56474 −2.15671 −0.459333 −8.14309
See next 80 embeddings (of 153 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.153
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(29\) \(1\)
\(277\) \(1\)

Hecke kernels

This newform can be constructed as the kernel of the linear operator \(T_{2}^{153} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\).