Properties

Label 8033.2.a.c
Level 8033
Weight 2
Character orbit 8033.a
Self dual Yes
Analytic conductor 64.144
Analytic rank 1
Dimension 154
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: \(154\)
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.

\(\operatorname{Tr}(f)(q) = \) \(154q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut -\mathstrut 36q^{3} \) \(\mathstrut +\mathstrut 142q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 68q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 146q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(154q \) \(\mathstrut -\mathstrut 12q^{2} \) \(\mathstrut -\mathstrut 36q^{3} \) \(\mathstrut +\mathstrut 142q^{4} \) \(\mathstrut -\mathstrut 9q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut -\mathstrut 68q^{7} \) \(\mathstrut -\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 146q^{9} \) \(\mathstrut -\mathstrut 40q^{10} \) \(\mathstrut -\mathstrut 36q^{11} \) \(\mathstrut -\mathstrut 67q^{12} \) \(\mathstrut -\mathstrut 51q^{13} \) \(\mathstrut -\mathstrut 19q^{14} \) \(\mathstrut -\mathstrut 48q^{15} \) \(\mathstrut +\mathstrut 122q^{16} \) \(\mathstrut -\mathstrut 54q^{17} \) \(\mathstrut -\mathstrut 46q^{18} \) \(\mathstrut -\mathstrut 73q^{19} \) \(\mathstrut -\mathstrut 21q^{20} \) \(\mathstrut -\mathstrut 8q^{21} \) \(\mathstrut -\mathstrut 23q^{22} \) \(\mathstrut -\mathstrut 38q^{23} \) \(\mathstrut -\mathstrut 17q^{24} \) \(\mathstrut +\mathstrut 133q^{25} \) \(\mathstrut -\mathstrut 20q^{26} \) \(\mathstrut -\mathstrut 129q^{27} \) \(\mathstrut -\mathstrut 99q^{28} \) \(\mathstrut +\mathstrut 154q^{29} \) \(\mathstrut -\mathstrut 10q^{30} \) \(\mathstrut -\mathstrut 91q^{31} \) \(\mathstrut -\mathstrut 88q^{32} \) \(\mathstrut -\mathstrut 39q^{33} \) \(\mathstrut -\mathstrut 42q^{34} \) \(\mathstrut -\mathstrut 36q^{35} \) \(\mathstrut +\mathstrut 101q^{36} \) \(\mathstrut -\mathstrut 50q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut -\mathstrut 33q^{39} \) \(\mathstrut -\mathstrut 92q^{40} \) \(\mathstrut -\mathstrut 31q^{41} \) \(\mathstrut -\mathstrut 62q^{42} \) \(\mathstrut -\mathstrut 154q^{43} \) \(\mathstrut -\mathstrut 42q^{44} \) \(\mathstrut -\mathstrut 14q^{45} \) \(\mathstrut -\mathstrut 24q^{46} \) \(\mathstrut -\mathstrut 140q^{47} \) \(\mathstrut -\mathstrut 118q^{48} \) \(\mathstrut +\mathstrut 126q^{49} \) \(\mathstrut -\mathstrut 5q^{50} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut -\mathstrut 133q^{52} \) \(\mathstrut -\mathstrut 40q^{53} \) \(\mathstrut +\mathstrut 14q^{54} \) \(\mathstrut -\mathstrut 203q^{55} \) \(\mathstrut -\mathstrut 44q^{56} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut -\mathstrut 12q^{58} \) \(\mathstrut +\mathstrut 5q^{59} \) \(\mathstrut -\mathstrut 28q^{60} \) \(\mathstrut -\mathstrut 106q^{61} \) \(\mathstrut -\mathstrut 30q^{62} \) \(\mathstrut -\mathstrut 145q^{63} \) \(\mathstrut +\mathstrut 111q^{64} \) \(\mathstrut -\mathstrut 15q^{65} \) \(\mathstrut -\mathstrut 49q^{66} \) \(\mathstrut -\mathstrut 78q^{67} \) \(\mathstrut -\mathstrut 118q^{68} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 43q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut -\mathstrut 152q^{72} \) \(\mathstrut -\mathstrut 137q^{73} \) \(\mathstrut +\mathstrut 9q^{74} \) \(\mathstrut -\mathstrut 129q^{75} \) \(\mathstrut -\mathstrut 204q^{76} \) \(\mathstrut -\mathstrut 76q^{77} \) \(\mathstrut +\mathstrut 15q^{78} \) \(\mathstrut -\mathstrut 141q^{79} \) \(\mathstrut -\mathstrut 44q^{80} \) \(\mathstrut +\mathstrut 122q^{81} \) \(\mathstrut -\mathstrut 71q^{82} \) \(\mathstrut -\mathstrut 90q^{83} \) \(\mathstrut +\mathstrut 92q^{84} \) \(\mathstrut -\mathstrut 41q^{85} \) \(\mathstrut +\mathstrut 9q^{86} \) \(\mathstrut -\mathstrut 36q^{87} \) \(\mathstrut -\mathstrut 109q^{88} \) \(\mathstrut -\mathstrut 51q^{89} \) \(\mathstrut -\mathstrut 82q^{90} \) \(\mathstrut -\mathstrut 22q^{91} \) \(\mathstrut -\mathstrut 8q^{92} \) \(\mathstrut -\mathstrut 10q^{93} \) \(\mathstrut -\mathstrut 106q^{94} \) \(\mathstrut -\mathstrut 55q^{95} \) \(\mathstrut -\mathstrut 49q^{96} \) \(\mathstrut -\mathstrut 140q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut -\mathstrut 101q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.82218 1.84090 5.96471 −0.0331224 −5.19535 1.38101 −11.1891 0.388906 0.0934774
1.2 −2.80099 −1.33349 5.84554 0.375260 3.73510 1.86520 −10.7713 −1.22179 −1.05110
1.3 −2.75023 2.46000 5.56375 3.61525 −6.76556 0.234720 −9.80113 3.05159 −9.94275
1.4 −2.73685 −2.64760 5.49034 −2.28975 7.24607 −2.70237 −9.55253 4.00977 6.26669
1.5 −2.71211 1.42746 5.35553 −2.33399 −3.87141 −3.68484 −9.10055 −0.962372 6.33003
1.6 −2.71067 −3.12256 5.34773 3.18562 8.46423 −1.32961 −9.07461 6.75039 −8.63517
1.7 −2.66581 −3.36665 5.10653 −1.10799 8.97484 −4.45627 −8.28140 8.33433 2.95369
1.8 −2.65912 −0.292744 5.07094 3.25351 0.778443 −0.266213 −8.16600 −2.91430 −8.65148
1.9 −2.60300 −1.50583 4.77561 −2.67375 3.91967 −1.75019 −7.22491 −0.732487 6.95977
1.10 −2.51869 0.856221 4.34380 2.85854 −2.15656 −2.09984 −5.90330 −2.26688 −7.19979
1.11 −2.50518 1.00988 4.27592 1.71073 −2.52992 5.05485 −5.70160 −1.98015 −4.28569
1.12 −2.49784 3.18584 4.23922 −0.569133 −7.95772 −1.98471 −5.59321 7.14957 1.42160
1.13 −2.47502 −2.70377 4.12575 2.22843 6.69190 4.05795 −5.26128 4.31037 −5.51542
1.14 −2.40713 −0.707338 3.79429 −1.84039 1.70266 −2.62774 −4.31910 −2.49967 4.43006
1.15 −2.38939 −1.95815 3.70919 −1.03440 4.67879 1.98730 −4.08392 0.834367 2.47157
1.16 −2.38444 0.0319476 3.68556 2.00388 −0.0761772 0.134217 −4.01912 −2.99898 −4.77812
1.17 −2.33752 2.79433 3.46401 −2.95818 −6.53182 2.23509 −3.42216 4.80831 6.91481
1.18 −2.33650 −1.34355 3.45924 −2.97087 3.13920 1.58277 −3.40951 −1.19488 6.94144
1.19 −2.30013 −2.89342 3.29061 2.38391 6.65525 −4.38144 −2.96858 5.37188 −5.48331
1.20 −2.25887 1.60047 3.10247 −3.14219 −3.61525 −0.353570 −2.49034 −0.438494 7.09779
See next 80 embeddings (of 154 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.154
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 \(T_{2}^{154} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\).