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
Inner twists $1$

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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: \(154\)
Twist minimal: yes
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.

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

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 −2.82218 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:

Atkin-Lehner signs

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

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 8033.2.a.c 154
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8033.2.a.c 154 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{154} + \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database