Properties

Label 8033.2.a.d
Level $8033$
Weight $2$
Character orbit 8033.a
Self dual yes
Analytic conductor $64.144$
Analytic rank $0$
Dimension $168$
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: \(0\)
Dimension: \(168\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 168q + 12q^{2} + 35q^{3} + 184q^{4} + 12q^{5} + 10q^{6} + 74q^{7} + 39q^{8} + 183q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 168q + 12q^{2} + 35q^{3} + 184q^{4} + 12q^{5} + 10q^{6} + 74q^{7} + 39q^{8} + 183q^{9} + 41q^{10} + 29q^{11} + 82q^{12} + 62q^{13} + 23q^{14} + 31q^{15} + 204q^{16} + 56q^{17} + 35q^{18} + 83q^{19} + 6q^{20} + 30q^{21} + 56q^{22} + 54q^{23} + 28q^{24} + 210q^{25} + 21q^{26} + 140q^{27} + 151q^{28} + 168q^{29} + 29q^{30} + 72q^{31} + 40q^{32} + 32q^{33} + 34q^{34} + 18q^{35} + 152q^{36} + 42q^{37} + 29q^{38} + 70q^{39} + 97q^{40} + 41q^{41} - 20q^{42} + 119q^{43} + 37q^{44} + 22q^{45} + 24q^{46} + 119q^{47} + 135q^{48} + 216q^{49} + 38q^{50} + 18q^{51} + 154q^{52} - 7q^{53} + 35q^{54} + 224q^{55} + 46q^{56} + 12q^{57} + 12q^{58} + 25q^{59} + 13q^{60} + 82q^{61} + 27q^{62} + 211q^{63} + 217q^{64} + 8q^{65} - 6q^{66} + 76q^{67} + 132q^{68} + 36q^{69} + 39q^{70} + 32q^{71} + 39q^{72} + 89q^{73} - q^{74} + 123q^{75} + 180q^{76} + 68q^{77} - 54q^{78} + 176q^{79} - 11q^{80} + 192q^{81} + 51q^{82} + 76q^{83} + 86q^{84} + 65q^{85} - 72q^{86} + 35q^{87} + 178q^{88} + 55q^{89} + 2q^{90} + 80q^{91} + 44q^{92} + 39q^{93} + 89q^{94} + 77q^{95} - 68q^{96} + 82q^{97} + 80q^{98} + 67q^{99} + O(q^{100}) \)

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 −2.81703 3.39159 5.93564 −2.93306 −9.55421 1.32517 −11.0868 8.50291 8.26251
1.2 −2.78974 1.21931 5.78265 −2.52098 −3.40156 3.27965 −10.5526 −1.51328 7.03288
1.3 −2.72891 1.81680 5.44695 0.385312 −4.95790 −3.34669 −9.40642 0.300780 −1.05148
1.4 −2.69929 0.546346 5.28617 −1.10957 −1.47475 1.76751 −8.87031 −2.70151 2.99504
1.5 −2.69133 −1.56780 5.24327 1.58955 4.21948 −0.425755 −8.72870 −0.541992 −4.27800
1.6 −2.62201 −2.34634 4.87492 −4.13917 6.15213 1.37941 −7.53807 2.50532 10.8529
1.7 −2.58554 −1.99550 4.68504 0.489761 5.15945 4.81577 −6.94230 0.982009 −1.26630
1.8 −2.57726 2.47639 4.64228 3.37343 −6.38231 −1.62921 −6.80985 3.13252 −8.69420
1.9 −2.53885 1.12516 4.44574 −4.00247 −2.85660 4.31591 −6.20937 −1.73402 10.1617
1.10 −2.52738 −1.64022 4.38763 1.90507 4.14544 −1.36071 −6.03443 −0.309688 −4.81483
1.11 −2.52129 1.55242 4.35693 3.41413 −3.91411 1.49471 −5.94251 −0.589992 −8.60803
1.12 −2.50804 0.217745 4.29026 −0.0259578 −0.546113 −4.91509 −5.74406 −2.95259 0.0651033
1.13 −2.50746 −1.63037 4.28734 3.92256 4.08808 3.39028 −5.73541 −0.341901 −9.83565
1.14 −2.46662 2.34956 4.08421 0.440108 −5.79546 2.07787 −5.14095 2.52042 −1.08558
1.15 −2.44996 −1.86877 4.00229 −1.18542 4.57841 −4.60968 −4.90553 0.492307 2.90424
1.16 −2.41744 −0.0531053 3.84399 −0.881470 0.128379 1.45309 −4.45773 −2.99718 2.13090
1.17 −2.40677 −1.38895 3.79253 −2.91778 3.34287 3.15140 −4.31420 −1.07083 7.02241
1.18 −2.40306 1.89974 3.77470 −4.37204 −4.56518 −3.13994 −4.26472 0.608994 10.5063
1.19 −2.34777 0.405872 3.51204 −3.82329 −0.952896 0.144242 −3.54992 −2.83527 8.97621
1.20 −2.33211 3.25701 3.43872 3.02617 −7.59569 3.43735 −3.35525 7.60809 −7.05735
See next 80 embeddings (of 168 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.168
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.d 168
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8033.2.a.d 168 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \(T_{2}^{168} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\).

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database