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

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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: \(168\)
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.

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

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 −2.81703 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:

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 \(T_{2}^{168} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\).