Properties

Label 8033.2.a.e
Level 8033
Weight 2
Character orbit 8033.a
Self dual Yes
Analytic conductor 64.144
Analytic rank 0
Dimension 169
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: \(169\)
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.

\(\operatorname{Tr}(f)(q) = \) \(169q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 183q^{4} \) \(\mathstrut +\mathstrut 13q^{5} \) \(\mathstrut +\mathstrut 17q^{6} \) \(\mathstrut +\mathstrut 76q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 181q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(169q \) \(\mathstrut +\mathstrut 3q^{2} \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut +\mathstrut 183q^{4} \) \(\mathstrut +\mathstrut 13q^{5} \) \(\mathstrut +\mathstrut 17q^{6} \) \(\mathstrut +\mathstrut 76q^{7} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 181q^{9} \) \(\mathstrut +\mathstrut 30q^{10} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 25q^{12} \) \(\mathstrut +\mathstrut 63q^{13} \) \(\mathstrut -\mathstrut 3q^{14} \) \(\mathstrut +\mathstrut 26q^{15} \) \(\mathstrut +\mathstrut 219q^{16} \) \(\mathstrut +\mathstrut 14q^{17} \) \(\mathstrut +\mathstrut 31q^{18} \) \(\mathstrut +\mathstrut 51q^{19} \) \(\mathstrut +\mathstrut 49q^{20} \) \(\mathstrut +\mathstrut 16q^{21} \) \(\mathstrut +\mathstrut 53q^{22} \) \(\mathstrut +\mathstrut 50q^{23} \) \(\mathstrut +\mathstrut 43q^{24} \) \(\mathstrut +\mathstrut 214q^{25} \) \(\mathstrut -\mathstrut 2q^{26} \) \(\mathstrut +\mathstrut 23q^{27} \) \(\mathstrut +\mathstrut 149q^{28} \) \(\mathstrut -\mathstrut 169q^{29} \) \(\mathstrut +\mathstrut 26q^{30} \) \(\mathstrut +\mathstrut 65q^{31} \) \(\mathstrut +\mathstrut 25q^{32} \) \(\mathstrut +\mathstrut 57q^{33} \) \(\mathstrut +\mathstrut 60q^{34} \) \(\mathstrut +\mathstrut 60q^{35} \) \(\mathstrut +\mathstrut 218q^{36} \) \(\mathstrut +\mathstrut 52q^{37} \) \(\mathstrut +\mathstrut 35q^{38} \) \(\mathstrut +\mathstrut 49q^{39} \) \(\mathstrut +\mathstrut 72q^{40} \) \(\mathstrut +\mathstrut 3q^{41} \) \(\mathstrut +\mathstrut 78q^{42} \) \(\mathstrut +\mathstrut 132q^{43} \) \(\mathstrut +\mathstrut 64q^{45} \) \(\mathstrut +\mathstrut 32q^{46} \) \(\mathstrut +\mathstrut 54q^{47} \) \(\mathstrut +\mathstrut 76q^{48} \) \(\mathstrut +\mathstrut 245q^{49} \) \(\mathstrut -\mathstrut 6q^{50} \) \(\mathstrut +\mathstrut 44q^{51} \) \(\mathstrut +\mathstrut 193q^{52} \) \(\mathstrut +\mathstrut 58q^{53} \) \(\mathstrut +\mathstrut 54q^{54} \) \(\mathstrut +\mathstrut 213q^{55} \) \(\mathstrut +\mathstrut 12q^{56} \) \(\mathstrut +\mathstrut 52q^{57} \) \(\mathstrut -\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 25q^{59} \) \(\mathstrut +\mathstrut 32q^{60} \) \(\mathstrut +\mathstrut 100q^{61} \) \(\mathstrut +\mathstrut 78q^{62} \) \(\mathstrut +\mathstrut 227q^{63} \) \(\mathstrut +\mathstrut 292q^{64} \) \(\mathstrut +\mathstrut 37q^{65} \) \(\mathstrut +\mathstrut 59q^{66} \) \(\mathstrut +\mathstrut 110q^{67} \) \(\mathstrut +\mathstrut 24q^{68} \) \(\mathstrut -\mathstrut 20q^{69} \) \(\mathstrut +\mathstrut 47q^{70} \) \(\mathstrut +\mathstrut 44q^{71} \) \(\mathstrut +\mathstrut 71q^{72} \) \(\mathstrut +\mathstrut 139q^{73} \) \(\mathstrut +\mathstrut 35q^{74} \) \(\mathstrut +\mathstrut 53q^{75} \) \(\mathstrut +\mathstrut 92q^{76} \) \(\mathstrut +\mathstrut 22q^{77} \) \(\mathstrut +\mathstrut 83q^{78} \) \(\mathstrut +\mathstrut 137q^{79} \) \(\mathstrut +\mathstrut 90q^{80} \) \(\mathstrut +\mathstrut 177q^{81} \) \(\mathstrut +\mathstrut 91q^{82} \) \(\mathstrut +\mathstrut 126q^{83} \) \(\mathstrut +\mathstrut 36q^{84} \) \(\mathstrut +\mathstrut 95q^{85} \) \(\mathstrut +\mathstrut 21q^{86} \) \(\mathstrut -\mathstrut 8q^{87} \) \(\mathstrut +\mathstrut 75q^{88} \) \(\mathstrut +\mathstrut 19q^{89} \) \(\mathstrut +\mathstrut 130q^{90} \) \(\mathstrut +\mathstrut 102q^{91} \) \(\mathstrut +\mathstrut 68q^{92} \) \(\mathstrut +\mathstrut 22q^{93} \) \(\mathstrut +\mathstrut 82q^{94} \) \(\mathstrut +\mathstrut 37q^{95} \) \(\mathstrut +\mathstrut 107q^{96} \) \(\mathstrut +\mathstrut 116q^{97} \) \(\mathstrut -\mathstrut 13q^{98} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.81826 0.318379 5.94259 3.64952 −0.897274 3.95184 −11.1113 −2.89864 −10.2853
1.2 −2.78256 −1.98361 5.74263 −0.893629 5.51951 2.13334 −10.4141 0.934708 2.48658
1.3 −2.77688 −0.579971 5.71104 −3.81454 1.61051 −2.45600 −10.3051 −2.66363 10.5925
1.4 −2.75139 −3.04076 5.57013 1.50173 8.36631 3.15937 −9.82282 6.24621 −4.13185
1.5 −2.74782 1.78651 5.55052 1.77314 −4.90901 −4.26973 −9.75621 0.191622 −4.87228
1.6 −2.68231 3.00048 5.19481 2.85837 −8.04822 2.57996 −8.56948 6.00286 −7.66705
1.7 −2.64249 2.27007 4.98277 1.28777 −5.99863 4.91822 −7.88196 2.15320 −3.40294
1.8 −2.64021 2.12352 4.97070 −3.10978 −5.60653 2.54835 −7.84326 1.50933 8.21046
1.9 −2.61964 −0.130833 4.86253 −0.647747 0.342735 −1.29837 −7.49880 −2.98288 1.69687
1.10 −2.61493 −1.04206 4.83784 −2.72711 2.72492 4.43987 −7.42074 −1.91410 7.13119
1.11 −2.59038 2.80961 4.71008 −2.74249 −7.27797 −2.16078 −7.02013 4.89393 7.10409
1.12 −2.56941 −2.98680 4.60185 −2.62071 7.67431 −0.147137 −6.68522 5.92098 6.73366
1.13 −2.52594 −2.31351 4.38038 1.97796 5.84380 −1.35042 −6.01269 2.35235 −4.99621
1.14 −2.49641 −2.16208 4.23205 4.42906 5.39744 1.14877 −5.57210 1.67460 −11.0567
1.15 −2.48374 0.850952 4.16898 −1.59831 −2.11355 3.64335 −5.38719 −2.27588 3.96978
1.16 −2.44776 0.458025 3.99150 1.76580 −1.12113 −1.33543 −4.87472 −2.79021 −4.32226
1.17 −2.36338 −0.800416 3.58557 2.26233 1.89169 3.86578 −3.74731 −2.35933 −5.34676
1.18 −2.31656 −0.263356 3.36647 −0.903221 0.610081 2.39669 −3.16552 −2.93064 2.09237
1.19 −2.30642 0.966593 3.31956 1.65248 −2.22937 −3.04982 −3.04346 −2.06570 −3.81132
1.20 −2.30030 0.878714 3.29139 2.14800 −2.02131 −2.80339 −2.97058 −2.22786 −4.94106
See next 80 embeddings (of 169 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.169
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 \(T_{2}^{169} - \cdots\) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8033))\).