Properties

Label 8049.2.a.a
Level 8049
Weight 2
Character orbit 8049.a
Self dual Yes
Analytic conductor 64.272
Analytic rank 1
Dimension 95
CM No

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Newspace parameters

Level: \( N \) = \( 8049 = 3 \cdot 2683 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8049.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2715885869\)
Analytic rank: \(1\)
Dimension: \(95\)
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.

\(\operatorname{Tr}(f)(q) = \) \(95q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 95q^{3} \) \(\mathstrut +\mathstrut 65q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 36q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut +\mathstrut 95q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(95q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut +\mathstrut 95q^{3} \) \(\mathstrut +\mathstrut 65q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut -\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 36q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut +\mathstrut 95q^{9} \) \(\mathstrut -\mathstrut 36q^{10} \) \(\mathstrut -\mathstrut 48q^{11} \) \(\mathstrut +\mathstrut 65q^{12} \) \(\mathstrut -\mathstrut 73q^{13} \) \(\mathstrut -\mathstrut 17q^{14} \) \(\mathstrut -\mathstrut 15q^{15} \) \(\mathstrut +\mathstrut 13q^{16} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut -\mathstrut 9q^{18} \) \(\mathstrut -\mathstrut 66q^{19} \) \(\mathstrut -\mathstrut 35q^{20} \) \(\mathstrut -\mathstrut 36q^{21} \) \(\mathstrut -\mathstrut 37q^{22} \) \(\mathstrut -\mathstrut 58q^{23} \) \(\mathstrut -\mathstrut 27q^{24} \) \(\mathstrut +\mathstrut 24q^{25} \) \(\mathstrut -\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 95q^{27} \) \(\mathstrut -\mathstrut 75q^{28} \) \(\mathstrut -\mathstrut 31q^{29} \) \(\mathstrut -\mathstrut 36q^{30} \) \(\mathstrut -\mathstrut 129q^{31} \) \(\mathstrut -\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 48q^{33} \) \(\mathstrut -\mathstrut 61q^{34} \) \(\mathstrut -\mathstrut 38q^{35} \) \(\mathstrut +\mathstrut 65q^{36} \) \(\mathstrut -\mathstrut 127q^{37} \) \(\mathstrut +\mathstrut q^{38} \) \(\mathstrut -\mathstrut 73q^{39} \) \(\mathstrut -\mathstrut 74q^{40} \) \(\mathstrut -\mathstrut 31q^{41} \) \(\mathstrut -\mathstrut 17q^{42} \) \(\mathstrut -\mathstrut 62q^{43} \) \(\mathstrut -\mathstrut 76q^{44} \) \(\mathstrut -\mathstrut 15q^{45} \) \(\mathstrut -\mathstrut 60q^{46} \) \(\mathstrut -\mathstrut 75q^{47} \) \(\mathstrut +\mathstrut 13q^{48} \) \(\mathstrut +\mathstrut 5q^{49} \) \(\mathstrut -\mathstrut 30q^{50} \) \(\mathstrut -\mathstrut 9q^{51} \) \(\mathstrut -\mathstrut 137q^{52} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut -\mathstrut 9q^{54} \) \(\mathstrut -\mathstrut 117q^{55} \) \(\mathstrut -\mathstrut 23q^{56} \) \(\mathstrut -\mathstrut 66q^{57} \) \(\mathstrut -\mathstrut 90q^{58} \) \(\mathstrut -\mathstrut 60q^{59} \) \(\mathstrut -\mathstrut 35q^{60} \) \(\mathstrut -\mathstrut 96q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut -\mathstrut 36q^{63} \) \(\mathstrut -\mathstrut 75q^{64} \) \(\mathstrut -\mathstrut 28q^{65} \) \(\mathstrut -\mathstrut 37q^{66} \) \(\mathstrut -\mathstrut 116q^{67} \) \(\mathstrut +\mathstrut 3q^{68} \) \(\mathstrut -\mathstrut 58q^{69} \) \(\mathstrut -\mathstrut 73q^{70} \) \(\mathstrut -\mathstrut 144q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut -\mathstrut 121q^{73} \) \(\mathstrut -\mathstrut 16q^{74} \) \(\mathstrut +\mathstrut 24q^{75} \) \(\mathstrut -\mathstrut 118q^{76} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 25q^{78} \) \(\mathstrut -\mathstrut 135q^{79} \) \(\mathstrut -\mathstrut 36q^{80} \) \(\mathstrut +\mathstrut 95q^{81} \) \(\mathstrut -\mathstrut 102q^{82} \) \(\mathstrut -\mathstrut 21q^{83} \) \(\mathstrut -\mathstrut 75q^{84} \) \(\mathstrut -\mathstrut 129q^{85} \) \(\mathstrut -\mathstrut 46q^{86} \) \(\mathstrut -\mathstrut 31q^{87} \) \(\mathstrut -\mathstrut 77q^{88} \) \(\mathstrut -\mathstrut 63q^{89} \) \(\mathstrut -\mathstrut 36q^{90} \) \(\mathstrut -\mathstrut 123q^{91} \) \(\mathstrut -\mathstrut 42q^{92} \) \(\mathstrut -\mathstrut 129q^{93} \) \(\mathstrut -\mathstrut 44q^{94} \) \(\mathstrut -\mathstrut 80q^{95} \) \(\mathstrut -\mathstrut 53q^{96} \) \(\mathstrut -\mathstrut 144q^{97} \) \(\mathstrut +\mathstrut 10q^{98} \) \(\mathstrut -\mathstrut 48q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.76182 1.00000 5.62766 1.63171 −2.76182 −0.505997 −10.0189 1.00000 −4.50650
1.2 −2.67709 1.00000 5.16680 1.53691 −2.67709 1.80566 −8.47779 1.00000 −4.11445
1.3 −2.56720 1.00000 4.59052 −3.13252 −2.56720 −0.347168 −6.65039 1.00000 8.04180
1.4 −2.55942 1.00000 4.55064 −0.0700614 −2.55942 −1.78635 −6.52816 1.00000 0.179317
1.5 −2.50719 1.00000 4.28600 −3.32561 −2.50719 −4.48246 −5.73145 1.00000 8.33794
1.6 −2.50349 1.00000 4.26747 3.53618 −2.50349 −0.351578 −5.67658 1.00000 −8.85279
1.7 −2.49336 1.00000 4.21683 −1.71250 −2.49336 −4.18090 −5.52734 1.00000 4.26986
1.8 −2.43614 1.00000 3.93477 0.978315 −2.43614 −0.911749 −4.71336 1.00000 −2.38331
1.9 −2.41240 1.00000 3.81966 4.15952 −2.41240 −1.40645 −4.38975 1.00000 −10.0344
1.10 −2.40517 1.00000 3.78485 0.506302 −2.40517 −0.320355 −4.29287 1.00000 −1.21774
1.11 −2.35419 1.00000 3.54222 −0.888451 −2.35419 0.154132 −3.63067 1.00000 2.09158
1.12 −2.32680 1.00000 3.41399 0.167407 −2.32680 5.19602 −3.29007 1.00000 −0.389523
1.13 −2.21332 1.00000 2.89880 −0.906600 −2.21332 −0.601026 −1.98934 1.00000 2.00660
1.14 −2.12258 1.00000 2.50534 −0.383524 −2.12258 2.66366 −1.07263 1.00000 0.814060
1.15 −1.98224 1.00000 1.92929 1.71154 −1.98224 −4.33478 0.140165 1.00000 −3.39268
1.16 −1.98008 1.00000 1.92072 −2.93482 −1.98008 2.42063 0.156981 1.00000 5.81119
1.17 −1.91515 1.00000 1.66780 2.10726 −1.91515 1.73510 0.636208 1.00000 −4.03573
1.18 −1.86344 1.00000 1.47242 −2.78098 −1.86344 2.31504 0.983118 1.00000 5.18220
1.19 −1.80117 1.00000 1.24420 2.31270 −1.80117 −0.312870 1.36132 1.00000 −4.16555
1.20 −1.77386 1.00000 1.14660 −0.218845 −1.77386 −4.33927 1.51382 1.00000 0.388201
See all 95 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.95
Significant digits:
Format:

Inner twists

This newform does not have CM; other inner twists have not been computed.

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(2683\) \(-1\)