Properties

Label 8049.2.a.b
Level 8049
Weight 2
Character orbit 8049.a
Self dual Yes
Analytic conductor 64.272
Analytic rank 1
Dimension 104
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: \(104\)
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.

\(\operatorname{Tr}(f)(q) = \) \(104q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 104q^{3} \) \(\mathstrut +\mathstrut 87q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut +\mathstrut 104q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(104q \) \(\mathstrut -\mathstrut 9q^{2} \) \(\mathstrut -\mathstrut 104q^{3} \) \(\mathstrut +\mathstrut 87q^{4} \) \(\mathstrut -\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut -\mathstrut 10q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut +\mathstrut 104q^{9} \) \(\mathstrut +\mathstrut 8q^{10} \) \(\mathstrut -\mathstrut 52q^{11} \) \(\mathstrut -\mathstrut 87q^{12} \) \(\mathstrut +\mathstrut 35q^{13} \) \(\mathstrut -\mathstrut 23q^{14} \) \(\mathstrut +\mathstrut 15q^{15} \) \(\mathstrut +\mathstrut 53q^{16} \) \(\mathstrut -\mathstrut 19q^{17} \) \(\mathstrut -\mathstrut 9q^{18} \) \(\mathstrut -\mathstrut 22q^{19} \) \(\mathstrut -\mathstrut 35q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut -\mathstrut q^{22} \) \(\mathstrut -\mathstrut 70q^{23} \) \(\mathstrut +\mathstrut 27q^{24} \) \(\mathstrut +\mathstrut 79q^{25} \) \(\mathstrut -\mathstrut 39q^{26} \) \(\mathstrut -\mathstrut 104q^{27} \) \(\mathstrut -\mathstrut 9q^{28} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 8q^{30} \) \(\mathstrut -\mathstrut 47q^{31} \) \(\mathstrut -\mathstrut 53q^{32} \) \(\mathstrut +\mathstrut 52q^{33} \) \(\mathstrut -\mathstrut 17q^{34} \) \(\mathstrut -\mathstrut 54q^{35} \) \(\mathstrut +\mathstrut 87q^{36} \) \(\mathstrut +\mathstrut 65q^{37} \) \(\mathstrut -\mathstrut 33q^{38} \) \(\mathstrut -\mathstrut 35q^{39} \) \(\mathstrut +\mathstrut 14q^{40} \) \(\mathstrut -\mathstrut 47q^{41} \) \(\mathstrut +\mathstrut 23q^{42} \) \(\mathstrut -\mathstrut 30q^{43} \) \(\mathstrut -\mathstrut 122q^{44} \) \(\mathstrut -\mathstrut 15q^{45} \) \(\mathstrut -\mathstrut 6q^{46} \) \(\mathstrut -\mathstrut 101q^{47} \) \(\mathstrut -\mathstrut 53q^{48} \) \(\mathstrut +\mathstrut 78q^{49} \) \(\mathstrut -\mathstrut 64q^{50} \) \(\mathstrut +\mathstrut 19q^{51} \) \(\mathstrut +\mathstrut 41q^{52} \) \(\mathstrut -\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 9q^{54} \) \(\mathstrut -\mathstrut 29q^{55} \) \(\mathstrut -\mathstrut 71q^{56} \) \(\mathstrut +\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut 2q^{58} \) \(\mathstrut -\mathstrut 86q^{59} \) \(\mathstrut +\mathstrut 35q^{60} \) \(\mathstrut +\mathstrut 34q^{61} \) \(\mathstrut -\mathstrut 36q^{62} \) \(\mathstrut -\mathstrut 10q^{63} \) \(\mathstrut -\mathstrut 15q^{64} \) \(\mathstrut -\mathstrut 64q^{65} \) \(\mathstrut +\mathstrut q^{66} \) \(\mathstrut -\mathstrut 38q^{67} \) \(\mathstrut -\mathstrut 33q^{68} \) \(\mathstrut +\mathstrut 70q^{69} \) \(\mathstrut -\mathstrut 29q^{70} \) \(\mathstrut -\mathstrut 176q^{71} \) \(\mathstrut -\mathstrut 27q^{72} \) \(\mathstrut +\mathstrut 69q^{73} \) \(\mathstrut -\mathstrut 86q^{74} \) \(\mathstrut -\mathstrut 79q^{75} \) \(\mathstrut -\mathstrut 54q^{76} \) \(\mathstrut -\mathstrut 45q^{77} \) \(\mathstrut +\mathstrut 39q^{78} \) \(\mathstrut -\mathstrut 101q^{79} \) \(\mathstrut -\mathstrut 76q^{80} \) \(\mathstrut +\mathstrut 104q^{81} \) \(\mathstrut +\mathstrut 38q^{82} \) \(\mathstrut -\mathstrut 67q^{83} \) \(\mathstrut +\mathstrut 9q^{84} \) \(\mathstrut +\mathstrut 3q^{85} \) \(\mathstrut -\mathstrut 90q^{86} \) \(\mathstrut +\mathstrut 37q^{87} \) \(\mathstrut +\mathstrut 7q^{88} \) \(\mathstrut -\mathstrut 91q^{89} \) \(\mathstrut +\mathstrut 8q^{90} \) \(\mathstrut -\mathstrut 47q^{91} \) \(\mathstrut -\mathstrut 136q^{92} \) \(\mathstrut +\mathstrut 47q^{93} \) \(\mathstrut -\mathstrut 20q^{94} \) \(\mathstrut -\mathstrut 130q^{95} \) \(\mathstrut +\mathstrut 53q^{96} \) \(\mathstrut +\mathstrut 86q^{97} \) \(\mathstrut -\mathstrut 44q^{98} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.70998 −1.00000 5.34399 −2.58706 2.70998 1.21378 −9.06215 1.00000 7.01089
1.2 −2.69984 −1.00000 5.28916 0.253804 2.69984 2.11001 −8.88022 1.00000 −0.685231
1.3 −2.68757 −1.00000 5.22302 2.72258 2.68757 −1.36352 −8.66207 1.00000 −7.31712
1.4 −2.67025 −1.00000 5.13022 −3.32329 2.67025 −3.25210 −8.35846 1.00000 8.87402
1.5 −2.64591 −1.00000 5.00085 1.12056 2.64591 4.16027 −7.94000 1.00000 −2.96491
1.6 −2.57733 −1.00000 4.64262 2.42154 2.57733 −2.34868 −6.81090 1.00000 −6.24111
1.7 −2.53392 −1.00000 4.42075 −2.15927 2.53392 −0.210471 −6.13399 1.00000 5.47142
1.8 −2.52808 −1.00000 4.39119 −2.04731 2.52808 3.64200 −6.04511 1.00000 5.17577
1.9 −2.51614 −1.00000 4.33096 −3.38392 2.51614 2.24516 −5.86503 1.00000 8.51441
1.10 −2.49098 −1.00000 4.20498 −3.30007 2.49098 −0.252788 −5.49255 1.00000 8.22041
1.11 −2.36016 −1.00000 3.57036 3.05076 2.36016 −4.76162 −3.70631 1.00000 −7.20028
1.12 −2.28384 −1.00000 3.21593 −0.172989 2.28384 5.09025 −2.77699 1.00000 0.395079
1.13 −2.24892 −1.00000 3.05765 3.28762 2.24892 3.22602 −2.37858 1.00000 −7.39360
1.14 −2.22425 −1.00000 2.94729 −0.996267 2.22425 −4.15468 −2.10702 1.00000 2.21595
1.15 −2.13514 −1.00000 2.55881 1.37673 2.13514 −0.308813 −1.19313 1.00000 −2.93951
1.16 −2.12836 −1.00000 2.52994 0.301462 2.12836 −3.41779 −1.12790 1.00000 −0.641620
1.17 −2.10025 −1.00000 2.41107 2.84518 2.10025 2.53466 −0.863342 1.00000 −5.97560
1.18 −2.00502 −1.00000 2.02010 −0.637068 2.00502 −2.14824 −0.0403022 1.00000 1.27733
1.19 −1.98457 −1.00000 1.93852 3.95408 1.98457 −0.848310 0.122004 1.00000 −7.84715
1.20 −1.91933 −1.00000 1.68384 0.443938 1.91933 −2.95964 0.606807 1.00000 −0.852066
See next 80 embeddings (of 104 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.104
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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