Properties

Label 8049.2.a.c
Level 8049
Weight 2
Character orbit 8049.a
Self dual Yes
Analytic conductor 64.272
Analytic rank 0
Dimension 119
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: \(0\)
Dimension: \(119\)
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.

\(\operatorname{Tr}(f)(q) = \) \(119q \) \(\mathstrut +\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 119q^{3} \) \(\mathstrut +\mathstrut 137q^{4} \) \(\mathstrut +\mathstrut 17q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(119q \) \(\mathstrut +\mathstrut 11q^{2} \) \(\mathstrut -\mathstrut 119q^{3} \) \(\mathstrut +\mathstrut 137q^{4} \) \(\mathstrut +\mathstrut 17q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 10q^{7} \) \(\mathstrut +\mathstrut 33q^{8} \) \(\mathstrut +\mathstrut 119q^{9} \) \(\mathstrut -\mathstrut 10q^{10} \) \(\mathstrut +\mathstrut 56q^{11} \) \(\mathstrut -\mathstrut 137q^{12} \) \(\mathstrut -\mathstrut 37q^{13} \) \(\mathstrut +\mathstrut 31q^{14} \) \(\mathstrut -\mathstrut 17q^{15} \) \(\mathstrut +\mathstrut 173q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 16q^{19} \) \(\mathstrut +\mathstrut 61q^{20} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut -\mathstrut 3q^{22} \) \(\mathstrut +\mathstrut 76q^{23} \) \(\mathstrut -\mathstrut 33q^{24} \) \(\mathstrut +\mathstrut 134q^{25} \) \(\mathstrut +\mathstrut 47q^{26} \) \(\mathstrut -\mathstrut 119q^{27} \) \(\mathstrut -\mathstrut q^{28} \) \(\mathstrut +\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 51q^{31} \) \(\mathstrut +\mathstrut 87q^{32} \) \(\mathstrut -\mathstrut 56q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 58q^{35} \) \(\mathstrut +\mathstrut 137q^{36} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 35q^{38} \) \(\mathstrut +\mathstrut 37q^{39} \) \(\mathstrut -\mathstrut 40q^{40} \) \(\mathstrut +\mathstrut 47q^{41} \) \(\mathstrut -\mathstrut 31q^{42} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 148q^{44} \) \(\mathstrut +\mathstrut 17q^{45} \) \(\mathstrut +\mathstrut 26q^{46} \) \(\mathstrut +\mathstrut 107q^{47} \) \(\mathstrut -\mathstrut 173q^{48} \) \(\mathstrut +\mathstrut 163q^{49} \) \(\mathstrut +\mathstrut 76q^{50} \) \(\mathstrut -\mathstrut 17q^{51} \) \(\mathstrut -\mathstrut 57q^{52} \) \(\mathstrut +\mathstrut 64q^{53} \) \(\mathstrut -\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 71q^{55} \) \(\mathstrut +\mathstrut 91q^{56} \) \(\mathstrut -\mathstrut 16q^{57} \) \(\mathstrut +\mathstrut 12q^{58} \) \(\mathstrut +\mathstrut 98q^{59} \) \(\mathstrut -\mathstrut 61q^{60} \) \(\mathstrut -\mathstrut 50q^{61} \) \(\mathstrut +\mathstrut 40q^{62} \) \(\mathstrut +\mathstrut 10q^{63} \) \(\mathstrut +\mathstrut 245q^{64} \) \(\mathstrut +\mathstrut 40q^{65} \) \(\mathstrut +\mathstrut 3q^{66} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 75q^{68} \) \(\mathstrut -\mathstrut 76q^{69} \) \(\mathstrut -\mathstrut 9q^{70} \) \(\mathstrut +\mathstrut 194q^{71} \) \(\mathstrut +\mathstrut 33q^{72} \) \(\mathstrut -\mathstrut 79q^{73} \) \(\mathstrut +\mathstrut 72q^{74} \) \(\mathstrut -\mathstrut 134q^{75} \) \(\mathstrut +\mathstrut 12q^{76} \) \(\mathstrut +\mathstrut 71q^{77} \) \(\mathstrut -\mathstrut 47q^{78} \) \(\mathstrut +\mathstrut 127q^{79} \) \(\mathstrut +\mathstrut 148q^{80} \) \(\mathstrut +\mathstrut 119q^{81} \) \(\mathstrut -\mathstrut 54q^{82} \) \(\mathstrut +\mathstrut 77q^{83} \) \(\mathstrut +\mathstrut q^{84} \) \(\mathstrut -\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 142q^{86} \) \(\mathstrut -\mathstrut 47q^{87} \) \(\mathstrut +\mathstrut q^{88} \) \(\mathstrut +\mathstrut 93q^{89} \) \(\mathstrut -\mathstrut 10q^{90} \) \(\mathstrut +\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 156q^{92} \) \(\mathstrut -\mathstrut 51q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut +\mathstrut 138q^{95} \) \(\mathstrut -\mathstrut 87q^{96} \) \(\mathstrut -\mathstrut 110q^{97} \) \(\mathstrut +\mathstrut 96q^{98} \) \(\mathstrut +\mathstrut 56q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.76674 −1.00000 5.65483 −0.357353 2.76674 −2.67071 −10.1119 1.00000 0.988701
1.2 −2.73168 −1.00000 5.46207 −0.892345 2.73168 −1.57860 −9.45726 1.00000 2.43760
1.3 −2.70718 −1.00000 5.32884 −1.26891 2.70718 −3.95115 −9.01180 1.00000 3.43519
1.4 −2.67169 −1.00000 5.13794 4.23533 2.67169 3.62248 −8.38362 1.00000 −11.3155
1.5 −2.65333 −1.00000 5.04016 2.95577 2.65333 2.19565 −8.06655 1.00000 −7.84263
1.6 −2.62888 −1.00000 4.91100 3.06865 2.62888 −2.79906 −7.65266 1.00000 −8.06710
1.7 −2.61270 −1.00000 4.82618 1.51274 2.61270 3.06130 −7.38394 1.00000 −3.95232
1.8 −2.60392 −1.00000 4.78038 3.66153 2.60392 −3.52018 −7.23988 1.00000 −9.53431
1.9 −2.46430 −1.00000 4.07278 −0.321627 2.46430 1.46780 −5.10794 1.00000 0.792584
1.10 −2.39135 −1.00000 3.71855 −1.51157 2.39135 2.32148 −4.10966 1.00000 3.61469
1.11 −2.34737 −1.00000 3.51014 −3.81233 2.34737 −0.357303 −3.54486 1.00000 8.94895
1.12 −2.34205 −1.00000 3.48520 0.568796 2.34205 −0.877328 −3.47840 1.00000 −1.33215
1.13 −2.28998 −1.00000 3.24400 0.0628594 2.28998 −3.99468 −2.84873 1.00000 −0.143947
1.14 −2.26557 −1.00000 3.13283 0.270785 2.26557 1.54301 −2.56650 1.00000 −0.613482
1.15 −2.25432 −1.00000 3.08196 −2.79786 2.25432 −0.509718 −2.43909 1.00000 6.30728
1.16 −2.24285 −1.00000 3.03036 −3.65739 2.24285 −4.78600 −2.31094 1.00000 8.20296
1.17 −2.22986 −1.00000 2.97225 2.09159 2.22986 2.90452 −2.16799 1.00000 −4.66395
1.18 −2.22780 −1.00000 2.96308 4.08366 2.22780 2.32778 −2.14554 1.00000 −9.09757
1.19 −2.21831 −1.00000 2.92089 1.70107 2.21831 0.0884207 −2.04282 1.00000 −3.77350
1.20 −2.08408 −1.00000 2.34338 −1.55135 2.08408 4.26949 −0.715634 1.00000 3.23314
See next 80 embeddings (of 119 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.119
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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