Properties

Label 6002.2.a.b
Level 6002
Weight 2
Character orbit 6002.a
Self dual Yes
Analytic conductor 47.926
Analytic rank 1
Dimension 56
CM No

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Newspace parameters

Level: \( N \) = \( 6002 = 2 \cdot 3001 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6002.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9262112932\)
Analytic rank: \(1\)
Dimension: \(56\)
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.

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

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 −1.00000 −3.33546 1.00000 0.467319 3.33546 1.63589 −1.00000 8.12527 −0.467319
1.2 −1.00000 −3.32670 1.00000 −1.32100 3.32670 −1.80854 −1.00000 8.06690 1.32100
1.3 −1.00000 −3.25643 1.00000 4.04919 3.25643 −2.73149 −1.00000 7.60432 −4.04919
1.4 −1.00000 −3.13871 1.00000 −2.43791 3.13871 −2.06269 −1.00000 6.85148 2.43791
1.5 −1.00000 −3.00129 1.00000 −0.204934 3.00129 −4.79366 −1.00000 6.00776 0.204934
1.6 −1.00000 −2.97926 1.00000 −2.47117 2.97926 1.46435 −1.00000 5.87597 2.47117
1.7 −1.00000 −2.77449 1.00000 2.09468 2.77449 −4.11800 −1.00000 4.69780 −2.09468
1.8 −1.00000 −2.57676 1.00000 1.81538 2.57676 4.12880 −1.00000 3.63972 −1.81538
1.9 −1.00000 −2.53853 1.00000 3.20594 2.53853 2.08261 −1.00000 3.44415 −3.20594
1.10 −1.00000 −2.29725 1.00000 −0.0563132 2.29725 2.55969 −1.00000 2.27735 0.0563132
1.11 −1.00000 −2.23559 1.00000 2.58834 2.23559 1.55053 −1.00000 1.99788 −2.58834
1.12 −1.00000 −2.14369 1.00000 −1.86034 2.14369 1.91377 −1.00000 1.59541 1.86034
1.13 −1.00000 −2.11800 1.00000 −3.39608 2.11800 −4.21736 −1.00000 1.48593 3.39608
1.14 −1.00000 −2.09636 1.00000 −1.63895 2.09636 0.351798 −1.00000 1.39473 1.63895
1.15 −1.00000 −2.01653 1.00000 −1.99229 2.01653 −2.17859 −1.00000 1.06638 1.99229
1.16 −1.00000 −1.91820 1.00000 2.08437 1.91820 −4.09357 −1.00000 0.679480 −2.08437
1.17 −1.00000 −1.79165 1.00000 2.16923 1.79165 −2.84770 −1.00000 0.210015 −2.16923
1.18 −1.00000 −1.64063 1.00000 −2.79431 1.64063 2.69140 −1.00000 −0.308341 2.79431
1.19 −1.00000 −1.59777 1.00000 0.373803 1.59777 0.398412 −1.00000 −0.447134 −0.373803
1.20 −1.00000 −1.48075 1.00000 3.81565 1.48075 2.08581 −1.00000 −0.807375 −3.81565
See all 56 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.56
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(3001\) \(1\)