Properties

Label 6002.2.a.c
Level 6002
Weight 2
Character orbit 6002.a
Self dual Yes
Analytic conductor 47.926
Analytic rank 0
Dimension 69
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: \(0\)
Dimension: \(69\)
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.

\(\operatorname{Tr}(f)(q) = \) \(69q \) \(\mathstrut -\mathstrut 69q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 23q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(69q \) \(\mathstrut -\mathstrut 69q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 69q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 11q^{6} \) \(\mathstrut +\mathstrut 23q^{7} \) \(\mathstrut -\mathstrut 69q^{8} \) \(\mathstrut +\mathstrut 72q^{9} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 14q^{11} \) \(\mathstrut +\mathstrut 11q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 23q^{14} \) \(\mathstrut +\mathstrut 34q^{15} \) \(\mathstrut +\mathstrut 69q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 72q^{18} \) \(\mathstrut +\mathstrut 17q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 14q^{22} \) \(\mathstrut +\mathstrut 33q^{23} \) \(\mathstrut -\mathstrut 11q^{24} \) \(\mathstrut +\mathstrut 119q^{25} \) \(\mathstrut -\mathstrut 31q^{26} \) \(\mathstrut +\mathstrut 44q^{27} \) \(\mathstrut +\mathstrut 23q^{28} \) \(\mathstrut -\mathstrut 25q^{29} \) \(\mathstrut -\mathstrut 34q^{30} \) \(\mathstrut +\mathstrut 49q^{31} \) \(\mathstrut -\mathstrut 69q^{32} \) \(\mathstrut +\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 4q^{34} \) \(\mathstrut -\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 72q^{36} \) \(\mathstrut +\mathstrut 73q^{37} \) \(\mathstrut -\mathstrut 17q^{38} \) \(\mathstrut +\mathstrut 31q^{39} \) \(\mathstrut +\mathstrut 2q^{40} \) \(\mathstrut -\mathstrut 46q^{41} \) \(\mathstrut +\mathstrut 11q^{42} \) \(\mathstrut +\mathstrut 76q^{43} \) \(\mathstrut -\mathstrut 14q^{44} \) \(\mathstrut +\mathstrut 9q^{45} \) \(\mathstrut -\mathstrut 33q^{46} \) \(\mathstrut +\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 11q^{48} \) \(\mathstrut +\mathstrut 100q^{49} \) \(\mathstrut -\mathstrut 119q^{50} \) \(\mathstrut +\mathstrut 25q^{51} \) \(\mathstrut +\mathstrut 31q^{52} \) \(\mathstrut +\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 44q^{54} \) \(\mathstrut +\mathstrut 81q^{55} \) \(\mathstrut -\mathstrut 23q^{56} \) \(\mathstrut +\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 34q^{60} \) \(\mathstrut +\mathstrut 13q^{61} \) \(\mathstrut -\mathstrut 49q^{62} \) \(\mathstrut +\mathstrut 65q^{63} \) \(\mathstrut +\mathstrut 69q^{64} \) \(\mathstrut -\mathstrut 27q^{65} \) \(\mathstrut -\mathstrut 10q^{66} \) \(\mathstrut +\mathstrut 105q^{67} \) \(\mathstrut -\mathstrut 4q^{68} \) \(\mathstrut +\mathstrut 19q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 51q^{71} \) \(\mathstrut -\mathstrut 72q^{72} \) \(\mathstrut +\mathstrut 43q^{73} \) \(\mathstrut -\mathstrut 73q^{74} \) \(\mathstrut +\mathstrut 77q^{75} \) \(\mathstrut +\mathstrut 17q^{76} \) \(\mathstrut -\mathstrut 19q^{77} \) \(\mathstrut -\mathstrut 31q^{78} \) \(\mathstrut +\mathstrut 89q^{79} \) \(\mathstrut -\mathstrut 2q^{80} \) \(\mathstrut +\mathstrut 73q^{81} \) \(\mathstrut +\mathstrut 46q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut -\mathstrut 11q^{84} \) \(\mathstrut +\mathstrut 44q^{85} \) \(\mathstrut -\mathstrut 76q^{86} \) \(\mathstrut +\mathstrut 57q^{87} \) \(\mathstrut +\mathstrut 14q^{88} \) \(\mathstrut -\mathstrut 28q^{89} \) \(\mathstrut -\mathstrut 9q^{90} \) \(\mathstrut +\mathstrut 76q^{91} \) \(\mathstrut +\mathstrut 33q^{92} \) \(\mathstrut +\mathstrut 59q^{93} \) \(\mathstrut -\mathstrut 23q^{94} \) \(\mathstrut +\mathstrut 72q^{95} \) \(\mathstrut -\mathstrut 11q^{96} \) \(\mathstrut +\mathstrut 89q^{97} \) \(\mathstrut -\mathstrut 100q^{98} \) \(\mathstrut -\mathstrut 17q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.40047 1.00000 −0.810151 3.40047 1.45096 −1.00000 8.56323 0.810151
1.2 −1.00000 −3.06382 1.00000 −3.70565 3.06382 4.91357 −1.00000 6.38702 3.70565
1.3 −1.00000 −2.95145 1.00000 1.54937 2.95145 1.05407 −1.00000 5.71107 −1.54937
1.4 −1.00000 −2.80010 1.00000 1.44998 2.80010 −0.125244 −1.00000 4.84055 −1.44998
1.5 −1.00000 −2.79134 1.00000 2.80110 2.79134 2.82300 −1.00000 4.79155 −2.80110
1.6 −1.00000 −2.68289 1.00000 −4.14764 2.68289 −3.25782 −1.00000 4.19789 4.14764
1.7 −1.00000 −2.66325 1.00000 −0.772436 2.66325 4.62727 −1.00000 4.09290 0.772436
1.8 −1.00000 −2.63767 1.00000 0.590977 2.63767 −1.00146 −1.00000 3.95729 −0.590977
1.9 −1.00000 −2.45213 1.00000 −3.61679 2.45213 0.0579543 −1.00000 3.01293 3.61679
1.10 −1.00000 −2.40560 1.00000 −3.03439 2.40560 −1.41996 −1.00000 2.78689 3.03439
1.11 −1.00000 −2.33178 1.00000 −0.767442 2.33178 −0.132499 −1.00000 2.43720 0.767442
1.12 −1.00000 −2.31615 1.00000 2.10238 2.31615 −3.46770 −1.00000 2.36454 −2.10238
1.13 −1.00000 −2.29088 1.00000 2.54707 2.29088 4.39407 −1.00000 2.24813 −2.54707
1.14 −1.00000 −2.19747 1.00000 −2.90019 2.19747 −0.534047 −1.00000 1.82886 2.90019
1.15 −1.00000 −2.02205 1.00000 3.59068 2.02205 0.941965 −1.00000 1.08869 −3.59068
1.16 −1.00000 −1.90243 1.00000 −0.692359 1.90243 −4.50666 −1.00000 0.619255 0.692359
1.17 −1.00000 −1.43088 1.00000 1.76140 1.43088 −2.51027 −1.00000 −0.952590 −1.76140
1.18 −1.00000 −1.36851 1.00000 0.212949 1.36851 −1.32734 −1.00000 −1.12718 −0.212949
1.19 −1.00000 −1.30456 1.00000 −4.01452 1.30456 3.40012 −1.00000 −1.29813 4.01452
1.20 −1.00000 −1.29953 1.00000 −2.92449 1.29953 −2.47331 −1.00000 −1.31122 2.92449
See all 69 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.69
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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