Properties

Label 6002.2.a.d
Level 6002
Weight 2
Character orbit 6002.a
Self dual Yes
Analytic conductor 47.926
Analytic rank 0
Dimension 79
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: \(79\)
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.

\(\operatorname{Tr}(f)(q) = \) \(79q \) \(\mathstrut +\mathstrut 79q^{2} \) \(\mathstrut +\mathstrut 17q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 17q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 79q^{8} \) \(\mathstrut +\mathstrut 118q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(79q \) \(\mathstrut +\mathstrut 79q^{2} \) \(\mathstrut +\mathstrut 17q^{3} \) \(\mathstrut +\mathstrut 79q^{4} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 17q^{6} \) \(\mathstrut +\mathstrut 19q^{7} \) \(\mathstrut +\mathstrut 79q^{8} \) \(\mathstrut +\mathstrut 118q^{9} \) \(\mathstrut +\mathstrut 18q^{10} \) \(\mathstrut +\mathstrut 28q^{11} \) \(\mathstrut +\mathstrut 17q^{12} \) \(\mathstrut +\mathstrut 47q^{13} \) \(\mathstrut +\mathstrut 19q^{14} \) \(\mathstrut +\mathstrut 14q^{15} \) \(\mathstrut +\mathstrut 79q^{16} \) \(\mathstrut +\mathstrut 36q^{17} \) \(\mathstrut +\mathstrut 118q^{18} \) \(\mathstrut +\mathstrut 29q^{19} \) \(\mathstrut +\mathstrut 18q^{20} \) \(\mathstrut +\mathstrut 45q^{21} \) \(\mathstrut +\mathstrut 28q^{22} \) \(\mathstrut +\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 17q^{24} \) \(\mathstrut +\mathstrut 161q^{25} \) \(\mathstrut +\mathstrut 47q^{26} \) \(\mathstrut +\mathstrut 50q^{27} \) \(\mathstrut +\mathstrut 19q^{28} \) \(\mathstrut +\mathstrut 53q^{29} \) \(\mathstrut +\mathstrut 14q^{30} \) \(\mathstrut +\mathstrut 29q^{31} \) \(\mathstrut +\mathstrut 79q^{32} \) \(\mathstrut +\mathstrut 34q^{33} \) \(\mathstrut +\mathstrut 36q^{34} \) \(\mathstrut +\mathstrut 33q^{35} \) \(\mathstrut +\mathstrut 118q^{36} \) \(\mathstrut +\mathstrut 89q^{37} \) \(\mathstrut +\mathstrut 29q^{38} \) \(\mathstrut -\mathstrut 7q^{39} \) \(\mathstrut +\mathstrut 18q^{40} \) \(\mathstrut +\mathstrut 58q^{41} \) \(\mathstrut +\mathstrut 45q^{42} \) \(\mathstrut +\mathstrut 88q^{43} \) \(\mathstrut +\mathstrut 28q^{44} \) \(\mathstrut +\mathstrut 45q^{45} \) \(\mathstrut +\mathstrut 23q^{46} \) \(\mathstrut +\mathstrut 3q^{47} \) \(\mathstrut +\mathstrut 17q^{48} \) \(\mathstrut +\mathstrut 162q^{49} \) \(\mathstrut +\mathstrut 161q^{50} \) \(\mathstrut +\mathstrut 29q^{51} \) \(\mathstrut +\mathstrut 47q^{52} \) \(\mathstrut +\mathstrut 88q^{53} \) \(\mathstrut +\mathstrut 50q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 19q^{56} \) \(\mathstrut +\mathstrut 54q^{57} \) \(\mathstrut +\mathstrut 53q^{58} \) \(\mathstrut +\mathstrut 37q^{59} \) \(\mathstrut +\mathstrut 14q^{60} \) \(\mathstrut +\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 29q^{62} \) \(\mathstrut +\mathstrut 21q^{63} \) \(\mathstrut +\mathstrut 79q^{64} \) \(\mathstrut +\mathstrut 55q^{65} \) \(\mathstrut +\mathstrut 34q^{66} \) \(\mathstrut +\mathstrut 107q^{67} \) \(\mathstrut +\mathstrut 36q^{68} \) \(\mathstrut +\mathstrut 39q^{69} \) \(\mathstrut +\mathstrut 33q^{70} \) \(\mathstrut -\mathstrut 5q^{71} \) \(\mathstrut +\mathstrut 118q^{72} \) \(\mathstrut +\mathstrut 71q^{73} \) \(\mathstrut +\mathstrut 89q^{74} \) \(\mathstrut +\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 29q^{76} \) \(\mathstrut +\mathstrut 61q^{77} \) \(\mathstrut -\mathstrut 7q^{78} \) \(\mathstrut +\mathstrut 29q^{79} \) \(\mathstrut +\mathstrut 18q^{80} \) \(\mathstrut +\mathstrut 215q^{81} \) \(\mathstrut +\mathstrut 58q^{82} \) \(\mathstrut +\mathstrut 42q^{83} \) \(\mathstrut +\mathstrut 45q^{84} \) \(\mathstrut +\mathstrut 84q^{85} \) \(\mathstrut +\mathstrut 88q^{86} \) \(\mathstrut +\mathstrut 15q^{87} \) \(\mathstrut +\mathstrut 28q^{88} \) \(\mathstrut +\mathstrut 72q^{89} \) \(\mathstrut +\mathstrut 45q^{90} \) \(\mathstrut +\mathstrut 70q^{91} \) \(\mathstrut +\mathstrut 23q^{92} \) \(\mathstrut +\mathstrut 97q^{93} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut -\mathstrut 18q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 93q^{97} \) \(\mathstrut +\mathstrut 162q^{98} \) \(\mathstrut +\mathstrut 49q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −3.35201 1.00000 1.77899 −3.35201 −4.18423 1.00000 8.23600 1.77899
1.2 1.00000 −3.34863 1.00000 −3.86481 −3.34863 −0.0235424 1.00000 8.21330 −3.86481
1.3 1.00000 −3.27666 1.00000 3.56247 −3.27666 2.04525 1.00000 7.73650 3.56247
1.4 1.00000 −3.13631 1.00000 1.68515 −3.13631 −2.68800 1.00000 6.83646 1.68515
1.5 1.00000 −3.08764 1.00000 −2.69580 −3.08764 −4.17911 1.00000 6.53354 −2.69580
1.6 1.00000 −2.95638 1.00000 −0.704147 −2.95638 −0.285333 1.00000 5.74016 −0.704147
1.7 1.00000 −2.83087 1.00000 4.29043 −2.83087 1.15444 1.00000 5.01383 4.29043
1.8 1.00000 −2.78890 1.00000 −1.90255 −2.78890 1.43646 1.00000 4.77794 −1.90255
1.9 1.00000 −2.71638 1.00000 −0.997028 −2.71638 0.847005 1.00000 4.37871 −0.997028
1.10 1.00000 −2.68976 1.00000 1.26880 −2.68976 4.90307 1.00000 4.23478 1.26880
1.11 1.00000 −2.51885 1.00000 −4.29358 −2.51885 3.16827 1.00000 3.34462 −4.29358
1.12 1.00000 −2.46943 1.00000 4.39243 −2.46943 −4.67132 1.00000 3.09808 4.39243
1.13 1.00000 −2.46614 1.00000 2.56513 −2.46614 4.43338 1.00000 3.08187 2.56513
1.14 1.00000 −2.38888 1.00000 −1.13195 −2.38888 −2.56197 1.00000 2.70673 −1.13195
1.15 1.00000 −2.13218 1.00000 −2.93673 −2.13218 2.83180 1.00000 1.54618 −2.93673
1.16 1.00000 −2.06582 1.00000 0.633869 −2.06582 −3.21505 1.00000 1.26759 0.633869
1.17 1.00000 −2.02789 1.00000 2.83925 −2.02789 −1.41231 1.00000 1.11233 2.83925
1.18 1.00000 −1.97835 1.00000 0.563154 −1.97835 3.00235 1.00000 0.913870 0.563154
1.19 1.00000 −1.93711 1.00000 −2.50082 −1.93711 −1.24216 1.00000 0.752399 −2.50082
1.20 1.00000 −1.66636 1.00000 2.51408 −1.66636 2.07406 1.00000 −0.223255 2.51408
See all 79 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.79
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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