Properties

Label 6029.2.a.b
Level 6029
Weight 2
Character orbit 6029.a
Self dual Yes
Analytic conductor 48.142
Analytic rank 0
Dimension 268
CM No

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Newspace parameters

Level: \( N \) = \( 6029 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6029.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.1418073786\)
Analytic rank: \(0\)
Dimension: \(268\)
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.

\(\operatorname{Tr}(f)(q) = \) \(268q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 43q^{3} \) \(\mathstrut +\mathstrut 300q^{4} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 34q^{6} \) \(\mathstrut +\mathstrut 59q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 295q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(268q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 43q^{3} \) \(\mathstrut +\mathstrut 300q^{4} \) \(\mathstrut +\mathstrut 18q^{5} \) \(\mathstrut +\mathstrut 34q^{6} \) \(\mathstrut +\mathstrut 59q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut 295q^{9} \) \(\mathstrut +\mathstrut 91q^{10} \) \(\mathstrut +\mathstrut 49q^{11} \) \(\mathstrut +\mathstrut 77q^{12} \) \(\mathstrut +\mathstrut 45q^{13} \) \(\mathstrut +\mathstrut 42q^{14} \) \(\mathstrut +\mathstrut 37q^{15} \) \(\mathstrut +\mathstrut 356q^{16} \) \(\mathstrut +\mathstrut 40q^{17} \) \(\mathstrut +\mathstrut 36q^{18} \) \(\mathstrut +\mathstrut 245q^{19} \) \(\mathstrut +\mathstrut 40q^{20} \) \(\mathstrut +\mathstrut 66q^{21} \) \(\mathstrut +\mathstrut 51q^{22} \) \(\mathstrut +\mathstrut 26q^{23} \) \(\mathstrut +\mathstrut 90q^{24} \) \(\mathstrut +\mathstrut 314q^{25} \) \(\mathstrut +\mathstrut 24q^{26} \) \(\mathstrut +\mathstrut 160q^{27} \) \(\mathstrut +\mathstrut 117q^{28} \) \(\mathstrut +\mathstrut 54q^{29} \) \(\mathstrut +\mathstrut 25q^{30} \) \(\mathstrut +\mathstrut 181q^{31} \) \(\mathstrut +\mathstrut 35q^{32} \) \(\mathstrut +\mathstrut 49q^{33} \) \(\mathstrut +\mathstrut 84q^{34} \) \(\mathstrut +\mathstrut 73q^{35} \) \(\mathstrut +\mathstrut 348q^{36} \) \(\mathstrut +\mathstrut 77q^{37} \) \(\mathstrut +\mathstrut 20q^{38} \) \(\mathstrut +\mathstrut 96q^{39} \) \(\mathstrut +\mathstrut 257q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut +\mathstrut 22q^{42} \) \(\mathstrut +\mathstrut 199q^{43} \) \(\mathstrut +\mathstrut 59q^{44} \) \(\mathstrut +\mathstrut 60q^{45} \) \(\mathstrut +\mathstrut 116q^{46} \) \(\mathstrut +\mathstrut 41q^{47} \) \(\mathstrut +\mathstrut 106q^{48} \) \(\mathstrut +\mathstrut 381q^{49} \) \(\mathstrut +\mathstrut 21q^{50} \) \(\mathstrut +\mathstrut 248q^{51} \) \(\mathstrut +\mathstrut 101q^{52} \) \(\mathstrut +\mathstrut 4q^{53} \) \(\mathstrut +\mathstrut 98q^{54} \) \(\mathstrut +\mathstrut 136q^{55} \) \(\mathstrut +\mathstrut 79q^{56} \) \(\mathstrut +\mathstrut 47q^{57} \) \(\mathstrut +\mathstrut 14q^{58} \) \(\mathstrut +\mathstrut 170q^{59} \) \(\mathstrut +\mathstrut 31q^{60} \) \(\mathstrut +\mathstrut 247q^{61} \) \(\mathstrut +\mathstrut 17q^{62} \) \(\mathstrut +\mathstrut 143q^{63} \) \(\mathstrut +\mathstrut 437q^{64} \) \(\mathstrut +\mathstrut 29q^{65} \) \(\mathstrut +\mathstrut 38q^{66} \) \(\mathstrut +\mathstrut 114q^{67} \) \(\mathstrut +\mathstrut 62q^{68} \) \(\mathstrut +\mathstrut 101q^{69} \) \(\mathstrut +\mathstrut 48q^{70} \) \(\mathstrut +\mathstrut 64q^{71} \) \(\mathstrut +\mathstrut 54q^{72} \) \(\mathstrut +\mathstrut 115q^{73} \) \(\mathstrut +\mathstrut 22q^{74} \) \(\mathstrut +\mathstrut 250q^{75} \) \(\mathstrut +\mathstrut 448q^{76} \) \(\mathstrut +\mathstrut 8q^{77} \) \(\mathstrut -\mathstrut 50q^{78} \) \(\mathstrut +\mathstrut 271q^{79} \) \(\mathstrut +\mathstrut 39q^{80} \) \(\mathstrut +\mathstrut 336q^{81} \) \(\mathstrut +\mathstrut 132q^{82} \) \(\mathstrut +\mathstrut 74q^{83} \) \(\mathstrut +\mathstrut 122q^{84} \) \(\mathstrut +\mathstrut 58q^{85} \) \(\mathstrut +\mathstrut 27q^{86} \) \(\mathstrut +\mathstrut 105q^{87} \) \(\mathstrut +\mathstrut 127q^{88} \) \(\mathstrut +\mathstrut 63q^{89} \) \(\mathstrut +\mathstrut 179q^{90} \) \(\mathstrut +\mathstrut 406q^{91} \) \(\mathstrut +\mathstrut 13q^{92} \) \(\mathstrut +\mathstrut q^{93} \) \(\mathstrut +\mathstrut 263q^{94} \) \(\mathstrut +\mathstrut 76q^{95} \) \(\mathstrut +\mathstrut 161q^{96} \) \(\mathstrut +\mathstrut 123q^{97} \) \(\mathstrut -\mathstrut 7q^{98} \) \(\mathstrut +\mathstrut 180q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.82279 1.45736 5.96816 −4.32160 −4.11382 −2.12666 −11.2013 −0.876107 12.1990
1.2 −2.79474 −0.330575 5.81059 −0.623259 0.923873 −2.39329 −10.6496 −2.89072 1.74185
1.3 −2.76630 −1.88876 5.65241 −2.53163 5.22487 3.60505 −10.1037 0.567402 7.00325
1.4 −2.76187 −2.45998 5.62792 2.94480 6.79415 1.83308 −10.0198 3.05151 −8.13315
1.5 −2.74676 2.86871 5.54471 2.35059 −7.87968 4.12455 −9.73648 5.22952 −6.45653
1.6 −2.73508 2.32253 5.48068 −2.83868 −6.35232 −0.0775144 −9.51993 2.39417 7.76402
1.7 −2.71891 −2.75648 5.39247 −2.65361 7.49462 −3.09784 −9.22383 4.59818 7.21494
1.8 −2.69661 0.0652072 5.27173 −0.769773 −0.175839 2.92622 −8.82260 −2.99575 2.07578
1.9 −2.67015 2.28839 5.12969 1.33703 −6.11033 −2.43023 −8.35672 2.23672 −3.57008
1.10 −2.66582 −1.97296 5.10658 1.39801 5.25954 −2.57413 −8.28157 0.892553 −3.72685
1.11 −2.66314 1.33494 5.09234 −1.13177 −3.55514 4.13938 −8.23535 −1.21793 3.01407
1.12 −2.66122 1.83704 5.08208 −0.683386 −4.88877 2.95312 −8.20207 0.374729 1.81864
1.13 −2.65863 −3.04392 5.06833 −3.14510 8.09266 2.18672 −8.15755 6.26543 8.36165
1.14 −2.64287 3.18125 4.98477 0.556594 −8.40764 −4.05191 −7.88836 7.12036 −1.47101
1.15 −2.64062 −0.800557 4.97285 2.95022 2.11396 2.31379 −7.85015 −2.35911 −7.79040
1.16 −2.62126 −0.553016 4.87101 −3.94850 1.44960 2.94765 −7.52568 −2.69417 10.3501
1.17 −2.54540 −3.20721 4.47904 0.372386 8.16363 −2.83053 −6.31014 7.28621 −0.947871
1.18 −2.51173 −2.30209 4.30878 −2.37349 5.78222 −4.88111 −5.79902 2.29960 5.96156
1.19 −2.51050 0.264508 4.30262 3.31299 −0.664049 1.39465 −5.78073 −2.93004 −8.31726
1.20 −2.50934 −1.29295 4.29679 −2.86314 3.24445 3.23051 −5.76344 −1.32829 7.18460
See next 80 embeddings (of 268 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.268
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

\( p \) Sign
\(6029\) \(-1\)