Properties

Label 6029.2.a.a
Level 6029
Weight 2
Character orbit 6029.a
Self dual Yes
Analytic conductor 48.142
Analytic rank 1
Dimension 234
CM No

Related objects

Downloads

Learn more about

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: \(1\)
Dimension: \(234\)
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.

\(\operatorname{Tr}(f)(q) = \) \(234q \) \(\mathstrut -\mathstrut 10q^{2} \) \(\mathstrut -\mathstrut 43q^{3} \) \(\mathstrut +\mathstrut 202q^{4} \) \(\mathstrut -\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 40q^{6} \) \(\mathstrut -\mathstrut 61q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut +\mathstrut 203q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(234q \) \(\mathstrut -\mathstrut 10q^{2} \) \(\mathstrut -\mathstrut 43q^{3} \) \(\mathstrut +\mathstrut 202q^{4} \) \(\mathstrut -\mathstrut 24q^{5} \) \(\mathstrut -\mathstrut 40q^{6} \) \(\mathstrut -\mathstrut 61q^{7} \) \(\mathstrut -\mathstrut 27q^{8} \) \(\mathstrut +\mathstrut 203q^{9} \) \(\mathstrut -\mathstrut 89q^{10} \) \(\mathstrut -\mathstrut 55q^{11} \) \(\mathstrut -\mathstrut 75q^{12} \) \(\mathstrut -\mathstrut 49q^{13} \) \(\mathstrut -\mathstrut 42q^{14} \) \(\mathstrut -\mathstrut 43q^{15} \) \(\mathstrut +\mathstrut 142q^{16} \) \(\mathstrut -\mathstrut 40q^{17} \) \(\mathstrut -\mathstrut 30q^{18} \) \(\mathstrut -\mathstrut 235q^{19} \) \(\mathstrut -\mathstrut 62q^{20} \) \(\mathstrut -\mathstrut 62q^{21} \) \(\mathstrut -\mathstrut 63q^{22} \) \(\mathstrut -\mathstrut 30q^{23} \) \(\mathstrut -\mathstrut 108q^{24} \) \(\mathstrut +\mathstrut 170q^{25} \) \(\mathstrut -\mathstrut 44q^{26} \) \(\mathstrut -\mathstrut 160q^{27} \) \(\mathstrut -\mathstrut 147q^{28} \) \(\mathstrut -\mathstrut 76q^{29} \) \(\mathstrut -\mathstrut 15q^{30} \) \(\mathstrut -\mathstrut 175q^{31} \) \(\mathstrut -\mathstrut 49q^{32} \) \(\mathstrut -\mathstrut 43q^{33} \) \(\mathstrut -\mathstrut 104q^{34} \) \(\mathstrut -\mathstrut 87q^{35} \) \(\mathstrut +\mathstrut 124q^{36} \) \(\mathstrut -\mathstrut 77q^{37} \) \(\mathstrut -\mathstrut 18q^{38} \) \(\mathstrut -\mathstrut 104q^{39} \) \(\mathstrut -\mathstrut 247q^{40} \) \(\mathstrut -\mathstrut 60q^{41} \) \(\mathstrut -\mathstrut 6q^{42} \) \(\mathstrut -\mathstrut 201q^{43} \) \(\mathstrut -\mathstrut 89q^{44} \) \(\mathstrut -\mathstrut 102q^{45} \) \(\mathstrut -\mathstrut 128q^{46} \) \(\mathstrut -\mathstrut 27q^{47} \) \(\mathstrut -\mathstrut 130q^{48} \) \(\mathstrut +\mathstrut 123q^{49} \) \(\mathstrut -\mathstrut 33q^{50} \) \(\mathstrut -\mathstrut 220q^{51} \) \(\mathstrut -\mathstrut 125q^{52} \) \(\mathstrut -\mathstrut 34q^{53} \) \(\mathstrut -\mathstrut 126q^{54} \) \(\mathstrut -\mathstrut 176q^{55} \) \(\mathstrut -\mathstrut 125q^{56} \) \(\mathstrut -\mathstrut 17q^{57} \) \(\mathstrut -\mathstrut 46q^{58} \) \(\mathstrut -\mathstrut 172q^{59} \) \(\mathstrut -\mathstrut 61q^{60} \) \(\mathstrut -\mathstrut 243q^{61} \) \(\mathstrut -\mathstrut 37q^{62} \) \(\mathstrut -\mathstrut 137q^{63} \) \(\mathstrut +\mathstrut 39q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut -\mathstrut 142q^{66} \) \(\mathstrut -\mathstrut 132q^{67} \) \(\mathstrut -\mathstrut 106q^{68} \) \(\mathstrut -\mathstrut 115q^{69} \) \(\mathstrut -\mathstrut 60q^{70} \) \(\mathstrut -\mathstrut 68q^{71} \) \(\mathstrut -\mathstrut 66q^{72} \) \(\mathstrut -\mathstrut 109q^{73} \) \(\mathstrut -\mathstrut 74q^{74} \) \(\mathstrut -\mathstrut 256q^{75} \) \(\mathstrut -\mathstrut 412q^{76} \) \(\mathstrut -\mathstrut 32q^{77} \) \(\mathstrut -\mathstrut 38q^{78} \) \(\mathstrut -\mathstrut 297q^{79} \) \(\mathstrut -\mathstrut 111q^{80} \) \(\mathstrut +\mathstrut 142q^{81} \) \(\mathstrut -\mathstrut 94q^{82} \) \(\mathstrut -\mathstrut 100q^{83} \) \(\mathstrut -\mathstrut 134q^{84} \) \(\mathstrut -\mathstrut 90q^{85} \) \(\mathstrut +\mathstrut q^{86} \) \(\mathstrut -\mathstrut 103q^{87} \) \(\mathstrut -\mathstrut 143q^{88} \) \(\mathstrut -\mathstrut 77q^{89} \) \(\mathstrut -\mathstrut 181q^{90} \) \(\mathstrut -\mathstrut 418q^{91} \) \(\mathstrut -\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 5q^{93} \) \(\mathstrut -\mathstrut 231q^{94} \) \(\mathstrut -\mathstrut 92q^{95} \) \(\mathstrut -\mathstrut 189q^{96} \) \(\mathstrut -\mathstrut 141q^{97} \) \(\mathstrut -\mathstrut 25q^{98} \) \(\mathstrut -\mathstrut 244q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 −2.80022 1.58457 5.84121 4.15609 −4.43714 −3.16901 −10.7562 −0.489138 −11.6379
1.2 −2.76066 −0.121634 5.62124 3.66459 0.335789 3.49852 −9.99702 −2.98521 −10.1167
1.3 −2.74392 −0.541748 5.52907 0.314458 1.48651 −1.33061 −9.68348 −2.70651 −0.862845
1.4 −2.69522 −2.18729 5.26421 −2.45102 5.89522 −1.76465 −8.79776 1.78423 6.60605
1.5 −2.69066 −3.28902 5.23964 1.48988 8.84962 3.81047 −8.71676 7.81762 −4.00877
1.6 −2.66544 −2.15906 5.10457 0.849689 5.75486 1.23234 −8.27506 1.66156 −2.26480
1.7 −2.65389 2.88360 5.04315 −1.32989 −7.65277 −0.791725 −8.07619 5.31516 3.52939
1.8 −2.64551 −0.0881828 4.99870 −0.825561 0.233288 −0.584332 −7.93309 −2.99222 2.18403
1.9 −2.64305 3.09579 4.98571 −1.08129 −8.18234 −0.0368624 −7.89138 6.58394 2.85790
1.10 −2.59814 1.65321 4.75033 2.01329 −4.29528 1.44236 −7.14575 −0.266887 −5.23080
1.11 −2.58537 1.21501 4.68413 −1.54408 −3.14124 −3.29615 −6.93947 −1.52375 3.99201
1.12 −2.57920 −2.40579 4.65225 2.56752 6.20501 −4.72770 −6.84068 2.78784 −6.62214
1.13 −2.56265 1.36912 4.56717 2.03853 −3.50857 −0.777924 −6.57875 −1.12552 −5.22404
1.14 −2.53440 2.84813 4.42317 1.96183 −7.21830 −0.128324 −6.14128 5.11186 −4.97206
1.15 −2.51561 0.109654 4.32830 −3.06491 −0.275847 2.34212 −5.85711 −2.98798 7.71012
1.16 −2.49760 −0.682777 4.23800 −3.80739 1.70530 −3.54561 −5.58962 −2.53382 9.50934
1.17 −2.46346 −0.561509 4.06866 1.69947 1.38326 −4.80905 −5.09606 −2.68471 −4.18658
1.18 −2.45423 2.05779 4.02326 −1.79809 −5.05030 3.33599 −4.96555 1.23450 4.41293
1.19 −2.40890 −0.528400 3.80280 3.29514 1.27286 −3.46004 −4.34278 −2.72079 −7.93767
1.20 −2.38600 0.681249 3.69302 0.452211 −1.62546 3.54719 −4.03955 −2.53590 −1.07898
See next 80 embeddings (of 234 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.234
Significant digits:
Format:

Inner twists

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

Atkin-Lehner signs

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