Properties

Label 27.5.f.a
Level 27
Weight 5
Character orbit 27.f
Analytic conductor 2.791
Analytic rank 0
Dimension 66
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 5 \)
Character orbit: \([\chi]\) = 27.f (of order \(18\) and degree \(6\))

Newform invariants

Self dual: No
Analytic conductor: \(2.79098900326\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{18})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \(66q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 90q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 108q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \(66q \) \(\mathstrut -\mathstrut 6q^{2} \) \(\mathstrut -\mathstrut 6q^{3} \) \(\mathstrut -\mathstrut 6q^{4} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 90q^{6} \) \(\mathstrut -\mathstrut 6q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut -\mathstrut 108q^{9} \) \(\mathstrut -\mathstrut 3q^{10} \) \(\mathstrut -\mathstrut 492q^{11} \) \(\mathstrut -\mathstrut 339q^{12} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut +\mathstrut 1137q^{14} \) \(\mathstrut +\mathstrut 1017q^{15} \) \(\mathstrut -\mathstrut 54q^{16} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 603q^{18} \) \(\mathstrut -\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 2487q^{20} \) \(\mathstrut -\mathstrut 2784q^{21} \) \(\mathstrut +\mathstrut 1002q^{22} \) \(\mathstrut -\mathstrut 2724q^{23} \) \(\mathstrut -\mathstrut 3312q^{24} \) \(\mathstrut +\mathstrut 435q^{25} \) \(\mathstrut +\mathstrut 1368q^{27} \) \(\mathstrut -\mathstrut 12q^{28} \) \(\mathstrut +\mathstrut 5016q^{29} \) \(\mathstrut +\mathstrut 10773q^{30} \) \(\mathstrut -\mathstrut 1671q^{31} \) \(\mathstrut +\mathstrut 10224q^{32} \) \(\mathstrut +\mathstrut 2925q^{33} \) \(\mathstrut -\mathstrut 342q^{34} \) \(\mathstrut -\mathstrut 2682q^{35} \) \(\mathstrut -\mathstrut 7704q^{36} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 6564q^{38} \) \(\mathstrut -\mathstrut 1983q^{39} \) \(\mathstrut -\mathstrut 1113q^{40} \) \(\mathstrut +\mathstrut 5754q^{41} \) \(\mathstrut +\mathstrut 8694q^{42} \) \(\mathstrut -\mathstrut 1266q^{43} \) \(\mathstrut -\mathstrut 4545q^{44} \) \(\mathstrut -\mathstrut 7029q^{45} \) \(\mathstrut -\mathstrut 3q^{46} \) \(\mathstrut -\mathstrut 9159q^{47} \) \(\mathstrut -\mathstrut 28383q^{48} \) \(\mathstrut +\mathstrut 5898q^{49} \) \(\mathstrut -\mathstrut 34977q^{50} \) \(\mathstrut -\mathstrut 14814q^{51} \) \(\mathstrut +\mathstrut 2871q^{52} \) \(\mathstrut +\mathstrut 13878q^{54} \) \(\mathstrut -\mathstrut 12q^{55} \) \(\mathstrut +\mathstrut 39243q^{56} \) \(\mathstrut +\mathstrut 15792q^{57} \) \(\mathstrut -\mathstrut 12291q^{58} \) \(\mathstrut +\mathstrut 24762q^{59} \) \(\mathstrut +\mathstrut 50670q^{60} \) \(\mathstrut -\mathstrut 8358q^{61} \) \(\mathstrut +\mathstrut 38304q^{62} \) \(\mathstrut +\mathstrut 21609q^{63} \) \(\mathstrut +\mathstrut 6141q^{64} \) \(\mathstrut +\mathstrut 23727q^{65} \) \(\mathstrut +\mathstrut 11349q^{66} \) \(\mathstrut +\mathstrut 15996q^{67} \) \(\mathstrut -\mathstrut 43533q^{68} \) \(\mathstrut -\mathstrut 26847q^{69} \) \(\mathstrut -\mathstrut 7251q^{70} \) \(\mathstrut -\mathstrut 19773q^{71} \) \(\mathstrut -\mathstrut 77580q^{72} \) \(\mathstrut +\mathstrut 6108q^{73} \) \(\mathstrut -\mathstrut 74847q^{74} \) \(\mathstrut -\mathstrut 49155q^{75} \) \(\mathstrut -\mathstrut 28614q^{76} \) \(\mathstrut -\mathstrut 33909q^{77} \) \(\mathstrut -\mathstrut 9108q^{78} \) \(\mathstrut -\mathstrut 5658q^{79} \) \(\mathstrut -\mathstrut 12600q^{81} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 18813q^{83} \) \(\mathstrut +\mathstrut 82356q^{84} \) \(\mathstrut +\mathstrut 24219q^{85} \) \(\mathstrut +\mathstrut 96474q^{86} \) \(\mathstrut +\mathstrut 84555q^{87} \) \(\mathstrut +\mathstrut 36042q^{88} \) \(\mathstrut +\mathstrut 110232q^{89} \) \(\mathstrut +\mathstrut 153540q^{90} \) \(\mathstrut -\mathstrut 6042q^{91} \) \(\mathstrut +\mathstrut 73545q^{92} \) \(\mathstrut +\mathstrut 1293q^{93} \) \(\mathstrut +\mathstrut 2631q^{94} \) \(\mathstrut -\mathstrut 65163q^{95} \) \(\mathstrut -\mathstrut 152226q^{96} \) \(\mathstrut -\mathstrut 3696q^{97} \) \(\mathstrut -\mathstrut 259938q^{98} \) \(\mathstrut -\mathstrut 162405q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
2.1 −7.11993 1.25544i 6.30423 6.42314i 34.0822 + 12.4049i −16.3502 19.4854i −52.9495 + 37.8177i −60.7132 + 22.0978i −126.911 73.2722i −1.51338 80.9859i 91.9496 + 159.261i
2.2 −6.19782 1.09284i −7.35835 + 5.18216i 22.1836 + 8.07418i −7.06026 8.41408i 51.2690 24.0766i 62.3269 22.6852i −41.4621 23.9381i 27.2905 76.2642i 34.5629 + 59.8648i
2.3 −4.35935 0.768672i −5.98497 6.72162i 3.37802 + 1.22950i 27.2417 + 32.4654i 20.9239 + 33.9024i −49.1081 + 17.8739i 47.5559 + 27.4564i −9.36028 + 80.4573i −93.8009 162.468i
2.4 −3.58910 0.632855i 8.76651 + 2.03673i −2.55397 0.929568i 12.8585 + 15.3241i −30.1749 12.8580i 75.5885 27.5120i 59.0773 + 34.1083i 72.7034 + 35.7101i −36.4523 63.1373i
2.5 −2.38785 0.421042i 1.69434 + 8.83907i −9.51055 3.46156i −12.2061 14.5467i −0.324205 21.8197i −77.2633 + 28.1215i 54.8497 + 31.6675i −75.2584 + 29.9528i 23.0216 + 39.8746i
2.6 −0.185922 0.0327832i 3.20767 8.40898i −15.0016 5.46013i −10.5929 12.6241i −0.872050 + 1.45826i 26.3432 9.58813i 5.22609 + 3.01729i −60.4218 53.9464i 1.55560 + 2.69438i
2.7 1.18141 + 0.208314i −8.94516 0.991988i −13.6827 4.98011i −12.1061 14.4275i −10.3613 3.03535i 0.372391 0.135539i −31.7501 18.3309i 79.0319 + 17.7470i −11.2968 19.5667i
2.8 2.89555 + 0.510564i −3.30987 + 8.36927i −6.91152 2.51559i 31.8237 + 37.9260i −13.8570 + 22.5438i 28.2667 10.2882i −59.4692 34.3346i −59.0895 55.4025i 72.7837 + 126.065i
2.9 4.49504 + 0.792597i 8.84760 + 1.64926i 4.54211 + 1.65319i −3.40574 4.05880i 38.4631 + 14.4261i −28.7185 + 10.4527i −44.1393 25.4838i 75.5599 + 29.1840i −12.0919 20.9439i
2.10 5.98494 + 1.05531i −1.69482 8.83898i 19.6707 + 7.15955i 10.5942 + 12.6257i −0.815584 54.6893i 7.09675 2.58301i 25.9633 + 14.9899i −75.2551 + 29.9610i 50.0816 + 86.7438i
2.11 7.34334 + 1.29483i −4.72310 + 7.66109i 37.2130 + 13.5444i −22.9421 27.3414i −44.6032 + 50.1424i 14.0427 5.11111i 152.408 + 87.9929i −36.3846 72.3682i −133.070 230.483i
5.1 −5.07357 6.04645i 4.83746 + 7.58940i −8.04003 + 45.5973i 2.20171 + 6.04914i 21.3457 67.7548i 3.89095 + 22.0667i 207.124 119.583i −34.1980 + 73.4268i 25.4053 44.0033i
5.2 −3.69447 4.40289i −2.23464 8.71817i −2.95802 + 16.7758i −4.30375 11.8244i −30.1294 + 42.0478i 8.03917 + 45.5924i 5.14963 2.97314i −71.0128 + 38.9638i −36.1617 + 62.6340i
5.3 −2.66286 3.17348i −8.41268 + 3.19794i −0.201747 + 1.14416i 12.7013 + 34.8965i 32.5504 + 18.1818i 4.71194 + 26.7227i −53.2345 + 30.7349i 60.5463 53.8065i 76.9216 133.232i
5.4 −2.46212 2.93424i 8.40252 3.22453i 0.230635 1.30800i 3.23200 + 8.87984i −30.1496 16.7158i −13.4127 76.0673i −57.4812 + 33.1868i 60.2048 54.1884i 18.0980 31.3467i
5.5 −1.73231 2.06448i −2.55344 + 8.63017i 1.51717 8.60428i −14.6121 40.1465i 22.2402 9.67858i −2.26393 12.8394i −57.7345 + 33.3330i −67.9598 44.0734i −57.5690 + 99.7125i
5.6 0.712681 + 0.849340i 5.75088 + 6.92296i 2.56491 14.5463i 9.60722 + 26.3956i −1.78140 + 9.81832i 2.66962 + 15.1401i 29.5458 17.0583i −14.8546 + 79.6262i −15.5720 + 26.9714i
5.7 0.868224 + 1.03471i −7.41018 5.10776i 2.46156 13.9602i −3.20330 8.80100i −1.14866 12.1021i −7.41386 42.0461i 35.2980 20.3793i 28.8216 + 75.6988i 6.32529 10.9557i
5.8 1.32398 + 1.57786i 6.23064 6.49455i 2.04165 11.5788i −6.36554 17.4892i 18.4968 + 1.23241i 14.2733 + 80.9481i 49.5136 28.5867i −3.35832 80.9304i 19.1677 33.1993i
5.9 3.59971 + 4.28997i −7.31429 + 5.24416i −2.66754 + 15.1284i 2.69449 + 7.40305i −48.8266 12.5006i 7.02945 + 39.8660i 3.09545 1.78716i 25.9976 76.7146i −22.0595 + 38.2081i
See all 66 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 23.11
Significant digits:
Format:

Inner twists

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

Hecke kernels

There are no other newforms in \(S_{5}^{\mathrm{new}}(27, [\chi])\).