Properties

 Label 287.2.s.a Level 287 Weight 2 Character orbit 287.s Analytic conductor 2.292 Analytic rank 0 Dimension 208 CM No

Related objects

Newspace parameters

 Level: $$N$$ = $$287 = 7 \cdot 41$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 287.s (of order $$15$$ and degree $$8$$)

Newform invariants

 Self dual: No Analytic conductor: $$2.29170653801$$ Analytic rank: $$0$$ Dimension: $$208$$ Relative dimension: $$26$$ over $$\Q(\zeta_{15})$$ Sato-Tate group: $\mathrm{SU}(2)[C_{15}]$

$q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$208q - 3q^{2} - 8q^{3} + 21q^{4} - 7q^{5} - 8q^{6} - 6q^{7} - 32q^{8} - 92q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$208q - 3q^{2} - 8q^{3} + 21q^{4} - 7q^{5} - 8q^{6} - 6q^{7} - 32q^{8} - 92q^{9} - 24q^{10} + q^{11} + 19q^{12} - 12q^{13} - 62q^{14} - 6q^{15} + 21q^{16} + 3q^{17} + q^{19} - 48q^{20} + 20q^{21} - 68q^{22} - 6q^{23} - 18q^{24} + 3q^{25} + 15q^{26} + 28q^{27} - 11q^{28} + 44q^{29} - 5q^{30} - 11q^{31} - 6q^{32} + 10q^{33} - 108q^{34} - 30q^{35} + 66q^{36} - 32q^{37} - 10q^{38} - 2q^{39} + 70q^{40} - 6q^{41} + 24q^{42} - 8q^{43} - 68q^{44} + 12q^{45} - 66q^{46} + 31q^{47} + 110q^{48} + 10q^{49} + 64q^{50} - 2q^{51} + 69q^{52} - 42q^{53} + 43q^{54} - 80q^{55} + 10q^{56} - 30q^{57} - q^{58} - 29q^{59} + 22q^{60} - 9q^{61} + 30q^{62} + 54q^{63} - 4q^{64} - 14q^{65} + 78q^{66} + q^{67} - 42q^{68} + 46q^{69} - 179q^{70} - 10q^{71} - 13q^{72} + 30q^{73} + 61q^{74} + 52q^{75} + 118q^{76} - 56q^{77} - 94q^{78} + 2q^{79} - 17q^{80} - 16q^{81} - 21q^{82} - 208q^{83} - 33q^{84} + 36q^{85} + 39q^{86} + 10q^{87} + 24q^{88} - 89q^{89} + 242q^{90} + 18q^{91} - 10q^{92} + 71q^{93} + 81q^{94} - 83q^{95} - 64q^{96} - 24q^{97} + 26q^{98} - 12q^{99} + O(q^{100})$$

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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
16.1 −1.79193 1.99014i −0.888984 1.53977i −0.540586 + 5.14333i 2.48601 1.10684i −1.47135 + 4.52835i 2.12797 1.57217i 6.87154 4.99247i −0.0805851 + 0.139577i −6.65752 2.96412i
16.2 −1.58204 1.75703i −0.785173 1.35996i −0.375257 + 3.57033i −2.10481 + 0.937122i −1.14732 + 3.53108i −2.29494 1.31653i 3.04131 2.20964i 0.267007 0.462470i 4.97644 + 2.21565i
16.3 −1.45256 1.61323i 1.19642 + 2.07226i −0.283525 + 2.69756i 0.0523239 0.0232961i 1.60516 4.94017i 2.62771 + 0.308433i 1.25116 0.909021i −1.36284 + 2.36051i −0.113585 0.0505714i
16.4 −1.40852 1.56432i −0.00539923 0.00935174i −0.254114 + 2.41773i −2.73261 + 1.21664i −0.00702421 + 0.0216183i 1.45160 + 2.21198i 0.734066 0.533330i 1.49994 2.59798i 5.75216 + 2.56103i
16.5 −1.36165 1.51226i 1.06741 + 1.84881i −0.223797 + 2.12929i 3.08312 1.37270i 1.34245 4.13164i −1.66849 2.05333i 0.232155 0.168671i −0.778739 + 1.34882i −6.27400 2.79336i
16.6 −1.26421 1.40404i −1.60782 2.78482i −0.164063 + 1.56096i 0.136536 0.0607897i −1.87740 + 5.77804i 0.467596 + 2.60410i −0.657931 + 0.478015i −3.67016 + 6.35691i −0.257961 0.114852i
16.7 −1.03481 1.14927i −0.454048 0.786434i −0.0409382 + 0.389501i 1.51713 0.675470i −0.433973 + 1.33563i −2.60050 + 0.487236i −2.01228 + 1.46200i 1.08768 1.88392i −2.34623 1.04461i
16.8 −0.814209 0.904270i 0.855083 + 1.48105i 0.0542878 0.516514i −2.80174 + 1.24741i 0.643051 1.97911i −0.668217 2.55998i −2.48012 + 1.80191i 0.0376673 0.0652417i 3.40920 + 1.51787i
16.9 −0.694207 0.770995i −0.378549 0.655666i 0.0965469 0.918582i 1.11713 0.497379i −0.242724 + 0.747028i 2.49934 0.867915i −2.45392 + 1.78288i 1.21340 2.10167i −1.15900 0.516020i
16.10 −0.693484 0.770192i 0.967334 + 1.67547i 0.0967811 0.920811i −2.15281 + 0.958491i 0.619605 1.90695i −2.14904 + 1.54325i −2.45324 + 1.78238i −0.371471 + 0.643406i 2.23116 + 0.993376i
16.11 −0.351292 0.390150i −1.33649 2.31487i 0.180246 1.71493i −2.89925 + 1.29083i −0.433647 + 1.33463i 0.722046 2.54532i −1.58186 + 1.14929i −2.07241 + 3.58953i 1.52210 + 0.677683i
16.12 −0.235894 0.261986i 0.717760 + 1.24320i 0.196066 1.86544i 2.30867 1.02789i 0.156386 0.481305i 0.417255 + 2.61264i −1.10539 + 0.803112i 0.469642 0.813444i −0.813892 0.362368i
16.13 0.00316337 + 0.00351327i −1.15072 1.99311i 0.209055 1.98902i 3.85465 1.71620i 0.00336219 0.0103478i −2.39244 1.12971i 0.0152987 0.0111151i −1.14833 + 1.98897i 0.0182232 + 0.00811347i
16.14 0.0783279 + 0.0869920i 1.70494 + 2.95304i 0.207625 1.97542i 0.329616 0.146754i −0.123347 + 0.379622i 1.89833 1.84291i 0.377514 0.274280i −4.31364 + 7.47144i 0.0385845 + 0.0171789i
16.15 0.247447 + 0.274817i −0.599885 1.03903i 0.194762 1.85304i −2.37234 + 1.05623i 0.137104 0.421964i −2.30414 + 1.30036i 1.15579 0.839734i 0.780276 1.35148i −0.877298 0.390598i
16.16 0.472483 + 0.524745i −1.44621 2.50492i 0.156939 1.49318i 1.37084 0.610336i 0.631132 1.94242i 2.23920 + 1.40925i 2.00021 1.45323i −2.68307 + 4.64721i 0.967968 + 0.430967i
16.17 0.555807 + 0.617286i 0.273386 + 0.473519i 0.136936 1.30286i 0.363286 0.161745i −0.140347 + 0.431943i 0.688603 2.55457i 2.22435 1.61609i 1.35052 2.33917i 0.301760 + 0.134352i
16.18 0.690406 + 0.766773i −0.203562 0.352579i 0.0977758 0.930274i −2.33072 + 1.03770i 0.129808 0.399508i 2.50481 + 0.852013i 2.45029 1.78024i 1.41713 2.45453i −2.40482 1.07070i
16.19 0.863852 + 0.959405i 1.34226 + 2.32487i 0.0348396 0.331477i −2.70729 + 1.20536i −1.07097 + 3.29611i −0.897579 + 2.48885i 2.43701 1.77059i −2.10333 + 3.64308i −3.49513 1.55613i
16.20 1.07005 + 1.18841i 1.15675 + 2.00356i −0.0582569 + 0.554278i 2.56833 1.14349i −1.14327 + 3.51861i −2.64569 + 0.0176917i 1.86646 1.35606i −1.17616 + 2.03717i 4.10718 + 1.82863i
See next 80 embeddings (of 208 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 256.26 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Inner twists

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

Hecke kernels

There are no other newforms in $$S_{2}^{\mathrm{new}}(287, [\chi])$$.