# Properties

 Label 287.2.w.a Level 287 Weight 2 Character orbit 287.w 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.w (of order $$24$$ and degree $$8$$)

## Newform invariants

 Self dual: No Analytic conductor: $$2.29170653801$$ Analytic rank: $$0$$ Dimension: $$208$$ Relative dimension: $$26$$ over $$\Q(\zeta_{24})$$ Sato-Tate group: $\mathrm{SU}(2)[C_{24}]$

## $q$-expansion

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

 $$\operatorname{Tr}(f)(q) =$$ $$208q - 4q^{2} - 12q^{3} - 12q^{5} - 8q^{7} - 32q^{8} + 4q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$208q - 4q^{2} - 12q^{3} - 12q^{5} - 8q^{7} - 32q^{8} + 4q^{9} - 24q^{10} - 4q^{11} - 12q^{12} - 4q^{14} + 8q^{15} + 72q^{16} + 24q^{17} - 8q^{18} + 12q^{19} - 48q^{21} - 96q^{22} - 60q^{24} - 36q^{26} - 24q^{28} + 16q^{29} - 36q^{30} + 48q^{32} + 48q^{33} + 32q^{35} - 80q^{36} + 16q^{37} + 72q^{38} - 4q^{39} + 80q^{42} - 64q^{43} - 12q^{44} - 44q^{46} + 12q^{47} - 72q^{49} - 8q^{50} + 16q^{51} + 12q^{52} - 28q^{53} - 180q^{54} - 32q^{56} - 16q^{57} - 24q^{59} - 4q^{60} - 12q^{61} + 36q^{63} - 8q^{65} + 4q^{67} - 84q^{68} + 20q^{70} + 32q^{71} - 48q^{73} + 40q^{74} + 168q^{75} - 104q^{77} - 48q^{78} - 120q^{80} + 132q^{82} + 112q^{84} + 64q^{85} - 144q^{87} - 32q^{88} + 36q^{89} - 56q^{91} + 16q^{92} + 4q^{93} + 96q^{94} - 4q^{95} + 12q^{96} - 136q^{98} - 224q^{99} + O(q^{100})$$

## 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 $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
3.1 −2.56100 0.686218i −0.904761 + 0.694247i 4.35578 + 2.51481i −1.05700 0.283223i 2.79350 1.15711i −0.803969 + 2.52064i −5.67989 5.67989i −0.439844 + 1.64152i 2.51263 + 1.45067i
3.2 −2.46478 0.660435i 2.16154 1.65861i 3.90691 + 2.25565i 1.76092 + 0.471838i −6.42311 + 2.66054i −2.53259 0.765512i −4.53126 4.53126i 1.14481 4.27250i −4.02867 2.32595i
3.3 −2.32636 0.623346i −0.340938 + 0.261611i 3.29134 + 1.90025i 4.19521 + 1.12410i 0.956220 0.396079i 2.58749 0.552173i −3.06629 3.06629i −0.728659 + 2.71939i −9.05885 5.23013i
3.4 −2.09048 0.560141i −2.51477 + 1.92965i 2.32428 + 1.34192i −1.10540 0.296191i 6.33795 2.62527i 2.23358 1.41814i −1.04651 1.04651i 1.82407 6.80751i 2.14490 + 1.23836i
3.5 −2.05371 0.550290i 0.683558 0.524512i 2.18286 + 1.26027i −3.50008 0.937845i −1.69246 + 0.701041i −1.22753 2.34375i −0.782599 0.782599i −0.584319 + 2.18071i 6.67207 + 3.85212i
3.6 −1.67812 0.449651i −1.39067 + 1.06710i 0.881854 + 0.509138i 0.769944 + 0.206306i 2.81353 1.16540i −2.27419 1.35207i 1.20602 + 1.20602i 0.0188054 0.0701826i −1.19929 0.692412i
3.7 −1.58699 0.425234i 0.715707 0.549181i 0.605675 + 0.349687i 1.24836 + 0.334498i −1.36935 + 0.567204i −0.971735 + 2.46084i 1.51102 + 1.51102i −0.565821 + 2.11167i −1.83890 1.06169i
3.8 −1.42899 0.382896i 0.0385589 0.0295873i 0.163340 + 0.0943042i −1.31495 0.352339i −0.0664289 + 0.0275158i 2.51506 0.821255i 1.89488 + 1.89488i −0.775846 + 2.89550i 1.74413 + 1.00697i
3.9 −1.05419 0.282470i 2.06157 1.58190i −0.700516 0.404443i 1.89345 + 0.507348i −2.62013 + 1.08530i 1.12649 2.39395i 2.16768 + 2.16768i 0.971213 3.62462i −1.85275 1.06969i
3.10 −0.866669 0.232223i 2.43423 1.86785i −1.03486 0.597479i −3.67938 0.985886i −2.54343 + 1.05352i −1.65100 + 2.06741i 2.02703 + 2.02703i 1.66016 6.19579i 2.95985 + 1.70887i
3.11 −0.626707 0.167926i −2.18400 + 1.67584i −1.36749 0.789519i −2.76165 0.739982i 1.65015 0.683514i −2.20483 + 1.46244i 1.64200 + 1.64200i 1.18496 4.42232i 1.60648 + 0.927504i
3.12 −0.389415 0.104344i −0.138074 + 0.105948i −1.59129 0.918734i −2.37555 0.636527i 0.0648230 0.0268506i 2.38380 + 1.14782i 1.09395 + 1.09395i −0.768618 + 2.86852i 0.858659 + 0.495747i
3.13 −0.376036 0.100759i −2.29715 + 1.76267i −1.60080 0.924222i 2.43497 + 0.652448i 1.04142 0.431369i 1.44457 + 2.21658i 1.05939 + 1.05939i 1.39346 5.20045i −0.849897 0.490688i
3.14 −0.0120160 0.00321968i 0.761682 0.584459i −1.73192 0.999923i 3.38537 + 0.907107i −0.0110342 + 0.00457050i −0.628724 + 2.56996i 0.0351840 + 0.0351840i −0.537890 + 2.00743i −0.0377581 0.0217996i
3.15 0.0492328 + 0.0131919i −1.37958 + 1.05859i −1.72980 0.998701i 2.44382 + 0.654820i −0.0818854 + 0.0339181i 0.674922 2.55822i −0.144070 0.144070i 0.00617438 0.0230431i 0.111678 + 0.0644773i
3.16 0.767199 + 0.205570i −0.489419 + 0.375544i −1.18572 0.684573i −1.27877 0.342645i −0.452682 + 0.187507i −2.38152 + 1.15254i −1.89221 1.89221i −0.677960 + 2.53018i −0.910632 0.525754i
3.17 0.772348 + 0.206950i 2.10066 1.61189i −1.17836 0.680325i 0.633392 + 0.169717i 1.95602 0.810211i 2.32510 + 1.26249i −1.90010 1.90010i 1.03812 3.87430i 0.454076 + 0.262161i
3.18 0.792178 + 0.212263i 1.39160 1.06781i −1.14956 0.663699i −1.93992 0.519800i 1.32905 0.550510i −1.09995 2.40626i −1.92961 1.92961i 0.0198671 0.0741452i −1.42643 0.823549i
3.19 1.28562 + 0.344480i −1.94647 + 1.49358i −0.197909 0.114263i −2.20971 0.592091i −3.01691 + 1.24965i 1.03924 2.43310i −2.09735 2.09735i 0.781503 2.91661i −2.63688 1.52240i
3.20 1.51317 + 0.405453i 1.09181 0.837772i 0.393242 + 0.227039i 4.15678 + 1.11381i 1.99177 0.825016i −1.89643 1.84487i −1.71245 1.71245i −0.286279 + 1.06841i 5.83832 + 3.37076i
See next 80 embeddings (of 208 total)
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 243.26 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 $$S_{2}^{\mathrm{new}}(287, [\chi])$$.