Properties

Label 287.2.be.a
Level 287
Weight 2
Character orbit 287.be
Analytic conductor 2.292
Analytic rank 0
Dimension 832
CM No

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Newspace parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 287.be (of order \(120\) and degree \(32\))

Newform invariants

Self dual: No
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(832\)
Relative dimension: \(26\) over \(\Q(\zeta_{120})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{120}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 832q - 16q^{2} - 48q^{3} - 20q^{4} - 48q^{5} - 32q^{7} - 48q^{8} - 24q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 832q - 16q^{2} - 48q^{3} - 20q^{4} - 48q^{5} - 32q^{7} - 48q^{8} - 24q^{9} - 36q^{10} - 16q^{11} - 48q^{12} - 36q^{14} - 88q^{15} - 92q^{16} - 84q^{17} - 12q^{18} - 72q^{19} + 8q^{21} + 16q^{22} - 20q^{23} - 20q^{25} - 24q^{26} - 16q^{28} - 96q^{29} + 56q^{30} - 60q^{31} - 68q^{32} - 108q^{33} - 32q^{35} + 24q^{37} - 132q^{38} - 16q^{39} - 16q^{43} + 112q^{44} - 60q^{45} + 24q^{46} - 72q^{47} + 72q^{49} - 72q^{50} + 24q^{51} - 72q^{52} + 8q^{53} + 120q^{54} - 8q^{56} - 64q^{57} - 20q^{58} - 36q^{59} - 16q^{60} - 48q^{61} - 76q^{63} - 80q^{64} - 12q^{65} - 60q^{66} - 24q^{67} + 324q^{68} - 260q^{70} - 112q^{71} - 20q^{72} - 12q^{73} - 60q^{74} + 252q^{75} - 16q^{77} - 32q^{78} - 20q^{79} + 60q^{80} + 528q^{82} - 352q^{84} - 144q^{85} - 20q^{86} + 84q^{87} + 12q^{88} + 144q^{89} - 144q^{91} - 96q^{92} - 24q^{93} - 156q^{94} - 16q^{95} + 528q^{96} - 4q^{98} + 144q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
12.1 −2.13508 1.72896i 0.574751 0.0756675i 1.15347 + 5.42664i −2.25766 0.118319i −1.35797 0.832164i 2.57570 0.604798i 4.42515 8.68484i −2.57316 + 0.689477i 4.61573 + 4.15603i
12.2 −1.93631 1.56800i −2.94781 + 0.388087i 0.874875 + 4.11596i 0.221276 + 0.0115966i 6.31640 + 3.87070i −0.519127 + 2.59432i 2.49748 4.90158i 5.64121 1.51156i −0.410277 0.369415i
12.3 −1.75506 1.42122i −1.39725 + 0.183952i 0.644551 + 3.03238i −1.12109 0.0587539i 2.71371 + 1.66296i −1.82427 1.91626i 1.12792 2.21366i −0.979297 + 0.262402i 1.88408 + 1.69644i
12.4 −1.57832 1.27810i 1.93183 0.254330i 0.441732 + 2.07818i 2.52470 + 0.132314i −3.37410 2.06765i 1.08801 2.41169i 0.114895 0.225494i 0.769501 0.206187i −3.81567 3.43565i
12.5 −1.47683 1.19591i 0.467879 0.0615975i 0.334995 + 1.57603i 1.04774 + 0.0549097i −0.764644 0.468574i −2.52863 + 0.778495i −0.335397 + 0.658253i −2.68266 + 0.718817i −1.48167 1.33410i
12.6 −1.25725 1.01810i 0.937421 0.123414i 0.128329 + 0.603740i −3.08596 0.161728i −1.30423 0.799230i 0.923496 + 2.47935i −1.01559 + 1.99321i −2.03425 + 0.545076i 3.71518 + 3.34517i
12.7 −1.16336 0.942069i −0.808069 + 0.106384i 0.0500848 + 0.235631i 3.26900 + 0.171321i 1.04029 + 0.637493i 1.66923 + 2.05272i −1.19550 + 2.34630i −2.25612 + 0.604526i −3.64162 3.27893i
12.8 −0.981014 0.794410i −2.00494 + 0.263955i −0.0845211 0.397641i −3.10557 0.162756i 2.17656 + 1.33380i 1.34026 2.28116i −1.37914 + 2.70672i 1.05233 0.281971i 2.91732 + 2.62676i
12.9 −0.833004 0.674554i −3.31166 + 0.435988i −0.176950 0.832483i 3.11222 + 0.163105i 3.05272 + 1.87071i −0.679716 2.55695i −1.38740 + 2.72292i 7.87923 2.11123i −2.48247 2.23523i
12.10 −0.740543 0.599680i 2.48641 0.327342i −0.227035 1.06812i 0.303565 + 0.0159092i −2.03759 1.24864i 2.34417 1.22673i −1.33762 + 2.62522i 3.17729 0.851352i −0.215262 0.193823i
12.11 −0.352928 0.285796i 3.08231 0.405794i −0.372944 1.75456i 1.87083 + 0.0980462i −1.20381 0.737695i −1.92896 + 1.81083i −0.782169 + 1.53509i 6.43819 1.72511i −0.632249 0.569279i
12.12 −0.299998 0.242934i 1.71407 0.225662i −0.384841 1.81054i −3.20616 0.168028i −0.569038 0.348707i −2.14081 1.55464i −0.674892 + 1.32455i −0.0106627 + 0.00285705i 0.921023 + 0.829293i
12.13 −0.213546 0.172926i −1.16847 + 0.153832i −0.400125 1.88244i −0.113709 0.00595924i 0.276122 + 0.169208i −2.51661 + 0.816511i −0.489574 + 0.960843i −1.55613 + 0.416963i 0.0232515 + 0.0209358i
12.14 −0.204200 0.165358i −1.26370 + 0.166369i −0.401469 1.88876i 0.217800 + 0.0114144i 0.285558 + 0.174990i 2.61379 + 0.409999i −0.468920 + 0.920306i −1.32852 + 0.355975i −0.0425873 0.0383458i
12.15 0.230806 + 0.186903i 0.352694 0.0464331i −0.397485 1.87002i 3.65558 + 0.191581i 0.0900824 + 0.0552026i −0.772639 2.53042i 0.527433 1.03515i −2.77554 + 0.743704i 0.807922 + 0.727456i
12.16 0.507849 + 0.411248i −3.12411 + 0.411296i −0.327038 1.53859i −1.16320 0.0609607i −1.75572 1.07591i 1.58731 + 2.11671i 1.06000 2.08038i 6.69310 1.79341i −0.565660 0.509323i
12.17 0.733425 + 0.593916i 2.06942 0.272444i −0.230647 1.08511i −1.92360 0.100812i 1.67957 + 1.02924i 2.62811 0.305040i 1.33220 2.61459i 1.31048 0.351142i −1.35095 1.21640i
12.18 0.841945 + 0.681794i 1.16780 0.153744i −0.171794 0.808229i 1.89300 + 0.0992078i 1.08804 + 0.666754i −0.193877 + 2.63864i 1.39009 2.72821i −1.55766 + 0.417374i 1.52616 + 1.37416i
12.19 1.03626 + 0.839145i −2.26410 + 0.298075i −0.0461574 0.217153i −0.220901 0.0115769i −2.59632 1.59103i −2.51050 0.835088i 1.34511 2.63992i 2.13953 0.573285i −0.219196 0.197365i
12.20 1.07419 + 0.869862i −1.03328 + 0.136034i −0.0185991 0.0875017i −4.03044 0.211227i −1.22827 0.752685i 0.549028 2.58816i 1.31117 2.57331i −1.84861 + 0.495335i −4.14572 3.73283i
See next 80 embeddings (of 832 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 276.26
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 \(S_{2}^{\mathrm{new}}(287, [\chi])\).