Properties

Label 287.2.n.a
Level 287
Weight 2
Character orbit 287.n
Analytic conductor 2.292
Analytic rank 0
Dimension 88
CM No

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Newspace parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 287.n (of order \(10\) and degree \(4\))

Newform invariants

Self dual: No
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{10})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 88q - 24q^{4} + 8q^{5} + 10q^{6} - 18q^{8} - 116q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 88q - 24q^{4} + 8q^{5} + 10q^{6} - 18q^{8} - 116q^{9} + 36q^{10} - 10q^{11} + 20q^{15} - 12q^{16} - 10q^{17} + 20q^{18} + 30q^{19} - 30q^{20} + 4q^{21} - 20q^{22} - 12q^{23} + 60q^{24} - 50q^{25} - 30q^{26} + 2q^{31} + 24q^{32} - 46q^{33} + 50q^{34} + 86q^{36} - 48q^{37} + 16q^{39} - 60q^{40} - 24q^{41} - 4q^{42} + 22q^{43} - 16q^{45} + 20q^{46} + 20q^{48} + 22q^{49} - 16q^{50} + 8q^{51} + 70q^{52} - 30q^{54} + 8q^{57} - 90q^{58} - 4q^{59} - 50q^{60} - 64q^{61} - 44q^{62} + 14q^{64} + 80q^{65} - 26q^{66} + 10q^{67} + 40q^{71} + 18q^{72} + 124q^{73} + 80q^{74} + 70q^{75} - 190q^{76} + 8q^{77} + 74q^{78} + 26q^{80} + 144q^{81} - 58q^{82} - 60q^{83} + 26q^{84} + 10q^{86} + 8q^{87} + 160q^{88} - 164q^{90} - 40q^{91} - 156q^{92} - 20q^{93} + 10q^{94} + 80q^{95} - 90q^{97} - 40q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
64.1 −0.849806 2.61543i 0.744022i −4.50028 + 3.26965i −1.22809 + 0.892261i 1.94594 0.632274i −0.951057 0.309017i 7.92627 + 5.75877i 2.44643 3.37729 + 2.45374i
64.2 −0.790312 2.43233i 2.98213i −3.67361 + 2.66903i −2.37875 + 1.72826i −7.25354 + 2.35682i 0.951057 + 0.309017i 5.25714 + 3.81954i −5.89312 6.08367 + 4.42004i
64.3 −0.723131 2.22557i 3.25739i −2.81220 + 2.04318i 0.0446777 0.0324603i 7.24954 2.35552i 0.951057 + 0.309017i 2.79446 + 2.03029i −7.61060 −0.104550 0.0759602i
64.4 −0.668701 2.05805i 2.12658i −2.17038 + 1.57687i 2.21996 1.61290i −4.37661 + 1.42205i −0.951057 0.309017i 1.19526 + 0.868404i −1.52235 −4.80391 3.49025i
64.5 −0.492340 1.51527i 1.02578i −0.435599 + 0.316481i −1.62966 + 1.18402i 1.55432 0.505030i 0.951057 + 0.309017i −1.88391 1.36874i 1.94778 2.59645 + 1.88643i
64.6 −0.460807 1.41822i 2.32068i −0.180963 + 0.131477i 2.65229 1.92700i 3.29122 1.06938i −0.951057 0.309017i −2.14296 1.55695i −2.38554 −3.95510 2.87355i
64.7 −0.359030 1.10498i 2.08630i 0.525953 0.382127i 0.921790 0.669719i −2.30532 + 0.749044i 0.951057 + 0.309017i −2.49098 1.80981i −1.35264 −1.07098 0.778111i
64.8 −0.277962 0.855478i 2.49605i 0.963455 0.699991i −3.42952 + 2.49169i 2.13531 0.693805i −0.951057 0.309017i −2.32206 1.68707i −3.23024 3.08486 + 2.24128i
64.9 −0.250116 0.769777i 0.394533i 1.08803 0.790504i 2.74556 1.99477i 0.303703 0.0986791i 0.951057 + 0.309017i −2.19027 1.59132i 2.84434 −2.22224 1.61455i
64.10 −0.226327 0.696562i 3.21415i 1.18406 0.860269i −2.01792 + 1.46611i −2.23886 + 0.727449i −0.951057 0.309017i −2.05228 1.49107i −7.33079 1.47794 + 1.07379i
64.11 −0.172550 0.531055i 0.766888i 1.36579 0.992303i −0.120197 + 0.0873281i −0.407260 + 0.132327i −0.951057 0.309017i −1.66612 1.21051i 2.41188 0.0671161 + 0.0487627i
64.12 0.0458641 + 0.141155i 2.46220i 1.60021 1.16262i 1.41155 1.02555i −0.347553 + 0.112927i 0.951057 + 0.309017i 0.477650 + 0.347033i −3.06244 0.209501 + 0.152212i
64.13 0.141463 + 0.435377i 0.534298i 1.44849 1.05239i 0.174269 0.126614i −0.232621 + 0.0755832i −0.951057 0.309017i 1.40380 + 1.01992i 2.71453 0.0797773 + 0.0579616i
64.14 0.179096 + 0.551200i 1.26578i 1.34629 0.978135i −1.88894 + 1.37240i −0.697700 + 0.226697i 0.951057 + 0.309017i 1.71802 + 1.24822i 1.39779 −1.09477 0.795395i
64.15 0.239839 + 0.738150i 2.56947i 1.13069 0.821496i 0.320630 0.232952i 1.89665 0.616259i 0.951057 + 0.309017i 2.13339 + 1.55000i −3.60216 0.248853 + 0.180802i
64.16 0.398778 + 1.22731i 3.33877i 0.270763 0.196720i 0.305659 0.222075i −4.09772 + 1.33143i −0.951057 0.309017i 2.43744 + 1.77090i −8.14741 0.394445 + 0.286581i
64.17 0.558769 + 1.71971i 0.528092i −1.02716 + 0.746273i 2.52635 1.83550i −0.908166 + 0.295081i −0.951057 0.309017i 1.06843 + 0.776261i 2.72112 4.56817 + 3.31897i
64.18 0.620352 + 1.90925i 1.77499i −1.64235 + 1.19324i −2.14247 + 1.55660i −3.38889 + 1.10112i 0.951057 + 0.309017i −0.0488123 0.0354642i −0.150586 −4.30101 3.12487i
64.19 0.668213 + 2.05655i 1.25017i −2.16485 + 1.57285i 0.888713 0.645688i 2.57104 0.835382i 0.951057 + 0.309017i −1.18242 0.859080i 1.43707 1.92174 + 1.39622i
64.20 0.738747 + 2.27363i 3.34025i −3.00561 + 2.18370i 1.60198 1.16390i 7.59449 2.46760i −0.951057 0.309017i −3.31718 2.41007i −8.15727 3.82974 + 2.78247i
See all 88 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 148.22
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 \(S_{2}^{\mathrm{new}}(287, [\chi])\).