Properties

Label 287.2.l.a
Level 287
Weight 2
Character orbit 287.l
Analytic conductor 2.292
Analytic rank 0
Dimension 104
CM No

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Newspace parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 287.l (of order \(8\) and degree \(4\))

Newform invariants

Self dual: No
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(104\)
Relative dimension: \(26\) over \(\Q(\zeta_{8})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 104q - 8q^{2} - 4q^{7} + 8q^{8} + 8q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 104q - 8q^{2} - 4q^{7} + 8q^{8} + 8q^{9} - 8q^{11} - 8q^{14} - 32q^{15} - 96q^{16} - 16q^{18} - 24q^{21} + 24q^{22} + 12q^{28} - 16q^{29} + 48q^{30} - 72q^{32} - 44q^{35} + 56q^{36} + 32q^{37} - 8q^{39} - 8q^{42} - 32q^{43} + 72q^{44} - 88q^{46} - 12q^{49} + 80q^{50} + 32q^{51} - 8q^{53} + 104q^{56} - 32q^{57} - 96q^{58} + 112q^{60} - 132q^{63} + 80q^{65} + 56q^{67} + 148q^{70} - 104q^{71} + 32q^{74} - 16q^{77} - 168q^{78} - 124q^{84} + 8q^{85} - 64q^{88} + 8q^{91} + 104q^{92} - 64q^{93} - 8q^{95} - 8q^{98} + 8q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
27.1 −1.82241 1.82241i −1.24228 2.99913i 4.64235i −1.81451 1.81451i −3.20170 + 7.72960i −0.372244 2.61943i 4.81545 4.81545i −5.33022 + 5.33022i 6.61356i
27.2 −1.82241 1.82241i 1.24228 + 2.99913i 4.64235i 1.81451 + 1.81451i 3.20170 7.72960i 1.58900 + 2.11544i 4.81545 4.81545i −5.33022 + 5.33022i 6.61356i
27.3 −1.72064 1.72064i −0.369209 0.891351i 3.92122i 2.00511 + 2.00511i −0.898418 + 2.16897i −2.56283 + 0.657199i 3.30574 3.30574i 1.46313 1.46313i 6.90017i
27.4 −1.72064 1.72064i 0.369209 + 0.891351i 3.92122i −2.00511 2.00511i 0.898418 2.16897i −2.27690 + 1.34748i 3.30574 3.30574i 1.46313 1.46313i 6.90017i
27.5 −1.55293 1.55293i −0.699693 1.68921i 2.82318i 1.29416 + 1.29416i −1.53665 + 3.70980i 2.12474 + 1.57654i 1.27834 1.27834i −0.242535 + 0.242535i 4.01948i
27.6 −1.55293 1.55293i 0.699693 + 1.68921i 2.82318i −1.29416 1.29416i 1.53665 3.70980i 0.387642 2.61720i 1.27834 1.27834i −0.242535 + 0.242535i 4.01948i
27.7 −1.17122 1.17122i −0.481548 1.16256i 0.743529i 0.511687 + 0.511687i −0.797616 + 1.92562i 1.67326 2.04944i −1.47161 + 1.47161i 1.00167 1.00167i 1.19860i
27.8 −1.17122 1.17122i 0.481548 + 1.16256i 0.743529i −0.511687 0.511687i 0.797616 1.92562i 2.63235 + 0.265998i −1.47161 + 1.47161i 1.00167 1.00167i 1.19860i
27.9 −0.717741 0.717741i −0.472410 1.14050i 0.969695i −1.70830 1.70830i −0.479514 + 1.15765i −2.54594 0.719863i −2.13147 + 2.13147i 1.04376 1.04376i 2.45224i
27.10 −0.717741 0.717741i 0.472410 + 1.14050i 0.969695i 1.70830 + 1.70830i 0.479514 1.15765i −1.29123 + 2.30927i −2.13147 + 2.13147i 1.04376 1.04376i 2.45224i
27.11 −0.300045 0.300045i −0.219160 0.529099i 1.81995i 1.73401 + 1.73401i −0.0929957 + 0.224511i −1.42530 2.22902i −1.14615 + 1.14615i 1.88941 1.88941i 1.04056i
27.12 −0.300045 0.300045i 0.219160 + 0.529099i 1.81995i −1.73401 1.73401i 0.0929957 0.224511i 0.568314 + 2.58399i −1.14615 + 1.14615i 1.88941 1.88941i 1.04056i
27.13 −0.0425840 0.0425840i −0.956654 2.30957i 1.99637i −1.57284 1.57284i −0.0576124 + 0.139089i 2.61468 0.404284i −0.170181 + 0.170181i −2.29759 + 2.29759i 0.133955i
27.14 −0.0425840 0.0425840i 0.956654 + 2.30957i 1.99637i 1.57284 + 1.57284i 0.0576124 0.139089i 2.13473 1.56299i −0.170181 + 0.170181i −2.29759 + 2.29759i 0.133955i
27.15 0.279520 + 0.279520i −0.739386 1.78504i 1.84374i 2.85060 + 2.85060i 0.292280 0.705627i 1.56158 + 2.13576i 1.07440 1.07440i −0.518341 + 0.518341i 1.59360i
27.16 0.279520 + 0.279520i 0.739386 + 1.78504i 1.84374i −2.85060 2.85060i −0.292280 + 0.705627i −0.406011 2.61441i 1.07440 1.07440i −0.518341 + 0.518341i 1.59360i
27.17 0.652493 + 0.652493i −1.09762 2.64989i 1.14851i 0.202079 + 0.202079i 1.01284 2.44522i −2.64411 0.0932944i 2.05438 2.05438i −3.69581 + 3.69581i 0.263710i
27.18 0.652493 + 0.652493i 1.09762 + 2.64989i 1.14851i −0.202079 0.202079i −1.01284 + 2.44522i −1.80370 + 1.93563i 2.05438 2.05438i −3.69581 + 3.69581i 0.263710i
27.19 0.814711 + 0.814711i −0.0360204 0.0869609i 0.672492i 0.788699 + 0.788699i 0.0415018 0.100194i −0.714546 2.54743i 2.17731 2.17731i 2.11506 2.11506i 1.28512i
27.20 0.814711 + 0.814711i 0.0360204 + 0.0869609i 0.672492i −0.788699 0.788699i −0.0415018 + 0.100194i 1.29605 + 2.30657i 2.17731 2.17731i 2.11506 2.11506i 1.28512i
See next 80 embeddings (of 104 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 202.26
Significant digits:
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Inner twists

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

Hecke kernels

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