Properties

Label 287.2.j.a
Level 287
Weight 2
Character orbit 287.j
Analytic conductor 2.292
Analytic rank 0
Dimension 52
CM No

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Newspace parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 287.j (of order \(6\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(2.29170653801\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(26\) over \(\Q(\zeta_{6})\)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 52q - 2q^{2} - 26q^{4} - 6q^{5} - 12q^{8} + 16q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 52q - 2q^{2} - 26q^{4} - 6q^{5} - 12q^{8} + 16q^{9} + 16q^{10} - 26q^{16} + 12q^{18} + 16q^{20} - 48q^{21} - 32q^{25} + 6q^{31} + 20q^{32} - 20q^{33} - 4q^{36} - 24q^{37} + 14q^{39} + 44q^{40} + 24q^{41} - 2q^{42} - 32q^{43} + 26q^{45} + 12q^{46} + 16q^{49} - 12q^{51} + 8q^{57} + 2q^{59} + 14q^{61} - 20q^{62} - 20q^{64} - 4q^{66} - 42q^{72} - 16q^{73} - 22q^{74} - 32q^{77} + 88q^{78} - 52q^{80} - 46q^{81} - 42q^{82} - 112q^{83} + 72q^{84} + 16q^{86} - 18q^{87} + 224q^{90} + 86q^{91} - 32q^{92} - 48q^{98} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
81.1 −1.30798 2.26549i −0.306987 0.177239i −2.42163 + 4.19439i 0.326729 + 0.565911i 0.927301i 0.262924 + 2.63265i 7.43789 −1.43717 2.48926i 0.854711 1.48040i
81.2 −1.30798 2.26549i 0.306987 + 0.177239i −2.42163 + 4.19439i 0.326729 + 0.565911i 0.927301i −0.262924 2.63265i 7.43789 −1.43717 2.48926i 0.854711 1.48040i
81.3 −1.10471 1.91341i −2.73490 1.57900i −1.44075 + 2.49545i 1.43765 + 2.49009i 6.97730i 2.25170 1.38919i 1.94760 3.48645 + 6.03872i 3.17637 5.50163i
81.4 −1.10471 1.91341i 2.73490 + 1.57900i −1.44075 + 2.49545i 1.43765 + 2.49009i 6.97730i −2.25170 + 1.38919i 1.94760 3.48645 + 6.03872i 3.17637 5.50163i
81.5 −1.02851 1.78143i −1.38029 0.796913i −1.11566 + 1.93238i −2.03101 3.51781i 3.27853i 2.61591 0.396236i 0.475827 −0.229860 0.398129i −4.17782 + 7.23619i
81.6 −1.02851 1.78143i 1.38029 + 0.796913i −1.11566 + 1.93238i −2.03101 3.51781i 3.27853i −2.61591 + 0.396236i 0.475827 −0.229860 0.398129i −4.17782 + 7.23619i
81.7 −0.749549 1.29826i −1.70608 0.985006i −0.123649 + 0.214166i −0.142717 0.247192i 2.95324i −1.33336 + 2.28520i −2.62747 0.440474 + 0.762924i −0.213946 + 0.370566i
81.8 −0.749549 1.29826i 1.70608 + 0.985006i −0.123649 + 0.214166i −0.142717 0.247192i 2.95324i 1.33336 2.28520i −2.62747 0.440474 + 0.762924i −0.213946 + 0.370566i
81.9 −0.655113 1.13469i −0.913309 0.527299i 0.141655 0.245353i 1.55927 + 2.70074i 1.38176i −2.26438 1.36842i −2.99165 −0.943911 1.63490i 2.04300 3.53858i
81.10 −0.655113 1.13469i 0.913309 + 0.527299i 0.141655 0.245353i 1.55927 + 2.70074i 1.38176i 2.26438 + 1.36842i −2.99165 −0.943911 1.63490i 2.04300 3.53858i
81.11 −0.158705 0.274885i −0.453525 0.261843i 0.949625 1.64480i −0.708472 1.22711i 0.166223i 1.98670 + 1.74729i −1.23766 −1.36288 2.36057i −0.224876 + 0.389497i
81.12 −0.158705 0.274885i 0.453525 + 0.261843i 0.949625 1.64480i −0.708472 1.22711i 0.166223i −1.98670 1.74729i −1.23766 −1.36288 2.36057i −0.224876 + 0.389497i
81.13 −0.143305 0.248211i −2.80985 1.62226i 0.958928 1.66091i −1.41048 2.44302i 0.929911i −1.71093 2.01810i −1.12289 3.76349 + 6.51855i −0.404256 + 0.700192i
81.14 −0.143305 0.248211i 2.80985 + 1.62226i 0.958928 1.66091i −1.41048 2.44302i 0.929911i 1.71093 + 2.01810i −1.12289 3.76349 + 6.51855i −0.404256 + 0.700192i
81.15 0.0647109 + 0.112083i −1.92881 1.11360i 0.991625 1.71754i 0.451146 + 0.781409i 0.288247i 2.43969 1.02368i 0.515519 0.980198 + 1.69775i −0.0583882 + 0.101131i
81.16 0.0647109 + 0.112083i 1.92881 + 1.11360i 0.991625 1.71754i 0.451146 + 0.781409i 0.288247i −2.43969 + 1.02368i 0.515519 0.980198 + 1.69775i −0.0583882 + 0.101131i
81.17 0.467463 + 0.809670i −0.691950 0.399498i 0.562956 0.975068i 1.41567 + 2.45201i 0.747002i −0.561364 2.58551i 2.92250 −1.18080 2.04521i −1.32355 + 2.29245i
81.18 0.467463 + 0.809670i 0.691950 + 0.399498i 0.562956 0.975068i 1.41567 + 2.45201i 0.747002i 0.561364 + 2.58551i 2.92250 −1.18080 2.04521i −1.32355 + 2.29245i
81.19 0.649153 + 1.12437i −0.800607 0.462230i 0.157202 0.272281i −1.62887 2.82129i 1.20023i −2.18878 + 1.48635i 3.00480 −1.07269 1.85795i 2.11478 3.66290i
81.20 0.649153 + 1.12437i 0.800607 + 0.462230i 0.157202 0.272281i −1.62887 2.82129i 1.20023i 2.18878 1.48635i 3.00480 −1.07269 1.85795i 2.11478 3.66290i
See all 52 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 163.26
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 \(S_{2}^{\mathrm{new}}(287, [\chi])\).