Properties

Label 287.3.b.a
Level 287
Weight 3
Character orbit 287.b
Analytic conductor 7.820
Analytic rank 0
Dimension 52
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 287 = 7 \cdot 41 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 287.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(52\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 52q + 2q^{2} + 90q^{4} + 12q^{7} - 2q^{8} - 140q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 52q + 2q^{2} + 90q^{4} + 12q^{7} - 2q^{8} - 140q^{9} + 24q^{11} - 14q^{14} + 44q^{15} + 194q^{16} + 70q^{18} - 16q^{21} - 48q^{22} - 80q^{23} - 304q^{25} + 64q^{28} - 12q^{29} + 64q^{30} - 166q^{32} + 30q^{35} - 70q^{36} + 36q^{37} - 68q^{39} + 164q^{42} - 172q^{43} + 72q^{44} + 68q^{46} - 172q^{49} - 234q^{50} + 156q^{51} + 64q^{53} - 234q^{56} + 140q^{57} - 556q^{58} + 152q^{60} - 130q^{63} + 334q^{64} - 76q^{65} + 160q^{67} + 202q^{70} - 408q^{71} - 40q^{72} + 398q^{74} - 248q^{77} + 390q^{78} + 264q^{79} - 116q^{81} - 418q^{84} + 232q^{85} + 368q^{86} - 220q^{88} + 32q^{91} - 74q^{92} + 240q^{93} - 44q^{95} + 838q^{98} - 24q^{99} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
83.1 −3.91995 3.45631i 11.3660 3.63802i 13.5486i 2.08600 6.68196i −28.8744 −2.94610 14.2609i
83.2 −3.91995 3.45631i 11.3660 3.63802i 13.5486i 2.08600 + 6.68196i −28.8744 −2.94610 14.2609i
83.3 −3.56913 1.37648i 8.73868 6.83538i 4.91282i −2.60551 + 6.49702i −16.9130 7.10532 24.3964i
83.4 −3.56913 1.37648i 8.73868 6.83538i 4.91282i −2.60551 6.49702i −16.9130 7.10532 24.3964i
83.5 −3.35920 4.56039i 7.28419 3.56634i 15.3193i 1.27295 + 6.88328i −11.0323 −11.7972 11.9800i
83.6 −3.35920 4.56039i 7.28419 3.56634i 15.3193i 1.27295 6.88328i −11.0323 −11.7972 11.9800i
83.7 −2.92667 4.64649i 4.56541 4.20752i 13.5988i 3.25112 6.19921i −1.65478 −12.5899 12.3140i
83.8 −2.92667 4.64649i 4.56541 4.20752i 13.5988i 3.25112 + 6.19921i −1.65478 −12.5899 12.3140i
83.9 −2.86582 0.616832i 4.21290 6.13459i 1.76773i 6.72196 + 1.95326i −0.610133 8.61952 17.5806i
83.10 −2.86582 0.616832i 4.21290 6.13459i 1.76773i 6.72196 1.95326i −0.610133 8.61952 17.5806i
83.11 −2.44013 4.97182i 1.95424 3.83331i 12.1319i −6.90407 1.15493i 4.99192 −15.7190 9.35378i
83.12 −2.44013 4.97182i 1.95424 3.83331i 12.1319i −6.90407 + 1.15493i 4.99192 −15.7190 9.35378i
83.13 −1.91914 2.33237i −0.316896 6.26237i 4.47614i −1.97015 6.71703i 8.28473 3.56006 12.0184i
83.14 −1.91914 2.33237i −0.316896 6.26237i 4.47614i −1.97015 + 6.71703i 8.28473 3.56006 12.0184i
83.15 −1.45610 1.32130i −1.87978 7.87741i 1.92394i −0.510666 6.98135i 8.56153 7.25417 11.4703i
83.16 −1.45610 1.32130i −1.87978 7.87741i 1.92394i −0.510666 + 6.98135i 8.56153 7.25417 11.4703i
83.17 −1.37538 3.94905i −2.10832 8.96232i 5.43145i −6.93022 + 0.985899i 8.40128 −6.59497 12.3266i
83.18 −1.37538 3.94905i −2.10832 8.96232i 5.43145i −6.93022 0.985899i 8.40128 −6.59497 12.3266i
83.19 −1.34917 3.09036i −2.17974 2.40453i 4.16942i 6.89193 + 1.22527i 8.33752 −0.550339 3.24412i
83.20 −1.34917 3.09036i −2.17974 2.40453i 4.16942i 6.89193 1.22527i 8.33752 −0.550339 3.24412i
See all 52 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 83.52
Significant digits:
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Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 287.3.b.a 52
7.b odd 2 1 inner 287.3.b.a 52
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
287.3.b.a 52 1.a even 1 1 trivial
287.3.b.a 52 7.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(287, [\chi])\).