Properties

Label 287.3.d.d
Level 287
Weight 3
Character orbit 287.d
Analytic conductor 7.820
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(7.82018358714\)
Analytic rank: \(0\)
Dimension: \(32\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32q + 4q^{2} + 68q^{4} - 88q^{8} + 44q^{9} + O(q^{10}) \)
\(\operatorname{Tr}(f)(q) = \) \( 32q + 4q^{2} + 68q^{4} - 88q^{8} + 44q^{9} - 92q^{16} - 48q^{18} - 72q^{21} + 140q^{23} - 500q^{25} + 92q^{32} - 284q^{36} + 312q^{37} + 140q^{39} + 8q^{42} - 120q^{43} - 344q^{46} - 552q^{49} + 416q^{50} - 364q^{51} - 316q^{57} - 320q^{64} + 972q^{72} + 680q^{74} + 428q^{77} + 1144q^{78} - 240q^{81} + 640q^{84} + 260q^{86} - 160q^{91} + 676q^{92} + 532q^{98} + O(q^{100}) \)

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 \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
286.1 −3.60835 −0.377109 9.02020 7.18702i 1.36074 −2.11657 6.67234i −18.1146 −8.85779 25.9333i
286.2 −3.60835 −0.377109 9.02020 7.18702i 1.36074 −2.11657 + 6.67234i −18.1146 −8.85779 25.9333i
286.3 −3.60835 0.377109 9.02020 7.18702i −1.36074 2.11657 + 6.67234i −18.1146 −8.85779 25.9333i
286.4 −3.60835 0.377109 9.02020 7.18702i −1.36074 2.11657 6.67234i −18.1146 −8.85779 25.9333i
286.5 −2.67431 −2.89735 3.15194 3.34396i 7.74841 4.11915 5.65974i 2.26798 −0.605380 8.94280i
286.6 −2.67431 −2.89735 3.15194 3.34396i 7.74841 4.11915 + 5.65974i 2.26798 −0.605380 8.94280i
286.7 −2.67431 2.89735 3.15194 3.34396i −7.74841 −4.11915 + 5.65974i 2.26798 −0.605380 8.94280i
286.8 −2.67431 2.89735 3.15194 3.34396i −7.74841 −4.11915 5.65974i 2.26798 −0.605380 8.94280i
286.9 −2.31240 −5.31887 1.34721 9.29617i 12.2994 −2.62328 + 6.48987i 6.13432 19.2904 21.4965i
286.10 −2.31240 −5.31887 1.34721 9.29617i 12.2994 −2.62328 6.48987i 6.13432 19.2904 21.4965i
286.11 −2.31240 5.31887 1.34721 9.29617i −12.2994 2.62328 6.48987i 6.13432 19.2904 21.4965i
286.12 −2.31240 5.31887 1.34721 9.29617i −12.2994 2.62328 + 6.48987i 6.13432 19.2904 21.4965i
286.13 0.517567 −2.41493 −3.73212 2.97759i −1.24989 2.38045 + 6.58281i −4.00189 −3.16813 1.54110i
286.14 0.517567 −2.41493 −3.73212 2.97759i −1.24989 2.38045 6.58281i −4.00189 −3.16813 1.54110i
286.15 0.517567 2.41493 −3.73212 2.97759i 1.24989 −2.38045 6.58281i −4.00189 −3.16813 1.54110i
286.16 0.517567 2.41493 −3.73212 2.97759i 1.24989 −2.38045 + 6.58281i −4.00189 −3.16813 1.54110i
286.17 1.16717 −4.43412 −2.63772 9.05049i −5.17535 6.69015 2.05957i −7.74732 10.6614 10.5634i
286.18 1.16717 −4.43412 −2.63772 9.05049i −5.17535 6.69015 + 2.05957i −7.74732 10.6614 10.5634i
286.19 1.16717 4.43412 −2.63772 9.05049i 5.17535 −6.69015 + 2.05957i −7.74732 10.6614 10.5634i
286.20 1.16717 4.43412 −2.63772 9.05049i 5.17535 −6.69015 2.05957i −7.74732 10.6614 10.5634i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 286.32
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
41.b even 2 1 inner
287.d 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.d.d 32
7.b odd 2 1 inner 287.3.d.d 32
41.b even 2 1 inner 287.3.d.d 32
287.d odd 2 1 inner 287.3.d.d 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
287.3.d.d 32 1.a even 1 1 trivial
287.3.d.d 32 7.b odd 2 1 inner
287.3.d.d 32 41.b even 2 1 inner
287.3.d.d 32 287.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(287, [\chi])\):

\(T_{2}^{8} - \cdots\)
\(T_{3}^{16} - \cdots\)