↑

Properties

Label 87.3.h.a
Level $87$
Weight $3$
Character orbit 87.h
Analytic conductor $2.371$
Analytic rank $0$
Dimension $108$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [87,3,Mod(5,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.5"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 11])) N = Newforms(chi, 3, names="a")
 
Level: \( N \) \(=\) \( 87 = 3 \cdot 29 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 87.h (of order \(14\), degree \(6\), minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.37057829993\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(18\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 108 q - 7 q^{3} - 42 q^{4} - 23 q^{6} - 18 q^{7} - 17 q^{9} - 14 q^{10} - 52 q^{13} - 7 q^{15} - 58 q^{16} + 42 q^{18} - 14 q^{19} - 217 q^{21} + 124 q^{22} - 49 q^{24} + 64 q^{25} + 119 q^{27} + 284 q^{28}+ \cdots + 728 q^{97}+O(q^{100}) \) Copy content Toggle raw display

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.

Copy content comment:embeddings in the coefficient field
 
Copy content gp:mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
5.1 −2.34994 − 2.94673i 2.97268 + 0.403951i −2.27092 + 9.94953i 2.46864 − 1.96867i −5.79527 − 9.70893i −2.78219 − 12.1896i 21.0720 − 10.1478i 8.67365 + 2.40163i −11.6023 − 2.64815i
5.2 −2.17865 − 2.73194i −2.77437 + 1.14144i −1.82689 + 8.00414i 0.834882 − 0.665796i 9.16270 + 5.09261i 0.965090 + 4.22833i 13.2540 − 6.38280i 6.39424 − 6.33353i −3.63783 − 0.830310i
5.3 −1.88804 − 2.36753i −0.617993 − 2.93566i −1.15042 + 5.04031i −4.23340 + 3.37602i −5.78347 + 7.00577i −1.24954 − 5.47458i 3.19192 − 1.53715i −8.23617 + 3.62843i 15.9857 + 3.64863i
5.4 −1.66316 − 2.08554i 1.39395 + 2.65648i −0.693283 + 3.03747i −3.47513 + 2.77132i 3.22184 − 7.32530i 1.88409 + 8.25475i −2.12555 + 1.02361i −5.11382 + 7.40600i 11.5594 + 2.63836i
5.5 −1.29552 − 1.62454i −1.90654 − 2.31627i −0.0706505 + 0.309540i 6.44504 − 5.13975i −1.29290 + 6.09803i −0.0581208 − 0.254644i −6.89396 + 3.31996i −1.73022 + 8.83212i −16.6994 − 3.81153i
5.6 −1.10180 − 1.38161i 2.60182 − 1.49349i 0.195190 − 0.855183i 2.81050 − 2.24130i −4.93012 − 1.94918i 0.995710 + 4.36249i −7.76519 + 3.73952i 4.53895 − 7.77161i −6.19322 − 1.41356i
5.7 −0.872644 − 1.09426i −1.74433 + 2.44076i 0.454184 − 1.98991i −1.47289 + 1.17459i 4.19301 − 0.221166i −2.14367 − 9.39203i −7.61785 + 3.66856i −2.91464 − 8.51498i 2.57062 + 0.586728i
5.8 −0.331920 − 0.416215i −2.84628 − 0.947981i 0.827020 − 3.62341i −6.29240 + 5.01802i 0.550176 + 1.49932i 2.44775 + 10.7243i −3.70118 + 1.78239i 7.20266 + 5.39645i 4.17715 + 0.953408i
5.9 −0.154619 − 0.193886i 2.15710 + 2.08492i 0.876399 − 3.83975i 2.50579 − 1.99830i 0.0707084 − 0.740602i −0.713108 − 3.12433i −1.77371 + 0.854173i 0.306195 + 8.99479i −0.774887 − 0.176863i
5.10 0.154619 + 0.193886i 1.03887 − 2.81438i 0.876399 − 3.83975i −2.50579 + 1.99830i 0.706300 − 0.233735i −0.713108 − 3.12433i 1.77371 − 0.854173i −6.84150 − 5.84755i −0.774887 − 0.176863i
5.11 0.331920 + 0.416215i −2.15310 + 2.08906i 0.827020 − 3.62341i 6.29240 − 5.01802i −1.58415 − 0.202751i 2.44775 + 10.7243i 3.70118 − 1.78239i 0.271674 − 8.99590i 4.17715 + 0.953408i
5.12 0.872644 + 1.09426i −2.63059 − 1.44222i 0.454184 − 1.98991i 1.47289 − 1.17459i −0.717411 − 4.13710i −2.14367 − 9.39203i 7.61785 − 3.66856i 4.84003 + 7.58776i 2.57062 + 0.586728i
5.13 1.10180 + 1.38161i 2.99216 + 0.216704i 0.195190 − 0.855183i −2.81050 + 2.24130i 2.99737 + 4.37278i 0.995710 + 4.36249i 7.76519 − 3.73952i 8.90608 + 1.29683i −6.19322 − 1.41356i
5.14 1.29552 + 1.62454i −0.712740 + 2.91410i −0.0706505 + 0.309540i −6.44504 + 5.13975i −5.65744 + 2.61742i −0.0581208 − 0.254644i 6.89396 − 3.31996i −7.98400 − 4.15400i −16.6994 − 3.81153i
5.15 1.66316 + 2.08554i 0.103297 − 2.99822i −0.693283 + 3.03747i 3.47513 − 2.77132i 6.42471 − 4.77110i 1.88409 + 8.25475i 2.12555 − 1.02361i −8.97866 − 0.619417i 11.5594 + 2.63836i
5.16 1.88804 + 2.36753i 0.716941 + 2.91307i −1.15042 + 5.04031i 4.23340 − 3.37602i −5.54318 + 7.19740i −1.24954 − 5.47458i −3.19192 + 1.53715i −7.97199 + 4.17700i 15.9857 + 3.64863i
5.17 2.17865 + 2.73194i −2.99487 + 0.175354i −1.82689 + 8.00414i −0.834882 + 0.665796i −7.00382 − 7.79976i 0.965090 + 4.22833i −13.2540 + 6.38280i 8.93850 − 1.05033i −3.63783 − 0.830310i
5.18 2.34994 + 2.94673i 2.50302 − 1.65374i −2.27092 + 9.94953i −2.46864 + 1.96867i 10.7551 + 3.48953i −2.78219 − 12.1896i −21.0720 + 10.1478i 3.53026 − 8.27872i −11.6023 − 2.64815i
35.1 −2.34994 + 2.94673i 2.97268 − 0.403951i −2.27092 − 9.94953i 2.46864 + 1.96867i −5.79527 + 9.70893i −2.78219 + 12.1896i 21.0720 + 10.1478i 8.67365 − 2.40163i −11.6023 + 2.64815i
35.2 −2.17865 + 2.73194i −2.77437 − 1.14144i −1.82689 − 8.00414i 0.834882 + 0.665796i 9.16270 − 5.09261i 0.965090 − 4.22833i 13.2540 + 6.38280i 6.39424 + 6.33353i −3.63783 + 0.830310i
See next 80 embeddings (of 108 total)
\(n\): e.g. 2-40 or 80-90
Embeddings: e.g. 1-3 or 5.18
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
29.e even 14 1 inner
87.h odd 14 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 87.3.h.a ✓ 108
3.b odd 2 1 inner 87.3.h.a ✓ 108
29.e even 14 1 inner 87.3.h.a ✓ 108
87.h odd 14 1 inner 87.3.h.a ✓ 108
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
87.3.h.a ✓ 108 1.a even 1 1 trivial
87.3.h.a ✓ 108 3.b odd 2 1 inner
87.3.h.a ✓ 108 29.e even 14 1 inner
87.3.h.a ✓ 108 87.h odd 14 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(87, [\chi])\).