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Properties

Label 1287.3.h.a
Level $1287$
Weight $3$
Character orbit 1287.h
Analytic conductor $35.068$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1287,3,Mod(584,1287)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1287, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1287.584");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1287 = 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1287.h (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(35.0682100232\)
Analytic rank: \(0\)
Dimension: \(96\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 208 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q + 208 q^{4} - 16 q^{10} + 40 q^{13} + 480 q^{16} + 624 q^{25} - 16 q^{40} - 80 q^{43} - 1072 q^{49} - 88 q^{52} + 368 q^{61} + 1456 q^{64} - 528 q^{79} + 736 q^{82} - 528 q^{88} + 272 q^{91} - 768 q^{94}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
584.1 −3.91080 0 11.2944 6.11866 0 − 7.64067i −28.5268 0 −23.9289
584.2 −3.91080 0 11.2944 6.11866 0 7.64067i −28.5268 0 −23.9289
584.3 −3.83836 0 10.7330 −2.14154 0 − 2.37623i −25.8439 0 8.22001
584.4 −3.83836 0 10.7330 −2.14154 0 2.37623i −25.8439 0 8.22001
584.5 −3.68983 0 9.61482 −9.17847 0 6.86447i −20.7177 0 33.8670
584.6 −3.68983 0 9.61482 −9.17847 0 − 6.86447i −20.7177 0 33.8670
584.7 −3.63574 0 9.21862 −2.36731 0 13.0148i −18.9736 0 8.60693
584.8 −3.63574 0 9.21862 −2.36731 0 − 13.0148i −18.9736 0 8.60693
584.9 −3.31796 0 7.00885 5.51637 0 3.89793i −9.98325 0 −18.3031
584.10 −3.31796 0 7.00885 5.51637 0 − 3.89793i −9.98325 0 −18.3031
584.11 −3.30753 0 6.93973 6.07201 0 0.234338i −9.72324 0 −20.0833
584.12 −3.30753 0 6.93973 6.07201 0 − 0.234338i −9.72324 0 −20.0833
584.13 −3.27587 0 6.73135 3.11266 0 12.7660i −8.94757 0 −10.1967
584.14 −3.27587 0 6.73135 3.11266 0 − 12.7660i −8.94757 0 −10.1967
584.15 −3.16357 0 6.00818 −7.12389 0 − 1.44438i −6.35300 0 22.5369
584.16 −3.16357 0 6.00818 −7.12389 0 1.44438i −6.35300 0 22.5369
584.17 −2.84410 0 4.08892 3.52466 0 − 9.26254i −0.252888 0 −10.0245
584.18 −2.84410 0 4.08892 3.52466 0 9.26254i −0.252888 0 −10.0245
584.19 −2.51490 0 2.32474 −3.73239 0 − 6.87723i 4.21313 0 9.38661
584.20 −2.51490 0 2.32474 −3.73239 0 6.87723i 4.21313 0 9.38661
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 584.96
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
13.b even 2 1 inner
39.d odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1287.3.h.a ✓ 96
3.b odd 2 1 inner 1287.3.h.a ✓ 96
13.b even 2 1 inner 1287.3.h.a ✓ 96
39.d odd 2 1 inner 1287.3.h.a ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1287.3.h.a ✓ 96 1.a even 1 1 trivial
1287.3.h.a ✓ 96 3.b odd 2 1 inner
1287.3.h.a ✓ 96 13.b even 2 1 inner
1287.3.h.a ✓ 96 39.d odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(1287, [\chi])\).