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Properties

Label 891.2.f.g
Level $891$
Weight $2$
Character orbit 891.f
Analytic conductor $7.115$
Analytic rank $0$
Dimension $48$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [891,2,Mod(82,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("891.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 891 = 3^{4} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 891.f (of order \(5\), degree \(4\), 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: \(7.11467082010\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 8 q^{4} - 14 q^{7} + 32 q^{10} - 14 q^{13} - 4 q^{16} - 8 q^{19} + 16 q^{22} - 20 q^{25} - 18 q^{28} - 4 q^{31} + 84 q^{34} - 12 q^{37} - 106 q^{40} + 84 q^{43} - 38 q^{46} - 54 q^{49} + 52 q^{52}+ \cdots - 66 q^{97}+O(q^{100}) \) 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.

comment: embeddings in the coefficient field
 
gp: mfembed(f)
 
Label   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
82.1 −0.795783 − 2.44917i 0 −3.74712 + 2.72245i −1.11871 + 3.44302i 0 −1.55240 + 1.12788i 5.48285 + 3.98353i 0 9.32280
82.2 −0.673315 − 2.07225i 0 −2.22283 + 1.61498i −0.467719 + 1.43949i 0 −0.546559 + 0.397099i 1.31779 + 0.957430i 0 3.29790
82.3 −0.627954 − 1.93264i 0 −1.72275 + 1.25165i 1.16487 − 3.58510i 0 −2.26910 + 1.64860i 0.212803 + 0.154610i 0 −7.66020
82.4 −0.379278 − 1.16730i 0 0.399302 − 0.290110i 0.0225318 − 0.0693456i 0 2.13821 − 1.55350i −2.47602 − 1.79893i 0 −0.0894928
82.5 −0.143360 − 0.441217i 0 1.44391 − 1.04906i 0.808655 − 2.48878i 0 1.43808 − 1.04482i −1.42051 − 1.03206i 0 −1.21402
82.6 −0.120315 − 0.370293i 0 1.49539 − 1.08647i −0.272242 + 0.837875i 0 −3.75331 + 2.72694i −1.21221 − 0.880722i 0 0.343014
82.7 0.120315 + 0.370293i 0 1.49539 − 1.08647i 0.272242 − 0.837875i 0 −3.75331 + 2.72694i 1.21221 + 0.880722i 0 0.343014
82.8 0.143360 + 0.441217i 0 1.44391 − 1.04906i −0.808655 + 2.48878i 0 1.43808 − 1.04482i 1.42051 + 1.03206i 0 −1.21402
82.9 0.379278 + 1.16730i 0 0.399302 − 0.290110i −0.0225318 + 0.0693456i 0 2.13821 − 1.55350i 2.47602 + 1.79893i 0 −0.0894928
82.10 0.627954 + 1.93264i 0 −1.72275 + 1.25165i −1.16487 + 3.58510i 0 −2.26910 + 1.64860i −0.212803 − 0.154610i 0 −7.66020
82.11 0.673315 + 2.07225i 0 −2.22283 + 1.61498i 0.467719 − 1.43949i 0 −0.546559 + 0.397099i −1.31779 − 0.957430i 0 3.29790
82.12 0.795783 + 2.44917i 0 −3.74712 + 2.72245i 1.11871 − 3.44302i 0 −1.55240 + 1.12788i −5.48285 − 3.98353i 0 9.32280
163.1 −0.795783 + 2.44917i 0 −3.74712 − 2.72245i −1.11871 − 3.44302i 0 −1.55240 − 1.12788i 5.48285 − 3.98353i 0 9.32280
163.2 −0.673315 + 2.07225i 0 −2.22283 − 1.61498i −0.467719 − 1.43949i 0 −0.546559 − 0.397099i 1.31779 − 0.957430i 0 3.29790
163.3 −0.627954 + 1.93264i 0 −1.72275 − 1.25165i 1.16487 + 3.58510i 0 −2.26910 − 1.64860i 0.212803 − 0.154610i 0 −7.66020
163.4 −0.379278 + 1.16730i 0 0.399302 + 0.290110i 0.0225318 + 0.0693456i 0 2.13821 + 1.55350i −2.47602 + 1.79893i 0 −0.0894928
163.5 −0.143360 + 0.441217i 0 1.44391 + 1.04906i 0.808655 + 2.48878i 0 1.43808 + 1.04482i −1.42051 + 1.03206i 0 −1.21402
163.6 −0.120315 + 0.370293i 0 1.49539 + 1.08647i −0.272242 − 0.837875i 0 −3.75331 − 2.72694i −1.21221 + 0.880722i 0 0.343014
163.7 0.120315 − 0.370293i 0 1.49539 + 1.08647i 0.272242 + 0.837875i 0 −3.75331 − 2.72694i 1.21221 − 0.880722i 0 0.343014
163.8 0.143360 − 0.441217i 0 1.44391 + 1.04906i −0.808655 − 2.48878i 0 1.43808 + 1.04482i 1.42051 − 1.03206i 0 −1.21402
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 82.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
11.c even 5 1 inner
33.h odd 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 891.2.f.g ✓ 48
3.b odd 2 1 inner 891.2.f.g ✓ 48
9.c even 3 2 891.2.n.l 96
9.d odd 6 2 891.2.n.l 96
11.c even 5 1 inner 891.2.f.g ✓ 48
11.c even 5 1 9801.2.a.cr 24
11.d odd 10 1 9801.2.a.cq 24
33.f even 10 1 9801.2.a.cq 24
33.h odd 10 1 inner 891.2.f.g ✓ 48
33.h odd 10 1 9801.2.a.cr 24
99.m even 15 2 891.2.n.l 96
99.n odd 30 2 891.2.n.l 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
891.2.f.g ✓ 48 1.a even 1 1 trivial
891.2.f.g ✓ 48 3.b odd 2 1 inner
891.2.f.g ✓ 48 11.c even 5 1 inner
891.2.f.g ✓ 48 33.h odd 10 1 inner
891.2.n.l 96 9.c even 3 2
891.2.n.l 96 9.d odd 6 2
891.2.n.l 96 99.m even 15 2
891.2.n.l 96 99.n odd 30 2
9801.2.a.cq 24 11.d odd 10 1
9801.2.a.cq 24 33.f even 10 1
9801.2.a.cr 24 11.c even 5 1
9801.2.a.cr 24 33.h odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{48} + 16 T_{2}^{46} + 180 T_{2}^{44} + 1718 T_{2}^{42} + 14576 T_{2}^{40} + 96790 T_{2}^{38} + \cdots + 707281 \) acting on \(S_{2}^{\mathrm{new}}(891, [\chi])\). Copy content Toggle raw display