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Properties

Label 891.2.f.c
Level $891$
Weight $2$
Character orbit 891.f
Analytic conductor $7.115$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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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: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 2 q^{2} - 8 q^{4} + 4 q^{5} + 7 q^{7} + 10 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 2 q^{2} - 8 q^{4} + 4 q^{5} + 7 q^{7} + 10 q^{8} - 16 q^{10} + 5 q^{11} + 7 q^{13} + 13 q^{14} + 2 q^{16} - 5 q^{17} + 4 q^{19} + 27 q^{20} - 2 q^{22} + 6 q^{23} - 2 q^{25} - 34 q^{26} - 9 q^{28} + 22 q^{29} + 2 q^{31} + 18 q^{32} - 42 q^{34} + 6 q^{37} - 5 q^{38} + 53 q^{40} + 10 q^{41} - 30 q^{43} + 59 q^{44} + 31 q^{46} + 4 q^{47} - 3 q^{49} + 9 q^{50} - 26 q^{52} + 17 q^{53} + 12 q^{55} - 48 q^{56} + 53 q^{58} + 11 q^{59} + 3 q^{61} - 2 q^{62} + 38 q^{64} - 68 q^{65} - 14 q^{67} + 22 q^{68} - 20 q^{70} - 36 q^{71} + 35 q^{73} + 3 q^{74} - 102 q^{76} - 88 q^{77} - 9 q^{79} - 37 q^{80} - 6 q^{82} + 32 q^{83} - 45 q^{85} - 110 q^{86} + 54 q^{88} + 34 q^{89} + 13 q^{91} - q^{92} - 25 q^{94} - 84 q^{95} + 15 q^{97} + 68 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
82.1 −0.858580 − 2.64244i 0 −4.62728 + 3.36192i 0.818647 − 2.51954i 0 0.0646331 − 0.0469587i 8.36097 + 6.07460i 0 −7.36059
82.2 −0.484676 − 1.49168i 0 −0.372161 + 0.270391i −0.165973 + 0.510812i 0 −2.28835 + 1.66258i −1.95408 − 1.41972i 0 0.842411
82.3 −0.344102 − 1.05904i 0 0.614881 − 0.446737i 0.290537 − 0.894180i 0 3.05510 − 2.21966i −2.48643 − 1.80650i 0 −1.04694
82.4 0.103393 + 0.318212i 0 1.52747 − 1.10977i −1.16132 + 3.57417i 0 0.249578 − 0.181329i 1.05245 + 0.764647i 0 −1.25742
82.5 0.330786 + 1.01805i 0 0.691018 − 0.502054i 1.08179 − 3.32942i 0 −0.632697 + 0.459681i 2.47172 + 1.79581i 0 3.74737
82.6 0.753178 + 2.31804i 0 −3.18802 + 2.31623i 0.136315 − 0.419536i 0 4.09682 − 2.97652i −3.82659 − 2.78018i 0 1.07517
163.1 −0.858580 + 2.64244i 0 −4.62728 − 3.36192i 0.818647 + 2.51954i 0 0.0646331 + 0.0469587i 8.36097 − 6.07460i 0 −7.36059
163.2 −0.484676 + 1.49168i 0 −0.372161 − 0.270391i −0.165973 − 0.510812i 0 −2.28835 − 1.66258i −1.95408 + 1.41972i 0 0.842411
163.3 −0.344102 + 1.05904i 0 0.614881 + 0.446737i 0.290537 + 0.894180i 0 3.05510 + 2.21966i −2.48643 + 1.80650i 0 −1.04694
163.4 0.103393 − 0.318212i 0 1.52747 + 1.10977i −1.16132 − 3.57417i 0 0.249578 + 0.181329i 1.05245 − 0.764647i 0 −1.25742
163.5 0.330786 − 1.01805i 0 0.691018 + 0.502054i 1.08179 + 3.32942i 0 −0.632697 − 0.459681i 2.47172 − 1.79581i 0 3.74737
163.6 0.753178 − 2.31804i 0 −3.18802 − 2.31623i 0.136315 + 0.419536i 0 4.09682 + 2.97652i −3.82659 + 2.78018i 0 1.07517
487.1 −2.12715 + 1.54546i 0 1.51827 − 4.67274i 0.193808 + 0.140810i 0 −0.366442 + 1.12779i 2.36698 + 7.28482i 0 −0.629874
487.2 −1.14839 + 0.834353i 0 0.00461626 − 0.0142074i 3.02955 + 2.20110i 0 −0.430288 + 1.32429i −0.870737 − 2.67985i 0 −5.31559
487.3 −0.275589 + 0.200227i 0 −0.582176 + 1.79175i −2.79895 − 2.03355i 0 −1.53328 + 4.71895i −0.408848 − 1.25830i 0 1.17853
487.4 −0.0412919 + 0.0300003i 0 −0.617229 + 1.89964i 0.498462 + 0.362154i 0 0.752525 − 2.31603i −0.0630473 − 0.194040i 0 −0.0314472
487.5 1.44769 − 1.05181i 0 0.371476 − 1.14329i −2.00827 − 1.45910i 0 0.991006 − 3.05000i 0.441202 + 1.35788i 0 −4.44205
487.6 1.64472 − 1.19496i 0 0.659148 − 2.02865i 2.08540 + 1.51513i 0 −0.458605 + 1.41144i −0.0835835 − 0.257243i 0 5.24043
730.1 −2.12715 − 1.54546i 0 1.51827 + 4.67274i 0.193808 − 0.140810i 0 −0.366442 − 1.12779i 2.36698 − 7.28482i 0 −0.629874
730.2 −1.14839 − 0.834353i 0 0.00461626 + 0.0142074i 3.02955 − 2.20110i 0 −0.430288 − 1.32429i −0.870737 + 2.67985i 0 −5.31559
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 82.6
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.c even 5 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 891.2.f.c ✓ 24
3.b odd 2 1 891.2.f.d yes 24
9.c even 3 2 891.2.n.k 48
9.d odd 6 2 891.2.n.j 48
11.c even 5 1 inner 891.2.f.c ✓ 24
11.c even 5 1 9801.2.a.cg 12
11.d odd 10 1 9801.2.a.cl 12
33.f even 10 1 9801.2.a.cf 12
33.h odd 10 1 891.2.f.d yes 24
33.h odd 10 1 9801.2.a.ck 12
99.m even 15 2 891.2.n.k 48
99.n odd 30 2 891.2.n.j 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
891.2.f.c ✓ 24 1.a even 1 1 trivial
891.2.f.c ✓ 24 11.c even 5 1 inner
891.2.f.d yes 24 3.b odd 2 1
891.2.f.d yes 24 33.h odd 10 1
891.2.n.j 48 9.d odd 6 2
891.2.n.j 48 99.n odd 30 2
891.2.n.k 48 9.c even 3 2
891.2.n.k 48 99.m even 15 2
9801.2.a.cf 12 33.f even 10 1
9801.2.a.cg 12 11.c even 5 1
9801.2.a.ck 12 33.h odd 10 1
9801.2.a.cl 12 11.d odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{24} + 2 T_{2}^{23} + 12 T_{2}^{22} + 14 T_{2}^{21} + 72 T_{2}^{20} + 62 T_{2}^{19} + 393 T_{2}^{18} + \cdots + 1 \) acting on \(S_{2}^{\mathrm{new}}(891, [\chi])\). Copy content Toggle raw display