↑

Properties

Label 891.2.f.e
Level $891$
Weight $2$
Character orbit 891.f
Analytic conductor $7.115$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

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: \(36\)
Relative dimension: \(9\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 99)
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.

\(\operatorname{Tr}(f)(q) = \) \( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 36 q - q^{2} - 11 q^{4} - 8 q^{5} + 2 q^{7} - 3 q^{8} - 4 q^{10} - 2 q^{11} + 11 q^{13} - 10 q^{14} + 9 q^{16} + 10 q^{17} + 4 q^{19} - 45 q^{20} + 16 q^{22} + 20 q^{23} - 11 q^{25} + 6 q^{26} - 27 q^{28} - 23 q^{29} - 3 q^{31} + 18 q^{32} - 8 q^{34} - 9 q^{35} - 21 q^{37} - q^{38} + 25 q^{40} + 10 q^{41} + 8 q^{43} - 19 q^{44} - 9 q^{46} - 34 q^{47} - q^{49} + 27 q^{52} - 2 q^{53} + 9 q^{55} + 114 q^{56} - q^{58} - 16 q^{59} + 3 q^{61} - 92 q^{62} + 13 q^{64} + 84 q^{65} - 10 q^{67} - 23 q^{68} + 46 q^{70} + 24 q^{71} - 20 q^{73} + 68 q^{74} - 16 q^{76} - 26 q^{77} - 19 q^{79} + 28 q^{80} + 47 q^{82} + 7 q^{83} - 25 q^{85} - 77 q^{86} - 18 q^{88} + 28 q^{89} + 10 q^{91} + 50 q^{92} + 63 q^{94} - 77 q^{95} + 33 q^{97} + 164 q^{98}+O(q^{100}) \) 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 −0.719701 − 2.21501i 0 −2.77028 + 2.01272i 0.0979645 − 0.301504i 0 1.14758 − 0.833769i 2.68358 + 1.94973i 0 −0.738340
82.2 −0.660945 − 2.03418i 0 −2.08301 + 1.51339i −0.517908 + 1.59396i 0 1.04819 − 0.761555i 0.994512 + 0.722555i 0 3.58471
82.3 −0.311049 − 0.957310i 0 0.798344 − 0.580031i 1.23333 − 3.79579i 0 −2.22988 + 1.62010i −2.43227 − 1.76714i 0 −4.01737
82.4 −0.209411 − 0.644501i 0 1.24651 − 0.905639i −0.0898605 + 0.276562i 0 −2.71465 + 1.97231i −1.94121 − 1.41037i 0 0.197063
82.5 −0.0881157 − 0.271192i 0 1.55225 − 1.12778i −0.837045 + 2.57616i 0 3.29540 − 2.39425i −0.904002 − 0.656796i 0 0.772391
82.6 0.450357 + 1.38606i 0 −0.100295 + 0.0728686i 0.928914 − 2.85890i 0 1.33502 − 0.969952i 2.21193 + 1.60706i 0 4.38094
82.7 0.458430 + 1.41090i 0 −0.162452 + 0.118028i 0.0223503 − 0.0687873i 0 −1.57776 + 1.14631i 2.15937 + 1.56887i 0 0.107298
82.8 0.585487 + 1.80194i 0 −1.28618 + 0.934461i −1.08558 + 3.34108i 0 2.77655 − 2.01728i 0.628765 + 0.456825i 0 −6.65603
82.9 0.803965 + 2.47435i 0 −3.85802 + 2.80301i −0.634128 + 1.95164i 0 −2.58046 + 1.87481i −5.82773 − 4.23409i 0 −5.33887
163.1 −0.719701 + 2.21501i 0 −2.77028 − 2.01272i 0.0979645 + 0.301504i 0 1.14758 + 0.833769i 2.68358 − 1.94973i 0 −0.738340
163.2 −0.660945 + 2.03418i 0 −2.08301 − 1.51339i −0.517908 − 1.59396i 0 1.04819 + 0.761555i 0.994512 − 0.722555i 0 3.58471
163.3 −0.311049 + 0.957310i 0 0.798344 + 0.580031i 1.23333 + 3.79579i 0 −2.22988 − 1.62010i −2.43227 + 1.76714i 0 −4.01737
163.4 −0.209411 + 0.644501i 0 1.24651 + 0.905639i −0.0898605 − 0.276562i 0 −2.71465 − 1.97231i −1.94121 + 1.41037i 0 0.197063
163.5 −0.0881157 + 0.271192i 0 1.55225 + 1.12778i −0.837045 − 2.57616i 0 3.29540 + 2.39425i −0.904002 + 0.656796i 0 0.772391
163.6 0.450357 − 1.38606i 0 −0.100295 − 0.0728686i 0.928914 + 2.85890i 0 1.33502 + 0.969952i 2.21193 − 1.60706i 0 4.38094
163.7 0.458430 − 1.41090i 0 −0.162452 − 0.118028i 0.0223503 + 0.0687873i 0 −1.57776 − 1.14631i 2.15937 − 1.56887i 0 0.107298
163.8 0.585487 − 1.80194i 0 −1.28618 − 0.934461i −1.08558 − 3.34108i 0 2.77655 + 2.01728i 0.628765 − 0.456825i 0 −6.65603
163.9 0.803965 − 2.47435i 0 −3.85802 − 2.80301i −0.634128 − 1.95164i 0 −2.58046 − 1.87481i −5.82773 + 4.23409i 0 −5.33887
487.1 −1.97840 + 1.43739i 0 1.22993 − 3.78534i −2.42938 − 1.76504i 0 1.20268 − 3.70148i 1.49636 + 4.60531i 0 7.34333
487.2 −1.62502 + 1.18065i 0 0.628732 − 1.93504i 0.00441059 + 0.00320448i 0 −1.18286 + 3.64046i 0.0214877 + 0.0661323i 0 −0.0109507
See all 36 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 82.9
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.e 36
3.b odd 2 1 891.2.f.f 36
9.c even 3 2 297.2.n.b 72
9.d odd 6 2 99.2.m.b ✓ 72
11.c even 5 1 inner 891.2.f.e 36
11.c even 5 1 9801.2.a.cp 18
11.d odd 10 1 9801.2.a.cn 18
33.f even 10 1 9801.2.a.co 18
33.h odd 10 1 891.2.f.f 36
33.h odd 10 1 9801.2.a.cm 18
99.m even 15 2 297.2.n.b 72
99.n odd 30 2 99.2.m.b ✓ 72
99.n odd 30 2 1089.2.e.p 36
99.p even 30 2 1089.2.e.o 36
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
99.2.m.b ✓ 72 9.d odd 6 2
99.2.m.b ✓ 72 99.n odd 30 2
297.2.n.b 72 9.c even 3 2
297.2.n.b 72 99.m even 15 2
891.2.f.e 36 1.a even 1 1 trivial
891.2.f.e 36 11.c even 5 1 inner
891.2.f.f 36 3.b odd 2 1
891.2.f.f 36 33.h odd 10 1
1089.2.e.o 36 99.p even 30 2
1089.2.e.p 36 99.n odd 30 2
9801.2.a.cm 18 33.h odd 10 1
9801.2.a.cn 18 11.d odd 10 1
9801.2.a.co 18 33.f even 10 1
9801.2.a.cp 18 11.c even 5 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{36} + T_{2}^{35} + 15 T_{2}^{34} + 17 T_{2}^{33} + 132 T_{2}^{32} + 121 T_{2}^{31} + 867 T_{2}^{30} + \cdots + 3025 \) acting on \(S_{2}^{\mathrm{new}}(891, [\chi])\). Copy content Toggle raw display