↑

Properties

Label 882.2.m.c
Level $882$
Weight $2$
Character orbit 882.m
Analytic conductor $7.043$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [882,2,Mod(293,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.293");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.m (of order \(6\), degree \(2\), 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q + 24 q^{4} - 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q + 24 q^{4} - 32 q^{9} + 48 q^{11} + 48 q^{15} - 24 q^{16} + 16 q^{18} + 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} - 64 q^{39} - 48 q^{50} - 80 q^{57} - 48 q^{64} + 32 q^{72} + 32 q^{78} + 48 q^{79} + 48 q^{85} + 96 q^{86} + 48 q^{92} + 96 q^{93} - 192 q^{95} + 104 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
293.1 −0.866025 + 0.500000i −1.73194 − 0.0197913i 0.500000 − 0.866025i −1.96067 + 3.39598i 1.50980 − 0.848829i 0 1.00000i 2.99922 + 0.0685547i − 3.92134i
293.2 −0.866025 + 0.500000i −1.54269 + 0.787461i 0.500000 − 0.866025i −0.724499 + 1.25487i 0.942282 − 1.45331i 0 1.00000i 1.75981 − 2.42962i − 1.44900i
293.3 −0.866025 + 0.500000i −0.963195 − 1.43953i 0.500000 − 0.866025i −0.474556 + 0.821956i 1.55392 + 0.765075i 0 1.00000i −1.14451 + 2.77310i − 0.949113i
293.4 −0.866025 + 0.500000i −0.676753 + 1.59437i 0.500000 − 0.866025i −0.584859 + 1.01301i −0.211098 − 1.71914i 0 1.00000i −2.08401 − 2.15799i − 1.16972i
293.5 −0.866025 + 0.500000i −0.414495 + 1.68172i 0.500000 − 0.866025i 0.712984 − 1.23492i −0.481898 − 1.66366i 0 1.00000i −2.65639 − 1.39413i 1.42597i
293.6 −0.866025 + 0.500000i −0.250882 + 1.71378i 0.500000 − 0.866025i 1.35026 − 2.33872i −0.639623 − 1.60962i 0 1.00000i −2.87412 − 0.859914i 2.70053i
293.7 −0.866025 + 0.500000i 0.250882 − 1.71378i 0.500000 − 0.866025i −1.35026 + 2.33872i 0.639623 + 1.60962i 0 1.00000i −2.87412 − 0.859914i − 2.70053i
293.8 −0.866025 + 0.500000i 0.414495 − 1.68172i 0.500000 − 0.866025i −0.712984 + 1.23492i 0.481898 + 1.66366i 0 1.00000i −2.65639 − 1.39413i − 1.42597i
293.9 −0.866025 + 0.500000i 0.676753 − 1.59437i 0.500000 − 0.866025i 0.584859 − 1.01301i 0.211098 + 1.71914i 0 1.00000i −2.08401 − 2.15799i 1.16972i
293.10 −0.866025 + 0.500000i 0.963195 + 1.43953i 0.500000 − 0.866025i 0.474556 − 0.821956i −1.55392 − 0.765075i 0 1.00000i −1.14451 + 2.77310i 0.949113i
293.11 −0.866025 + 0.500000i 1.54269 − 0.787461i 0.500000 − 0.866025i 0.724499 − 1.25487i −0.942282 + 1.45331i 0 1.00000i 1.75981 − 2.42962i 1.44900i
293.12 −0.866025 + 0.500000i 1.73194 + 0.0197913i 0.500000 − 0.866025i 1.96067 − 3.39598i −1.50980 + 0.848829i 0 1.00000i 2.99922 + 0.0685547i 3.92134i
293.13 0.866025 − 0.500000i −1.56901 − 0.733620i 0.500000 − 0.866025i −0.948881 + 1.64351i −1.72562 + 0.149173i 0 − 1.00000i 1.92360 + 2.30212i 1.89776i
293.14 0.866025 − 0.500000i −1.32246 − 1.11852i 0.500000 − 0.866025i 1.55067 − 2.68584i −1.70455 − 0.307440i 0 − 1.00000i 0.497807 + 2.95841i − 3.10134i
293.15 0.866025 − 0.500000i −1.18969 − 1.25882i 0.500000 − 0.866025i −0.995200 + 1.72374i −1.65972 − 0.495324i 0 − 1.00000i −0.169259 + 2.99522i 1.99040i
293.16 0.866025 − 0.500000i −1.12483 + 1.31710i 0.500000 − 0.866025i −0.220087 + 0.381202i −0.315583 + 1.70306i 0 − 1.00000i −0.469507 − 2.96303i 0.440174i
293.17 0.866025 − 0.500000i −0.325254 + 1.70124i 0.500000 − 0.866025i −1.55389 + 2.69141i 0.568941 + 1.63594i 0 − 1.00000i −2.78842 − 1.10667i 3.10777i
293.18 0.866025 − 0.500000i −0.0537332 + 1.73122i 0.500000 − 0.866025i 1.99341 − 3.45268i 0.819074 + 1.52614i 0 − 1.00000i −2.99423 − 0.186048i − 3.98682i
293.19 0.866025 − 0.500000i 0.0537332 − 1.73122i 0.500000 − 0.866025i −1.99341 + 3.45268i −0.819074 − 1.52614i 0 − 1.00000i −2.99423 − 0.186048i 3.98682i
293.20 0.866025 − 0.500000i 0.325254 − 1.70124i 0.500000 − 0.866025i 1.55389 − 2.69141i −0.568941 − 1.63594i 0 − 1.00000i −2.78842 − 1.10667i − 3.10777i
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 293.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
7.b odd 2 1 inner
9.d odd 6 1 inner
63.o even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 882.2.m.c ✓ 48
3.b odd 2 1 2646.2.m.c 48
7.b odd 2 1 inner 882.2.m.c ✓ 48
7.c even 3 1 882.2.l.c 48
7.c even 3 1 882.2.t.c 48
7.d odd 6 1 882.2.l.c 48
7.d odd 6 1 882.2.t.c 48
9.c even 3 1 2646.2.m.c 48
9.d odd 6 1 inner 882.2.m.c ✓ 48
21.c even 2 1 2646.2.m.c 48
21.g even 6 1 2646.2.l.c 48
21.g even 6 1 2646.2.t.c 48
21.h odd 6 1 2646.2.l.c 48
21.h odd 6 1 2646.2.t.c 48
63.g even 3 1 2646.2.l.c 48
63.h even 3 1 2646.2.t.c 48
63.i even 6 1 882.2.t.c 48
63.j odd 6 1 882.2.t.c 48
63.k odd 6 1 2646.2.l.c 48
63.l odd 6 1 2646.2.m.c 48
63.n odd 6 1 882.2.l.c 48
63.o even 6 1 inner 882.2.m.c ✓ 48
63.s even 6 1 882.2.l.c 48
63.t odd 6 1 2646.2.t.c 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
882.2.l.c 48 7.c even 3 1
882.2.l.c 48 7.d odd 6 1
882.2.l.c 48 63.n odd 6 1
882.2.l.c 48 63.s even 6 1
882.2.m.c ✓ 48 1.a even 1 1 trivial
882.2.m.c ✓ 48 7.b odd 2 1 inner
882.2.m.c ✓ 48 9.d odd 6 1 inner
882.2.m.c ✓ 48 63.o even 6 1 inner
882.2.t.c 48 7.c even 3 1
882.2.t.c 48 7.d odd 6 1
882.2.t.c 48 63.i even 6 1
882.2.t.c 48 63.j odd 6 1
2646.2.l.c 48 21.g even 6 1
2646.2.l.c 48 21.h odd 6 1
2646.2.l.c 48 63.g even 3 1
2646.2.l.c 48 63.k odd 6 1
2646.2.m.c 48 3.b odd 2 1
2646.2.m.c 48 9.c even 3 1
2646.2.m.c 48 21.c even 2 1
2646.2.m.c 48 63.l odd 6 1
2646.2.t.c 48 21.g even 6 1
2646.2.t.c 48 21.h odd 6 1
2646.2.t.c 48 63.h even 3 1
2646.2.t.c 48 63.t odd 6 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{48} + 72 T_{5}^{46} + 2976 T_{5}^{44} + 83216 T_{5}^{42} + 1745790 T_{5}^{40} + \cdots + 5801854959616 \) acting on \(S_{2}^{\mathrm{new}}(882, [\chi])\). Copy content Toggle raw display