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Properties

Label 880.2.bs.b
Level $880$
Weight $2$
Character orbit 880.bs
Analytic conductor $7.027$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [880,2,Mod(79,880)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(880, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 0, 5, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.79");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.bs (of order \(10\), 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: \(7.02683537787\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(24\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 2 q^{5} - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q + 2 q^{5} - 40 q^{9} + 18 q^{25} - 40 q^{41} + 104 q^{45} + 124 q^{49} + 60 q^{61} + 76 q^{69} + 76 q^{81} - 170 q^{85} - 56 q^{89}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
79.1 0 −2.58207 + 1.87598i 0 −0.355372 + 2.20765i 0 −0.655955 + 0.902845i 0 2.22072 − 6.83468i 0
79.2 0 −2.58207 + 1.87598i 0 1.58513 + 1.57714i 0 −0.655955 + 0.902845i 0 2.22072 − 6.83468i 0
79.3 0 −1.82511 + 1.32602i 0 −2.10647 + 0.750201i 0 2.18260 − 3.00410i 0 0.645643 − 1.98708i 0
79.4 0 −1.82511 + 1.32602i 0 2.14512 − 0.631225i 0 2.18260 − 3.00410i 0 0.645643 − 1.98708i 0
79.5 0 −1.81153 + 1.31615i 0 −1.65164 − 1.50735i 0 −2.15679 + 2.96856i 0 0.622330 − 1.91533i 0
79.6 0 −1.81153 + 1.31615i 0 0.450206 − 2.19028i 0 −2.15679 + 2.96856i 0 0.622330 − 1.91533i 0
79.7 0 −1.28391 + 0.932815i 0 −2.10658 − 0.749883i 0 0.926530 − 1.27526i 0 −0.148771 + 0.457869i 0
79.8 0 −1.28391 + 0.932815i 0 1.26349 − 1.84488i 0 0.926530 − 1.27526i 0 −0.148771 + 0.457869i 0
79.9 0 −0.940304 + 0.683171i 0 0.168810 + 2.22969i 0 1.47413 − 2.02897i 0 −0.509602 + 1.56839i 0
79.10 0 −0.940304 + 0.683171i 0 1.17401 + 1.90308i 0 1.47413 − 2.02897i 0 −0.509602 + 1.56839i 0
79.11 0 −0.381913 + 0.277476i 0 −1.97253 + 1.05316i 0 −1.04574 + 1.43934i 0 −0.858186 + 2.64123i 0
79.12 0 −0.381913 + 0.277476i 0 2.21484 − 0.307400i 0 −1.04574 + 1.43934i 0 −0.858186 + 2.64123i 0
79.13 0 0.381913 − 0.277476i 0 −1.97253 + 1.05316i 0 1.04574 − 1.43934i 0 −0.858186 + 2.64123i 0
79.14 0 0.381913 − 0.277476i 0 2.21484 − 0.307400i 0 1.04574 − 1.43934i 0 −0.858186 + 2.64123i 0
79.15 0 0.940304 − 0.683171i 0 0.168810 + 2.22969i 0 −1.47413 + 2.02897i 0 −0.509602 + 1.56839i 0
79.16 0 0.940304 − 0.683171i 0 1.17401 + 1.90308i 0 −1.47413 + 2.02897i 0 −0.509602 + 1.56839i 0
79.17 0 1.28391 − 0.932815i 0 −2.10658 − 0.749883i 0 −0.926530 + 1.27526i 0 −0.148771 + 0.457869i 0
79.18 0 1.28391 − 0.932815i 0 1.26349 − 1.84488i 0 −0.926530 + 1.27526i 0 −0.148771 + 0.457869i 0
79.19 0 1.81153 − 1.31615i 0 −1.65164 − 1.50735i 0 2.15679 − 2.96856i 0 0.622330 − 1.91533i 0
79.20 0 1.81153 − 1.31615i 0 0.450206 − 2.19028i 0 2.15679 − 2.96856i 0 0.622330 − 1.91533i 0
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 79.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
4.b odd 2 1 inner
5.b even 2 1 inner
11.d odd 10 1 inner
20.d odd 2 1 inner
44.g even 10 1 inner
55.h odd 10 1 inner
220.o even 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 880.2.bs.b ✓ 96
4.b odd 2 1 inner 880.2.bs.b ✓ 96
5.b even 2 1 inner 880.2.bs.b ✓ 96
11.d odd 10 1 inner 880.2.bs.b ✓ 96
20.d odd 2 1 inner 880.2.bs.b ✓ 96
44.g even 10 1 inner 880.2.bs.b ✓ 96
55.h odd 10 1 inner 880.2.bs.b ✓ 96
220.o even 10 1 inner 880.2.bs.b ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
880.2.bs.b ✓ 96 1.a even 1 1 trivial
880.2.bs.b ✓ 96 4.b odd 2 1 inner
880.2.bs.b ✓ 96 5.b even 2 1 inner
880.2.bs.b ✓ 96 11.d odd 10 1 inner
880.2.bs.b ✓ 96 20.d odd 2 1 inner
880.2.bs.b ✓ 96 44.g even 10 1 inner
880.2.bs.b ✓ 96 55.h odd 10 1 inner
880.2.bs.b ✓ 96 220.o even 10 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{48} + 28 T_{3}^{46} + 459 T_{3}^{44} + 5869 T_{3}^{42} + 68657 T_{3}^{40} + 636533 T_{3}^{38} + \cdots + 153760000 \) acting on \(S_{2}^{\mathrm{new}}(880, [\chi])\). Copy content Toggle raw display