↑

Properties

Label 1120.2.bv.a
Level $1120$
Weight $2$
Character orbit 1120.bv
Analytic conductor $8.943$
Analytic rank $0$
Dimension $88$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1120,2,Mod(529,1120)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1120, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1120.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1120.bv (of order \(6\), degree \(2\), not 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: \(8.94324502638\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(44\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 280)
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.

\(\operatorname{Tr}(f)(q) = \) \( 88 q - 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 88 q - 40 q^{9} - 4 q^{15} - 2 q^{25} + 28 q^{31} + 16 q^{39} - 16 q^{41} - 8 q^{49} + 28 q^{55} - 12 q^{65} - 16 q^{71} + 4 q^{79} - 20 q^{81} + 4 q^{89} + 34 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
529.1 0 −1.62181 + 2.80906i 0 2.02644 + 0.945271i 0 1.16173 − 2.37705i 0 −3.76055 − 6.51347i 0
529.2 0 −1.62181 + 2.80906i 0 −0.194592 + 2.22758i 0 −1.16173 + 2.37705i 0 −3.76055 − 6.51347i 0
529.3 0 −1.40092 + 2.42646i 0 −1.41569 − 1.73084i 0 2.13463 + 1.56312i 0 −2.42513 − 4.20044i 0
529.4 0 −1.40092 + 2.42646i 0 −0.791109 − 2.09145i 0 −2.13463 − 1.56312i 0 −2.42513 − 4.20044i 0
529.5 0 −1.37008 + 2.37305i 0 2.18145 − 0.491206i 0 2.02537 + 1.70232i 0 −2.25425 − 3.90447i 0
529.6 0 −1.37008 + 2.37305i 0 −1.51612 + 1.64359i 0 −2.02537 − 1.70232i 0 −2.25425 − 3.90447i 0
529.7 0 −1.22223 + 2.11697i 0 −2.23601 − 0.0158492i 0 2.60788 − 0.446057i 0 −1.48770 − 2.57677i 0
529.8 0 −1.22223 + 2.11697i 0 1.10428 − 1.94437i 0 −2.60788 + 0.446057i 0 −1.48770 − 2.57677i 0
529.9 0 −0.945048 + 1.63687i 0 1.91034 + 1.16216i 0 −1.18371 + 2.36619i 0 −0.286230 − 0.495764i 0
529.10 0 −0.945048 + 1.63687i 0 0.0512873 + 2.23548i 0 1.18371 − 2.36619i 0 −0.286230 − 0.495764i 0
529.11 0 −0.866705 + 1.50118i 0 1.99503 − 1.00988i 0 −1.01592 − 2.44293i 0 −0.00235378 − 0.00407687i 0
529.12 0 −0.866705 + 1.50118i 0 −1.87210 + 1.22281i 0 1.01592 + 2.44293i 0 −0.00235378 − 0.00407687i 0
529.13 0 −0.755963 + 1.30937i 0 −0.632393 − 2.14478i 0 0.727432 − 2.54379i 0 0.357040 + 0.618411i 0
529.14 0 −0.755963 + 1.30937i 0 −1.54124 − 1.62006i 0 −0.727432 + 2.54379i 0 0.357040 + 0.618411i 0
529.15 0 −0.496594 + 0.860127i 0 1.87027 − 1.22560i 0 2.24690 − 1.39695i 0 1.00679 + 1.74381i 0
529.16 0 −0.496594 + 0.860127i 0 −1.99653 + 1.00690i 0 −2.24690 + 1.39695i 0 1.00679 + 1.74381i 0
529.17 0 −0.390744 + 0.676788i 0 −2.21752 − 0.287435i 0 −1.02493 − 2.43916i 0 1.19464 + 2.06917i 0
529.18 0 −0.390744 + 0.676788i 0 0.859833 − 2.06414i 0 1.02493 + 2.43916i 0 1.19464 + 2.06917i 0
529.19 0 −0.299892 + 0.519428i 0 2.04027 + 0.915040i 0 2.46748 + 0.954749i 0 1.32013 + 2.28653i 0
529.20 0 −0.299892 + 0.519428i 0 −0.227688 + 2.22445i 0 −2.46748 − 0.954749i 0 1.32013 + 2.28653i 0
See all 88 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 529.44
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.c even 3 1 inner
8.b even 2 1 inner
35.j even 6 1 inner
40.f even 2 1 inner
56.p even 6 1 inner
280.bf even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1120.2.bv.a 88
4.b odd 2 1 280.2.bf.a ✓ 88
5.b even 2 1 inner 1120.2.bv.a 88
7.c even 3 1 inner 1120.2.bv.a 88
8.b even 2 1 inner 1120.2.bv.a 88
8.d odd 2 1 280.2.bf.a ✓ 88
20.d odd 2 1 280.2.bf.a ✓ 88
28.g odd 6 1 280.2.bf.a ✓ 88
35.j even 6 1 inner 1120.2.bv.a 88
40.e odd 2 1 280.2.bf.a ✓ 88
40.f even 2 1 inner 1120.2.bv.a 88
56.k odd 6 1 280.2.bf.a ✓ 88
56.p even 6 1 inner 1120.2.bv.a 88
140.p odd 6 1 280.2.bf.a ✓ 88
280.bf even 6 1 inner 1120.2.bv.a 88
280.bi odd 6 1 280.2.bf.a ✓ 88
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.2.bf.a ✓ 88 4.b odd 2 1
280.2.bf.a ✓ 88 8.d odd 2 1
280.2.bf.a ✓ 88 20.d odd 2 1
280.2.bf.a ✓ 88 28.g odd 6 1
280.2.bf.a ✓ 88 40.e odd 2 1
280.2.bf.a ✓ 88 56.k odd 6 1
280.2.bf.a ✓ 88 140.p odd 6 1
280.2.bf.a ✓ 88 280.bi odd 6 1
1120.2.bv.a 88 1.a even 1 1 trivial
1120.2.bv.a 88 5.b even 2 1 inner
1120.2.bv.a 88 7.c even 3 1 inner
1120.2.bv.a 88 8.b even 2 1 inner
1120.2.bv.a 88 35.j even 6 1 inner
1120.2.bv.a 88 40.f even 2 1 inner
1120.2.bv.a 88 56.p even 6 1 inner
1120.2.bv.a 88 280.bf even 6 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(1120, [\chi])\).