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Properties

Label 880.2.cd.d
Level $880$
Weight $2$
Character orbit 880.cd
Analytic conductor $7.027$
Analytic rank $0$
Dimension $24$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [880,2,Mod(49,880)]
 
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([0, 0, 5, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("880.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 880.cd (of order \(10\), degree \(4\), 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: \(7.02683537787\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{10})\)
Twist minimal: no (minimal twist has level 220)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + q^{5} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + q^{5} + 14 q^{9} + 2 q^{11} + q^{15} - 8 q^{19} - 28 q^{21} + 27 q^{25} - 16 q^{29} + 26 q^{31} - 17 q^{35} - 12 q^{39} + 10 q^{41} - 40 q^{45} - 46 q^{49} + 12 q^{51} + 33 q^{55} + 48 q^{59} - 10 q^{61} - 22 q^{65} - 58 q^{69} - 42 q^{71} + 17 q^{75} + 64 q^{79} + 36 q^{81} - 17 q^{85} + 72 q^{89} - 10 q^{91} - 67 q^{95} - 156 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
49.1 0 −1.60349 + 2.20702i 0 −1.89499 − 1.18702i 0 1.00600 + 1.38464i 0 −1.37268 − 4.22469i 0
49.2 0 −1.22731 + 1.68925i 0 1.67152 + 1.48527i 0 −1.67492 − 2.30533i 0 −0.420216 − 1.29329i 0
49.3 0 −0.447653 + 0.616141i 0 1.93649 − 1.11803i 0 2.82695 + 3.89096i 0 0.747814 + 2.30153i 0
49.4 0 0.447653 − 0.616141i 0 −0.909494 − 2.04275i 0 −2.82695 − 3.89096i 0 0.747814 + 2.30153i 0
49.5 0 1.22731 − 1.68925i 0 −2.22531 + 0.219109i 0 1.67492 + 2.30533i 0 −0.420216 − 1.29329i 0
49.6 0 1.60349 − 2.20702i 0 2.23079 + 0.153527i 0 −1.00600 − 1.38464i 0 −1.37268 − 4.22469i 0
289.1 0 −2.93917 + 0.954994i 0 −1.75524 − 1.38533i 0 2.42366 + 0.787496i 0 5.29965 − 3.85042i 0
289.2 0 −1.89864 + 0.616907i 0 0.978101 + 2.01080i 0 −0.430637 − 0.139922i 0 0.797226 − 0.579219i 0
289.3 0 −0.989226 + 0.321419i 0 1.37039 − 1.76693i 0 −2.15207 − 0.699249i 0 −1.55179 + 1.12744i 0
289.4 0 0.989226 − 0.321419i 0 −1.25698 + 1.84933i 0 2.15207 + 0.699249i 0 −1.55179 + 1.12744i 0
289.5 0 1.89864 − 0.616907i 0 2.21463 + 0.308858i 0 0.430637 + 0.139922i 0 0.797226 − 0.579219i 0
289.6 0 2.93917 − 0.954994i 0 −1.85993 − 1.24124i 0 −2.42366 − 0.787496i 0 5.29965 − 3.85042i 0
449.1 0 −1.60349 − 2.20702i 0 −1.89499 + 1.18702i 0 1.00600 − 1.38464i 0 −1.37268 + 4.22469i 0
449.2 0 −1.22731 − 1.68925i 0 1.67152 − 1.48527i 0 −1.67492 + 2.30533i 0 −0.420216 + 1.29329i 0
449.3 0 −0.447653 − 0.616141i 0 1.93649 + 1.11803i 0 2.82695 − 3.89096i 0 0.747814 − 2.30153i 0
449.4 0 0.447653 + 0.616141i 0 −0.909494 + 2.04275i 0 −2.82695 + 3.89096i 0 0.747814 − 2.30153i 0
449.5 0 1.22731 + 1.68925i 0 −2.22531 − 0.219109i 0 1.67492 − 2.30533i 0 −0.420216 + 1.29329i 0
449.6 0 1.60349 + 2.20702i 0 2.23079 − 0.153527i 0 −1.00600 + 1.38464i 0 −1.37268 + 4.22469i 0
609.1 0 −2.93917 − 0.954994i 0 −1.75524 + 1.38533i 0 2.42366 − 0.787496i 0 5.29965 + 3.85042i 0
609.2 0 −1.89864 − 0.616907i 0 0.978101 − 2.01080i 0 −0.430637 + 0.139922i 0 0.797226 + 0.579219i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 49.6
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
11.c even 5 1 inner
55.j 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.cd.d 24
4.b odd 2 1 220.2.t.a ✓ 24
5.b even 2 1 inner 880.2.cd.d 24
11.c even 5 1 inner 880.2.cd.d 24
20.d odd 2 1 220.2.t.a ✓ 24
20.e even 4 2 1100.2.n.f 24
44.g even 10 1 2420.2.b.h 12
44.h odd 10 1 220.2.t.a ✓ 24
44.h odd 10 1 2420.2.b.i 12
55.j even 10 1 inner 880.2.cd.d 24
220.n odd 10 1 220.2.t.a ✓ 24
220.n odd 10 1 2420.2.b.i 12
220.o even 10 1 2420.2.b.h 12
220.v even 20 2 1100.2.n.f 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
220.2.t.a ✓ 24 4.b odd 2 1
220.2.t.a ✓ 24 20.d odd 2 1
220.2.t.a ✓ 24 44.h odd 10 1
220.2.t.a ✓ 24 220.n odd 10 1
880.2.cd.d 24 1.a even 1 1 trivial
880.2.cd.d 24 5.b even 2 1 inner
880.2.cd.d 24 11.c even 5 1 inner
880.2.cd.d 24 55.j even 10 1 inner
1100.2.n.f 24 20.e even 4 2
1100.2.n.f 24 220.v even 20 2
2420.2.b.h 12 44.g even 10 1
2420.2.b.h 12 220.o even 10 1
2420.2.b.i 12 44.h odd 10 1
2420.2.b.i 12 220.n odd 10 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} - 16 T_{3}^{22} + 155 T_{3}^{20} - 1189 T_{3}^{18} + 10679 T_{3}^{16} - 49589 T_{3}^{14} + \cdots + 600625 \) acting on \(S_{2}^{\mathrm{new}}(880, [\chi])\). Copy content Toggle raw display