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Properties

Label 1100.2.n.f
Level $1100$
Weight $2$
Character orbit 1100.n
Analytic conductor $8.784$
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] = [1100,2,Mod(201,1100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1100, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1100.201");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.n (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: \(8.78354422234\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(6\) over \(\Q(\zeta_{5})\)
Twist minimal: no (minimal twist has level 220)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 14 q^{9} - 2 q^{11} - 8 q^{19} - 28 q^{21} + 16 q^{29} - 26 q^{31} - 12 q^{39} + 10 q^{41} + 46 q^{49} - 12 q^{51} + 48 q^{59} - 10 q^{61} + 58 q^{69} + 42 q^{71} + 64 q^{79} + 36 q^{81} - 72 q^{89} + 10 q^{91} - 156 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
201.1 0 −0.954994 − 2.93917i 0 0 0 0.787496 − 2.42366i 0 −5.29965 + 3.85042i 0
201.2 0 −0.616907 − 1.89864i 0 0 0 −0.139922 + 0.430637i 0 −0.797226 + 0.579219i 0
201.3 0 −0.321419 − 0.989226i 0 0 0 −0.699249 + 2.15207i 0 1.55179 − 1.12744i 0
201.4 0 0.321419 + 0.989226i 0 0 0 0.699249 − 2.15207i 0 1.55179 − 1.12744i 0
201.5 0 0.616907 + 1.89864i 0 0 0 0.139922 − 0.430637i 0 −0.797226 + 0.579219i 0
201.6 0 0.954994 + 2.93917i 0 0 0 −0.787496 + 2.42366i 0 −5.29965 + 3.85042i 0
301.1 0 −0.954994 + 2.93917i 0 0 0 0.787496 + 2.42366i 0 −5.29965 − 3.85042i 0
301.2 0 −0.616907 + 1.89864i 0 0 0 −0.139922 − 0.430637i 0 −0.797226 − 0.579219i 0
301.3 0 −0.321419 + 0.989226i 0 0 0 −0.699249 − 2.15207i 0 1.55179 + 1.12744i 0
301.4 0 0.321419 − 0.989226i 0 0 0 0.699249 + 2.15207i 0 1.55179 + 1.12744i 0
301.5 0 0.616907 − 1.89864i 0 0 0 0.139922 + 0.430637i 0 −0.797226 − 0.579219i 0
301.6 0 0.954994 − 2.93917i 0 0 0 −0.787496 − 2.42366i 0 −5.29965 − 3.85042i 0
401.1 0 −2.20702 − 1.60349i 0 0 0 1.38464 − 1.00600i 0 1.37268 + 4.22469i 0
401.2 0 −1.68925 − 1.22731i 0 0 0 −2.30533 + 1.67492i 0 0.420216 + 1.29329i 0
401.3 0 −0.616141 − 0.447653i 0 0 0 3.89096 − 2.82695i 0 −0.747814 − 2.30153i 0
401.4 0 0.616141 + 0.447653i 0 0 0 −3.89096 + 2.82695i 0 −0.747814 − 2.30153i 0
401.5 0 1.68925 + 1.22731i 0 0 0 2.30533 − 1.67492i 0 0.420216 + 1.29329i 0
401.6 0 2.20702 + 1.60349i 0 0 0 −1.38464 + 1.00600i 0 1.37268 + 4.22469i 0
801.1 0 −2.20702 + 1.60349i 0 0 0 1.38464 + 1.00600i 0 1.37268 − 4.22469i 0
801.2 0 −1.68925 + 1.22731i 0 0 0 −2.30533 − 1.67492i 0 0.420216 − 1.29329i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 201.6
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 1100.2.n.f 24
5.b even 2 1 inner 1100.2.n.f 24
5.c odd 4 2 220.2.t.a ✓ 24
11.c even 5 1 inner 1100.2.n.f 24
20.e even 4 2 880.2.cd.d 24
55.j even 10 1 inner 1100.2.n.f 24
55.k odd 20 2 220.2.t.a ✓ 24
55.k odd 20 2 2420.2.b.i 12
55.l even 20 2 2420.2.b.h 12
220.v even 20 2 880.2.cd.d 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
220.2.t.a ✓ 24 5.c odd 4 2
220.2.t.a ✓ 24 55.k odd 20 2
880.2.cd.d 24 20.e even 4 2
880.2.cd.d 24 220.v even 20 2
1100.2.n.f 24 1.a even 1 1 trivial
1100.2.n.f 24 5.b even 2 1 inner
1100.2.n.f 24 11.c even 5 1 inner
1100.2.n.f 24 55.j even 10 1 inner
2420.2.b.h 12 55.l even 20 2
2420.2.b.i 12 55.k odd 20 2

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 \(S_{2}^{\mathrm{new}}(1100, [\chi])\). Copy content Toggle raw display