↑

Properties

Label 1100.2.cb.d
Level $1100$
Weight $2$
Character orbit 1100.cb
Analytic conductor $8.784$
Analytic rank $0$
Dimension $32$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1100,2,Mod(49,1100)]
 
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, 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("1100.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1100.cb (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: \(8.78354422234\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q - 10 q^{11} - 26 q^{19} - 12 q^{21} + 14 q^{29} + 4 q^{31} + 34 q^{39} - 30 q^{41} + 48 q^{49} + 26 q^{51} - 12 q^{59} + 48 q^{61} + 106 q^{69} + 72 q^{71} + 90 q^{79} + 34 q^{81} - 36 q^{89} + 76 q^{91} - 80 q^{99}+O(q^{100}) \) 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 −1.76353 + 2.42729i 0 0 0 0.992679 + 1.36631i 0 −1.85465 − 5.70802i 0
49.2 0 −1.19189 + 1.64050i 0 0 0 2.39570 + 3.29740i 0 −0.343577 − 1.05742i 0
49.3 0 −0.753625 + 1.03728i 0 0 0 −1.05965 − 1.45849i 0 0.419060 + 1.28974i 0
49.4 0 −0.545259 + 0.750484i 0 0 0 0.343369 + 0.472607i 0 0.661131 + 2.03475i 0
49.5 0 0.545259 − 0.750484i 0 0 0 −0.343369 − 0.472607i 0 0.661131 + 2.03475i 0
49.6 0 0.753625 − 1.03728i 0 0 0 1.05965 + 1.45849i 0 0.419060 + 1.28974i 0
49.7 0 1.19189 − 1.64050i 0 0 0 −2.39570 − 3.29740i 0 −0.343577 − 1.05742i 0
49.8 0 1.76353 − 2.42729i 0 0 0 −0.992679 − 1.36631i 0 −1.85465 − 5.70802i 0
449.1 0 −1.76353 − 2.42729i 0 0 0 0.992679 − 1.36631i 0 −1.85465 + 5.70802i 0
449.2 0 −1.19189 − 1.64050i 0 0 0 2.39570 − 3.29740i 0 −0.343577 + 1.05742i 0
449.3 0 −0.753625 − 1.03728i 0 0 0 −1.05965 + 1.45849i 0 0.419060 − 1.28974i 0
449.4 0 −0.545259 − 0.750484i 0 0 0 0.343369 − 0.472607i 0 0.661131 − 2.03475i 0
449.5 0 0.545259 + 0.750484i 0 0 0 −0.343369 + 0.472607i 0 0.661131 − 2.03475i 0
449.6 0 0.753625 + 1.03728i 0 0 0 1.05965 − 1.45849i 0 0.419060 − 1.28974i 0
449.7 0 1.19189 + 1.64050i 0 0 0 −2.39570 + 3.29740i 0 −0.343577 + 1.05742i 0
449.8 0 1.76353 + 2.42729i 0 0 0 −0.992679 + 1.36631i 0 −1.85465 + 5.70802i 0
949.1 0 −2.98723 + 0.970609i 0 0 0 −2.09053 − 0.679254i 0 5.55439 − 4.03550i 0
949.2 0 −1.46529 + 0.476102i 0 0 0 −3.83001 − 1.24445i 0 −0.506649 + 0.368102i 0
949.3 0 −0.727256 + 0.236300i 0 0 0 2.00099 + 0.650161i 0 −1.95399 + 1.41965i 0
949.4 0 −0.710352 + 0.230807i 0 0 0 3.74048 + 1.21535i 0 −1.97572 + 1.43545i 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 49.8
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.cb.d 32
5.b even 2 1 inner 1100.2.cb.d 32
5.c odd 4 1 1100.2.n.d ✓ 16
5.c odd 4 1 1100.2.n.e yes 16
11.c even 5 1 inner 1100.2.cb.d 32
55.j even 10 1 inner 1100.2.cb.d 32
55.k odd 20 1 1100.2.n.d ✓ 16
55.k odd 20 1 1100.2.n.e yes 16
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1100.2.n.d ✓ 16 5.c odd 4 1
1100.2.n.d ✓ 16 55.k odd 20 1
1100.2.n.e yes 16 5.c odd 4 1
1100.2.n.e yes 16 55.k odd 20 1
1100.2.cb.d 32 1.a even 1 1 trivial
1100.2.cb.d 32 5.b even 2 1 inner
1100.2.cb.d 32 11.c even 5 1 inner
1100.2.cb.d 32 55.j even 10 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{32} - 12 T_{3}^{30} + 122 T_{3}^{28} - 1121 T_{3}^{26} + 11295 T_{3}^{24} - 31788 T_{3}^{22} + \cdots + 160000 \) acting on \(S_{2}^{\mathrm{new}}(1100, [\chi])\). Copy content Toggle raw display