↑

Properties

Label 1881.2.h.g
Level $1881$
Weight $2$
Character orbit 1881.h
Analytic conductor $15.020$
Analytic rank $0$
Dimension $24$
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1881,2,Mod(208,1881)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1881, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1881.208");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1881 = 3^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1881.h (of order \(2\), degree \(1\), 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: \(15.0198606202\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: no (minimal twist has level 627)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 24 q^{4} - 10 q^{11} - 16 q^{16} - 104 q^{20} + 20 q^{23} - 16 q^{25} + 32 q^{26} + 4 q^{38} + 36 q^{44} + 20 q^{47} - 24 q^{49} - 46 q^{55} + 60 q^{58} - 68 q^{64} + 22 q^{77} - 12 q^{80} + 56 q^{82}+ \cdots + 120 q^{92}+O(q^{100}) \) Copy content Toggle raw display

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
208.1 −2.41530 0 3.83365 −2.83365 0 0.748883i −4.42881 0 6.84411
208.2 −2.41530 0 3.83365 −2.83365 0 − 0.748883i −4.42881 0 6.84411
208.3 −2.29042 0 3.24604 −2.24604 0 − 2.78846i −2.85397 0 5.14439
208.4 −2.29042 0 3.24604 −2.24604 0 2.78846i −2.85397 0 5.14439
208.5 −1.89680 0 1.59785 −0.597854 0 2.59222i 0.762791 0 1.13401
208.6 −1.89680 0 1.59785 −0.597854 0 − 2.59222i 0.762791 0 1.13401
208.7 −1.38599 0 −0.0790327 1.07903 0 4.79678i 2.88152 0 −1.49553
208.8 −1.38599 0 −0.0790327 1.07903 0 − 4.79678i 2.88152 0 −1.49553
208.9 −1.15985 0 −0.654748 1.65475 0 − 0.0488797i 3.07911 0 −1.91926
208.10 −1.15985 0 −0.654748 1.65475 0 0.0488797i 3.07911 0 −1.91926
208.11 −0.237132 0 −1.94377 2.94377 0 3.15160i 0.935194 0 −0.698062
208.12 −0.237132 0 −1.94377 2.94377 0 − 3.15160i 0.935194 0 −0.698062
208.13 0.237132 0 −1.94377 2.94377 0 − 3.15160i −0.935194 0 0.698062
208.14 0.237132 0 −1.94377 2.94377 0 3.15160i −0.935194 0 0.698062
208.15 1.15985 0 −0.654748 1.65475 0 − 0.0488797i −3.07911 0 1.91926
208.16 1.15985 0 −0.654748 1.65475 0 0.0488797i −3.07911 0 1.91926
208.17 1.38599 0 −0.0790327 1.07903 0 4.79678i −2.88152 0 1.49553
208.18 1.38599 0 −0.0790327 1.07903 0 − 4.79678i −2.88152 0 1.49553
208.19 1.89680 0 1.59785 −0.597854 0 2.59222i −0.762791 0 −1.13401
208.20 1.89680 0 1.59785 −0.597854 0 − 2.59222i −0.762791 0 −1.13401
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 208.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.b odd 2 1 inner
19.b odd 2 1 inner
209.d even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1881.2.h.g 24
3.b odd 2 1 627.2.h.b ✓ 24
11.b odd 2 1 inner 1881.2.h.g 24
19.b odd 2 1 inner 1881.2.h.g 24
33.d even 2 1 627.2.h.b ✓ 24
57.d even 2 1 627.2.h.b ✓ 24
209.d even 2 1 inner 1881.2.h.g 24
627.b odd 2 1 627.2.h.b ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
627.2.h.b ✓ 24 3.b odd 2 1
627.2.h.b ✓ 24 33.d even 2 1
627.2.h.b ✓ 24 57.d even 2 1
627.2.h.b ✓ 24 627.b odd 2 1
1881.2.h.g 24 1.a even 1 1 trivial
1881.2.h.g 24 11.b odd 2 1 inner
1881.2.h.g 24 19.b odd 2 1 inner
1881.2.h.g 24 209.d even 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(1881, [\chi])\):

\( T_{2}^{12} - 18T_{2}^{10} + 122T_{2}^{8} - 385T_{2}^{6} + 563T_{2}^{4} - 315T_{2}^{2} + 16 \) Copy content Toggle raw display
\( T_{5}^{6} - 13T_{5}^{4} + T_{5}^{3} + 41T_{5}^{2} - 12T_{5} - 20 \) Copy content Toggle raw display