↑

Properties

Label 192.11.h.c
Level $192$
Weight $11$
Character orbit 192.h
Analytic conductor $121.989$
Analytic rank $0$
Dimension $24$
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] = [192,11,Mod(161,192)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(192, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 11, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("192.161");
 
S:= CuspForms(chi, 11);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 192.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: \(121.988592513\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

The dimension is sufficiently large that we do not compute an algebraic \(q\)-expansion, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 328392 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 328392 q^{9} + 47919720 q^{25} - 29516256 q^{33} + 1766081064 q^{49} + 4276148496 q^{57} + 9990750000 q^{73} - 12450970728 q^{81} - 48470791152 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
161.1 0 −240.092 − 37.4802i 0 −2531.56 0 −27251.1 0 56239.5 + 17997.4i 0
161.2 0 −240.092 − 37.4802i 0 2531.56 0 27251.1 0 56239.5 + 17997.4i 0
161.3 0 −240.092 + 37.4802i 0 −2531.56 0 −27251.1 0 56239.5 − 17997.4i 0
161.4 0 −240.092 + 37.4802i 0 2531.56 0 27251.1 0 56239.5 − 17997.4i 0
161.5 0 −194.524 − 145.635i 0 −4363.03 0 17194.1 0 16630.1 + 56658.8i 0
161.6 0 −194.524 − 145.635i 0 4363.03 0 −17194.1 0 16630.1 + 56658.8i 0
161.7 0 −194.524 + 145.635i 0 −4363.03 0 17194.1 0 16630.1 − 56658.8i 0
161.8 0 −194.524 + 145.635i 0 4363.03 0 −17194.1 0 16630.1 − 56658.8i 0
161.9 0 −116.680 − 213.154i 0 −3137.20 0 5470.49 0 −31820.6 + 49741.7i 0
161.10 0 −116.680 − 213.154i 0 3137.20 0 −5470.49 0 −31820.6 + 49741.7i 0
161.11 0 −116.680 + 213.154i 0 −3137.20 0 5470.49 0 −31820.6 − 49741.7i 0
161.12 0 −116.680 + 213.154i 0 3137.20 0 −5470.49 0 −31820.6 − 49741.7i 0
161.13 0 116.680 − 213.154i 0 −3137.20 0 −5470.49 0 −31820.6 − 49741.7i 0
161.14 0 116.680 − 213.154i 0 3137.20 0 5470.49 0 −31820.6 − 49741.7i 0
161.15 0 116.680 + 213.154i 0 −3137.20 0 −5470.49 0 −31820.6 + 49741.7i 0
161.16 0 116.680 + 213.154i 0 3137.20 0 5470.49 0 −31820.6 + 49741.7i 0
161.17 0 194.524 − 145.635i 0 −4363.03 0 −17194.1 0 16630.1 − 56658.8i 0
161.18 0 194.524 − 145.635i 0 4363.03 0 17194.1 0 16630.1 − 56658.8i 0
161.19 0 194.524 + 145.635i 0 −4363.03 0 −17194.1 0 16630.1 + 56658.8i 0
161.20 0 194.524 + 145.635i 0 4363.03 0 17194.1 0 16630.1 + 56658.8i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 161.24
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
4.b odd 2 1 inner
8.b even 2 1 inner
8.d odd 2 1 inner
12.b even 2 1 inner
24.f even 2 1 inner
24.h odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 192.11.h.c ✓ 24
3.b odd 2 1 inner 192.11.h.c ✓ 24
4.b odd 2 1 inner 192.11.h.c ✓ 24
8.b even 2 1 inner 192.11.h.c ✓ 24
8.d odd 2 1 inner 192.11.h.c ✓ 24
12.b even 2 1 inner 192.11.h.c ✓ 24
24.f even 2 1 inner 192.11.h.c ✓ 24
24.h odd 2 1 inner 192.11.h.c ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
192.11.h.c ✓ 24 1.a even 1 1 trivial
192.11.h.c ✓ 24 3.b odd 2 1 inner
192.11.h.c ✓ 24 4.b odd 2 1 inner
192.11.h.c ✓ 24 8.b even 2 1 inner
192.11.h.c ✓ 24 8.d odd 2 1 inner
192.11.h.c ✓ 24 12.b even 2 1 inner
192.11.h.c ✓ 24 24.f even 2 1 inner
192.11.h.c ✓ 24 24.h odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{11}^{\mathrm{new}}(192, [\chi])\):

\( T_{5}^{6} - 35286840T_{5}^{4} + 372426332144400T_{5}^{2} - 1200705720965775360000 \) Copy content Toggle raw display
\( T_{7}^{6} - 1068185880T_{7}^{4} + 250618633668562320T_{7}^{2} - 6570226059173631598464000 \) Copy content Toggle raw display