Properties

Label 96.9.h.c
Level $96$
Weight $9$
Character orbit 96.h
Analytic conductor $39.108$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [96,9,Mod(17,96)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(96, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("96.17");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 96 = 2^{5} \cdot 3 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 96.h (of order \(2\), degree \(1\), 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: \(39.1083465659\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: no (minimal twist has level 24)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 9592 q^{7} - 13124 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - 9592 q^{7} - 13124 q^{9} + 153416 q^{15} + 1000084 q^{25} - 2991608 q^{31} + 637656 q^{33} - 3838144 q^{39} - 25755372 q^{49} + 8933520 q^{55} + 3542240 q^{57} - 10817272 q^{63} + 11921592 q^{73} - 41160184 q^{79} - 78940132 q^{81} - 63134136 q^{87} - 194894984 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
17.1 0 −80.2470 11.0190i 0 414.987 0 −1996.89 0 6318.16 + 1768.49i 0
17.2 0 −80.2470 + 11.0190i 0 414.987 0 −1996.89 0 6318.16 1768.49i 0
17.3 0 −71.4947 38.0725i 0 −867.471 0 1776.55 0 3661.97 + 5443.96i 0
17.4 0 −71.4947 + 38.0725i 0 −867.471 0 1776.55 0 3661.97 5443.96i 0
17.5 0 −67.2364 45.1693i 0 −629.567 0 123.057 0 2480.47 + 6074.04i 0
17.6 0 −67.2364 + 45.1693i 0 −629.567 0 123.057 0 2480.47 6074.04i 0
17.7 0 −49.3241 64.2506i 0 530.205 0 1274.95 0 −1695.27 + 6338.20i 0
17.8 0 −49.3241 + 64.2506i 0 530.205 0 1274.95 0 −1695.27 6338.20i 0
17.9 0 −48.8926 64.5795i 0 −274.212 0 −3670.87 0 −1780.03 + 6314.92i 0
17.10 0 −48.8926 + 64.5795i 0 −274.212 0 −3670.87 0 −1780.03 6314.92i 0
17.11 0 −16.8860 79.2203i 0 1141.88 0 −2365.96 0 −5990.73 + 2675.43i 0
17.12 0 −16.8860 + 79.2203i 0 1141.88 0 −2365.96 0 −5990.73 2675.43i 0
17.13 0 −11.9463 80.1142i 0 55.8511 0 2461.17 0 −6275.57 + 1914.14i 0
17.14 0 −11.9463 + 80.1142i 0 55.8511 0 2461.17 0 −6275.57 1914.14i 0
17.15 0 11.9463 80.1142i 0 −55.8511 0 2461.17 0 −6275.57 1914.14i 0
17.16 0 11.9463 + 80.1142i 0 −55.8511 0 2461.17 0 −6275.57 + 1914.14i 0
17.17 0 16.8860 79.2203i 0 −1141.88 0 −2365.96 0 −5990.73 2675.43i 0
17.18 0 16.8860 + 79.2203i 0 −1141.88 0 −2365.96 0 −5990.73 + 2675.43i 0
17.19 0 48.8926 64.5795i 0 274.212 0 −3670.87 0 −1780.03 6314.92i 0
17.20 0 48.8926 + 64.5795i 0 274.212 0 −3670.87 0 −1780.03 + 6314.92i 0
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 17.28
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
8.b 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 96.9.h.c 28
3.b odd 2 1 inner 96.9.h.c 28
4.b odd 2 1 24.9.h.c 28
8.b even 2 1 inner 96.9.h.c 28
8.d odd 2 1 24.9.h.c 28
12.b even 2 1 24.9.h.c 28
24.f even 2 1 24.9.h.c 28
24.h odd 2 1 inner 96.9.h.c 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
24.9.h.c 28 4.b odd 2 1
24.9.h.c 28 8.d odd 2 1
24.9.h.c 28 12.b even 2 1
24.9.h.c 28 24.f even 2 1
96.9.h.c 28 1.a even 1 1 trivial
96.9.h.c 28 3.b odd 2 1 inner
96.9.h.c 28 8.b even 2 1 inner
96.9.h.c 28 24.h odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{14} - 2984396 T_{5}^{12} + 3184387077168 T_{5}^{10} + \cdots - 44\!\cdots\!00 \) acting on \(S_{9}^{\mathrm{new}}(96, [\chi])\). Copy content Toggle raw display