↑

Properties

Label 882.2.v.a
Level $882$
Weight $2$
Character orbit 882.v
Analytic conductor $7.043$
Analytic rank $0$
Dimension $96$
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] = [882,2,Mod(125,882)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(882, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("882.125");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.v (of order \(14\), degree \(6\), 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: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(16\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 96 q + 16 q^{4}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 96 q + 16 q^{4} - 16 q^{16} + 20 q^{22} - 8 q^{25} + 76 q^{37} + 28 q^{40} - 8 q^{43} + 112 q^{49} + 28 q^{52} + 28 q^{55} + 20 q^{58} + 84 q^{61} + 16 q^{64} - 8 q^{67} + 28 q^{70} + 112 q^{85} + 8 q^{88} - 56 q^{91} - 56 q^{94}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
125.1 −0.433884 − 0.900969i 0 −0.623490 + 0.781831i −0.607230 + 2.66045i 0 2.54507 − 0.722921i 0.974928 + 0.222521i 0 2.66045 − 0.607230i
125.2 −0.433884 − 0.900969i 0 −0.623490 + 0.781831i −0.557353 + 2.44192i 0 −0.727506 + 2.54376i 0.974928 + 0.222521i 0 2.44192 − 0.557353i
125.3 −0.433884 − 0.900969i 0 −0.623490 + 0.781831i −0.187845 + 0.823003i 0 1.99819 + 1.73414i 0.974928 + 0.222521i 0 0.823003 − 0.187845i
125.4 −0.433884 − 0.900969i 0 −0.623490 + 0.781831i −0.174791 + 0.765808i 0 −2.23823 − 1.41079i 0.974928 + 0.222521i 0 0.765808 − 0.174791i
125.5 −0.433884 − 0.900969i 0 −0.623490 + 0.781831i 0.0909226 − 0.398358i 0 0.754120 − 2.53600i 0.974928 + 0.222521i 0 −0.398358 + 0.0909226i
125.6 −0.433884 − 0.900969i 0 −0.623490 + 0.781831i 0.259056 − 1.13500i 0 −2.63739 − 0.210196i 0.974928 + 0.222521i 0 −1.13500 + 0.259056i
125.7 −0.433884 − 0.900969i 0 −0.623490 + 0.781831i 0.606551 − 2.65747i 0 1.33782 + 2.28260i 0.974928 + 0.222521i 0 −2.65747 + 0.606551i
125.8 −0.433884 − 0.900969i 0 −0.623490 + 0.781831i 0.956882 − 4.19237i 0 −2.38897 + 1.13703i 0.974928 + 0.222521i 0 −4.19237 + 0.956882i
125.9 0.433884 + 0.900969i 0 −0.623490 + 0.781831i −0.956882 + 4.19237i 0 −2.38897 + 1.13703i −0.974928 − 0.222521i 0 −4.19237 + 0.956882i
125.10 0.433884 + 0.900969i 0 −0.623490 + 0.781831i −0.606551 + 2.65747i 0 1.33782 + 2.28260i −0.974928 − 0.222521i 0 −2.65747 + 0.606551i
125.11 0.433884 + 0.900969i 0 −0.623490 + 0.781831i −0.259056 + 1.13500i 0 −2.63739 − 0.210196i −0.974928 − 0.222521i 0 −1.13500 + 0.259056i
125.12 0.433884 + 0.900969i 0 −0.623490 + 0.781831i −0.0909226 + 0.398358i 0 0.754120 − 2.53600i −0.974928 − 0.222521i 0 −0.398358 + 0.0909226i
125.13 0.433884 + 0.900969i 0 −0.623490 + 0.781831i 0.174791 − 0.765808i 0 −2.23823 − 1.41079i −0.974928 − 0.222521i 0 0.765808 − 0.174791i
125.14 0.433884 + 0.900969i 0 −0.623490 + 0.781831i 0.187845 − 0.823003i 0 1.99819 + 1.73414i −0.974928 − 0.222521i 0 0.823003 − 0.187845i
125.15 0.433884 + 0.900969i 0 −0.623490 + 0.781831i 0.557353 − 2.44192i 0 −0.727506 + 2.54376i −0.974928 − 0.222521i 0 2.44192 − 0.557353i
125.16 0.433884 + 0.900969i 0 −0.623490 + 0.781831i 0.607230 − 2.66045i 0 2.54507 − 0.722921i −0.974928 − 0.222521i 0 2.66045 − 0.607230i
251.1 −0.781831 − 0.623490i 0 0.222521 + 0.974928i −2.40184 − 1.15666i 0 −0.0714045 − 2.64479i 0.433884 − 0.900969i 0 1.15666 + 2.40184i
251.2 −0.781831 − 0.623490i 0 0.222521 + 0.974928i −2.19901 − 1.05899i 0 2.42198 + 1.06489i 0.433884 − 0.900969i 0 1.05899 + 2.19901i
251.3 −0.781831 − 0.623490i 0 0.222521 + 0.974928i −1.35279 − 0.651468i 0 1.05127 + 2.42793i 0.433884 − 0.900969i 0 0.651468 + 1.35279i
251.4 −0.781831 − 0.623490i 0 0.222521 + 0.974928i 0.815549 + 0.392748i 0 −2.62718 − 0.312901i 0.433884 − 0.900969i 0 −0.392748 − 0.815549i
See all 96 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 125.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
49.f odd 14 1 inner
147.k even 14 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 882.2.v.a ✓ 96
3.b odd 2 1 inner 882.2.v.a ✓ 96
49.f odd 14 1 inner 882.2.v.a ✓ 96
147.k even 14 1 inner 882.2.v.a ✓ 96
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
882.2.v.a ✓ 96 1.a even 1 1 trivial
882.2.v.a ✓ 96 3.b odd 2 1 inner
882.2.v.a ✓ 96 49.f odd 14 1 inner
882.2.v.a ✓ 96 147.k even 14 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(882, [\chi])\).