↑

Properties

Label 950.3.d.b
Level $950$
Weight $3$
Character orbit 950.d
Analytic conductor $25.886$
Analytic rank $0$
Dimension $24$
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] = [950,3,Mod(949,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.949");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 950.d (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: \(25.8856251142\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 48 q^{4} - 16 q^{6} + 56 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 48 q^{4} - 16 q^{6} + 56 q^{9} + 8 q^{11} + 96 q^{16} + 24 q^{19} - 32 q^{24} - 32 q^{26} + 112 q^{36} - 200 q^{39} + 16 q^{44} + 216 q^{49} - 224 q^{54} - 152 q^{61} + 192 q^{64} + 16 q^{66} - 144 q^{74} + 48 q^{76} - 264 q^{81} - 64 q^{96} - 256 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
949.1 −1.41421 −1.82347 2.00000 0 2.57878 13.1234i −2.82843 −5.67494 0
949.2 −1.41421 5.15516 2.00000 0 −7.29050 − 6.80618i −2.82843 17.5757 0
949.3 −1.41421 −4.45124 2.00000 0 6.29500 − 3.02287i −2.82843 10.8135 0
949.4 −1.41421 −1.48153 2.00000 0 2.09520 − 3.07378i −2.82843 −6.80506 0
949.5 −1.41421 3.53663 2.00000 0 −5.00155 0.146462i −2.82843 3.50774 0
949.6 −1.41421 1.89288 2.00000 0 −2.67694 1.68650i −2.82843 −5.41699 0
949.7 −1.41421 1.89288 2.00000 0 −2.67694 − 1.68650i −2.82843 −5.41699 0
949.8 −1.41421 3.53663 2.00000 0 −5.00155 − 0.146462i −2.82843 3.50774 0
949.9 −1.41421 −1.48153 2.00000 0 2.09520 3.07378i −2.82843 −6.80506 0
949.10 −1.41421 −4.45124 2.00000 0 6.29500 3.02287i −2.82843 10.8135 0
949.11 −1.41421 5.15516 2.00000 0 −7.29050 6.80618i −2.82843 17.5757 0
949.12 −1.41421 −1.82347 2.00000 0 2.57878 − 13.1234i −2.82843 −5.67494 0
949.13 1.41421 1.82347 2.00000 0 2.57878 13.1234i 2.82843 −5.67494 0
949.14 1.41421 −5.15516 2.00000 0 −7.29050 − 6.80618i 2.82843 17.5757 0
949.15 1.41421 4.45124 2.00000 0 6.29500 − 3.02287i 2.82843 10.8135 0
949.16 1.41421 1.48153 2.00000 0 2.09520 − 3.07378i 2.82843 −6.80506 0
949.17 1.41421 −3.53663 2.00000 0 −5.00155 0.146462i 2.82843 3.50774 0
949.18 1.41421 −1.89288 2.00000 0 −2.67694 1.68650i 2.82843 −5.41699 0
949.19 1.41421 −1.89288 2.00000 0 −2.67694 − 1.68650i 2.82843 −5.41699 0
949.20 1.41421 −3.53663 2.00000 0 −5.00155 − 0.146462i 2.82843 3.50774 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 949.24
Significant digits:
Format:

Inner twists

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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 950.3.d.b 24
5.b even 2 1 inner 950.3.d.b 24
5.c odd 4 1 950.3.c.b ✓ 12
5.c odd 4 1 950.3.c.c yes 12
19.b odd 2 1 inner 950.3.d.b 24
95.d odd 2 1 inner 950.3.d.b 24
95.g even 4 1 950.3.c.b ✓ 12
95.g even 4 1 950.3.c.c yes 12
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
950.3.c.b ✓ 12 5.c odd 4 1
950.3.c.b ✓ 12 95.g even 4 1
950.3.c.c yes 12 5.c odd 4 1
950.3.c.c yes 12 95.g even 4 1
950.3.d.b 24 1.a even 1 1 trivial
950.3.d.b 24 5.b even 2 1 inner
950.3.d.b 24 19.b odd 2 1 inner
950.3.d.b 24 95.d odd 2 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{12} - 68T_{3}^{10} + 1670T_{3}^{8} - 18282T_{3}^{6} + 91461T_{3}^{4} - 207270T_{3}^{2} + 172225 \) acting on \(S_{3}^{\mathrm{new}}(950, [\chi])\). Copy content Toggle raw display