Properties

Label 950.3.d.c
Level $950$
Weight $3$
Character orbit 950.d
Analytic conductor $25.886$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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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: \(32\)
Twist minimal: no (minimal twist has level 190)
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.

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 64 q^{4} + 32 q^{6} + 128 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 64 q^{4} + 32 q^{6} + 128 q^{9} - 64 q^{11} + 128 q^{16} + 32 q^{19} + 64 q^{24} - 128 q^{26} + 256 q^{36} + 448 q^{39} - 128 q^{44} - 672 q^{49} + 352 q^{54} + 96 q^{61} + 256 q^{64} + 352 q^{66} + 288 q^{74} + 64 q^{76} + 1728 q^{81} + 128 q^{96} - 352 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
949.1 −1.41421 3.15928 2.00000 0 −4.46790 13.6136i −2.82843 0.981053 0
949.2 −1.41421 −5.26410 2.00000 0 7.44456 12.5505i −2.82843 18.7107 0
949.3 −1.41421 1.23540 2.00000 0 −1.74712 8.54633i −2.82843 −7.47378 0
949.4 −1.41421 −5.62107 2.00000 0 7.94939 6.51823i −2.82843 22.5964 0
949.5 −1.41421 −1.95901 2.00000 0 2.77046 5.01111i −2.82843 −5.16227 0
949.6 −1.41421 5.15315 2.00000 0 −7.28765 0.0751428i −2.82843 17.5549 0
949.7 −1.41421 −1.12134 2.00000 0 1.58581 6.17053i −2.82843 −7.74260 0
949.8 −1.41421 −1.23917 2.00000 0 1.75244 6.19957i −2.82843 −7.46447 0
949.9 −1.41421 −1.23917 2.00000 0 1.75244 6.19957i −2.82843 −7.46447 0
949.10 −1.41421 −1.12134 2.00000 0 1.58581 6.17053i −2.82843 −7.74260 0
949.11 −1.41421 5.15315 2.00000 0 −7.28765 0.0751428i −2.82843 17.5549 0
949.12 −1.41421 −1.95901 2.00000 0 2.77046 5.01111i −2.82843 −5.16227 0
949.13 −1.41421 −5.62107 2.00000 0 7.94939 6.51823i −2.82843 22.5964 0
949.14 −1.41421 1.23540 2.00000 0 −1.74712 8.54633i −2.82843 −7.47378 0
949.15 −1.41421 −5.26410 2.00000 0 7.44456 12.5505i −2.82843 18.7107 0
949.16 −1.41421 3.15928 2.00000 0 −4.46790 13.6136i −2.82843 0.981053 0
949.17 1.41421 −3.15928 2.00000 0 −4.46790 13.6136i 2.82843 0.981053 0
949.18 1.41421 5.26410 2.00000 0 7.44456 12.5505i 2.82843 18.7107 0
949.19 1.41421 −1.23540 2.00000 0 −1.74712 8.54633i 2.82843 −7.47378 0
949.20 1.41421 5.62107 2.00000 0 7.94939 6.51823i 2.82843 22.5964 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 949.32
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.c 32
5.b even 2 1 inner 950.3.d.c 32
5.c odd 4 1 190.3.c.a 16
5.c odd 4 1 950.3.c.d 16
15.e even 4 1 1710.3.h.a 16
19.b odd 2 1 inner 950.3.d.c 32
20.e even 4 1 1520.3.h.c 16
95.d odd 2 1 inner 950.3.d.c 32
95.g even 4 1 190.3.c.a 16
95.g even 4 1 950.3.c.d 16
285.j odd 4 1 1710.3.h.a 16
380.j odd 4 1 1520.3.h.c 16
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.3.c.a 16 5.c odd 4 1
190.3.c.a 16 95.g even 4 1
950.3.c.d 16 5.c odd 4 1
950.3.c.d 16 95.g even 4 1
950.3.d.c 32 1.a even 1 1 trivial
950.3.d.c 32 5.b even 2 1 inner
950.3.d.c 32 19.b odd 2 1 inner
950.3.d.c 32 95.d odd 2 1 inner
1520.3.h.c 16 20.e even 4 1
1520.3.h.c 16 380.j odd 4 1
1710.3.h.a 16 15.e even 4 1
1710.3.h.a 16 285.j odd 4 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{16} - 104 T_{3}^{14} + 4112 T_{3}^{12} - 76896 T_{3}^{10} + 699096 T_{3}^{8} - 3068640 T_{3}^{6} + 6595840 T_{3}^{4} - 6739200 T_{3}^{2} + 2624400 \) acting on \(S_{3}^{\mathrm{new}}(950, [\chi])\). Copy content Toggle raw display