Properties

Label 950.4.a.a
Level $950$
Weight $4$
Character orbit 950.a
Self dual yes
Analytic conductor $56.052$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,4,Mod(1,950)]
 
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([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)

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: yes
Analytic conductor: \(56.0518145055\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \( q - 2 q^{2} + 4 q^{3} + 4 q^{4} - 8 q^{6} + 20 q^{7} - 8 q^{8} - 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( q - 2 q^{2} + 4 q^{3} + 4 q^{4} - 8 q^{6} + 20 q^{7} - 8 q^{8} - 11 q^{9} - 44 q^{11} + 16 q^{12} - 42 q^{13} - 40 q^{14} + 16 q^{16} + 86 q^{17} + 22 q^{18} + 19 q^{19} + 80 q^{21} + 88 q^{22} + 164 q^{23} - 32 q^{24} + 84 q^{26} - 152 q^{27} + 80 q^{28} - 162 q^{29} - 312 q^{31} - 32 q^{32} - 176 q^{33} - 172 q^{34} - 44 q^{36} - 226 q^{37} - 38 q^{38} - 168 q^{39} + 34 q^{41} - 160 q^{42} + 432 q^{43} - 176 q^{44} - 328 q^{46} - 580 q^{47} + 64 q^{48} + 57 q^{49} + 344 q^{51} - 168 q^{52} - 506 q^{53} + 304 q^{54} - 160 q^{56} + 76 q^{57} + 324 q^{58} + 364 q^{59} + 518 q^{61} + 624 q^{62} - 220 q^{63} + 64 q^{64} + 352 q^{66} - 924 q^{67} + 344 q^{68} + 656 q^{69} + 320 q^{71} + 88 q^{72} + 542 q^{73} + 452 q^{74} + 76 q^{76} - 880 q^{77} + 336 q^{78} - 1208 q^{79} - 311 q^{81} - 68 q^{82} + 1120 q^{83} + 320 q^{84} - 864 q^{86} - 648 q^{87} + 352 q^{88} - 1022 q^{89} - 840 q^{91} + 656 q^{92} - 1248 q^{93} + 1160 q^{94} - 128 q^{96} - 1166 q^{97} - 114 q^{98} + 484 q^{99}+O(q^{100}) \) 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   \(\iota_m(\nu)\) \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1
0
−2.00000 4.00000 4.00000 0 −8.00000 20.0000 −8.00000 −11.0000 0
\(n\): e.g. 2-40 or 990-1000
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(5\) \(1\)
\(19\) \(-1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 950.4.a.a 1
5.b even 2 1 190.4.a.c 1
5.c odd 4 2 950.4.b.a 2
15.d odd 2 1 1710.4.a.b 1
20.d odd 2 1 1520.4.a.g 1
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.4.a.c 1 5.b even 2 1
950.4.a.a 1 1.a even 1 1 trivial
950.4.b.a 2 5.c odd 4 2
1520.4.a.g 1 20.d odd 2 1
1710.4.a.b 1 15.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(950))\):

\( T_{3} - 4 \) Copy content Toggle raw display
\( T_{7} - 20 \) Copy content Toggle raw display

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( T + 2 \) Copy content Toggle raw display
$3$ \( T - 4 \) Copy content Toggle raw display
$5$ \( T \) Copy content Toggle raw display
$7$ \( T - 20 \) Copy content Toggle raw display
$11$ \( T + 44 \) Copy content Toggle raw display
$13$ \( T + 42 \) Copy content Toggle raw display
$17$ \( T - 86 \) Copy content Toggle raw display
$19$ \( T - 19 \) Copy content Toggle raw display
$23$ \( T - 164 \) Copy content Toggle raw display
$29$ \( T + 162 \) Copy content Toggle raw display
$31$ \( T + 312 \) Copy content Toggle raw display
$37$ \( T + 226 \) Copy content Toggle raw display
$41$ \( T - 34 \) Copy content Toggle raw display
$43$ \( T - 432 \) Copy content Toggle raw display
$47$ \( T + 580 \) Copy content Toggle raw display
$53$ \( T + 506 \) Copy content Toggle raw display
$59$ \( T - 364 \) Copy content Toggle raw display
$61$ \( T - 518 \) Copy content Toggle raw display
$67$ \( T + 924 \) Copy content Toggle raw display
$71$ \( T - 320 \) Copy content Toggle raw display
$73$ \( T - 542 \) Copy content Toggle raw display
$79$ \( T + 1208 \) Copy content Toggle raw display
$83$ \( T - 1120 \) Copy content Toggle raw display
$89$ \( T + 1022 \) Copy content Toggle raw display
$97$ \( T + 1166 \) Copy content Toggle raw display
show more
show less