↑

Properties

Label 950.2.l.l
Level $950$
Weight $2$
Character orbit 950.l
Analytic conductor $7.586$
Analytic rank $0$
Dimension $30$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(101,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.101");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.l (of order \(9\), 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: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(5\) over \(\Q(\zeta_{9})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 30 q - 12 q^{7} + 15 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 30 q - 12 q^{7} + 15 q^{8} + 6 q^{11} + 6 q^{14} - 30 q^{18} + 24 q^{19} + 24 q^{21} + 3 q^{22} + 3 q^{23} + 3 q^{26} - 18 q^{27} + 3 q^{28} + 12 q^{29} - 30 q^{33} + 24 q^{37} - 12 q^{38} - 24 q^{39} - 3 q^{41} + 12 q^{42} + 6 q^{43} - 3 q^{44} + 48 q^{47} + 15 q^{49} - 90 q^{51} - 18 q^{53} + 18 q^{54} - 24 q^{56} - 42 q^{57} + 36 q^{58} - 18 q^{59} - 60 q^{61} - 24 q^{62} - 21 q^{63} - 15 q^{64} - 78 q^{66} - 30 q^{67} - 12 q^{68} + 24 q^{69} + 30 q^{73} - 9 q^{74} - 3 q^{76} + 78 q^{77} - 6 q^{79} + 60 q^{81} + 3 q^{82} - 42 q^{83} - 6 q^{84} + 12 q^{86} - 54 q^{87} - 6 q^{88} - 30 q^{89} - 6 q^{91} - 6 q^{92} + 72 q^{93} - 78 q^{94} - 42 q^{97} + 6 q^{98} - 99 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
101.1 −0.766044 + 0.642788i −3.03100 − 1.10319i 0.173648 − 0.984808i 0 3.03100 − 1.10319i −1.36166 + 2.35847i 0.500000 + 0.866025i 5.67178 + 4.75918i 0
101.2 −0.766044 + 0.642788i −0.476729 − 0.173515i 0.173648 − 0.984808i 0 0.476729 − 0.173515i 0.753583 − 1.30524i 0.500000 + 0.866025i −2.10097 − 1.76292i 0
101.3 −0.766044 + 0.642788i −0.0808150 − 0.0294142i 0.173648 − 0.984808i 0 0.0808150 − 0.0294142i −1.91879 + 3.32344i 0.500000 + 0.866025i −2.29247 − 1.92361i 0
101.4 −0.766044 + 0.642788i 0.845354 + 0.307684i 0.173648 − 0.984808i 0 −0.845354 + 0.307684i 1.06731 − 1.84863i 0.500000 + 0.866025i −1.67818 − 1.40816i 0
101.5 −0.766044 + 0.642788i 2.74319 + 0.998438i 0.173648 − 0.984808i 0 −2.74319 + 0.998438i −0.366794 + 0.635305i 0.500000 + 0.866025i 4.23006 + 3.54944i 0
251.1 0.939693 + 0.342020i −0.419293 − 2.37793i 0.766044 + 0.642788i 0 0.419293 − 2.37793i −1.31398 + 2.27588i 0.500000 + 0.866025i −2.65966 + 0.968036i 0
251.2 0.939693 + 0.342020i −0.260779 − 1.47895i 0.766044 + 0.642788i 0 0.260779 − 1.47895i 1.51251 − 2.61975i 0.500000 + 0.866025i 0.699782 − 0.254700i 0
251.3 0.939693 + 0.342020i −0.0989733 − 0.561305i 0.766044 + 0.642788i 0 0.0989733 − 0.561305i −2.10163 + 3.64013i 0.500000 + 0.866025i 2.51381 − 0.914952i 0
251.4 0.939693 + 0.342020i 0.237849 + 1.34891i 0.766044 + 0.642788i 0 −0.237849 + 1.34891i 0.816213 − 1.41372i 0.500000 + 0.866025i 1.05609 − 0.384387i 0
251.5 0.939693 + 0.342020i 0.541196 + 3.06928i 0.766044 + 0.642788i 0 −0.541196 + 3.06928i −0.147073 + 0.254737i 0.500000 + 0.866025i −6.30849 + 2.29610i 0
301.1 −0.766044 − 0.642788i −3.03100 + 1.10319i 0.173648 + 0.984808i 0 3.03100 + 1.10319i −1.36166 − 2.35847i 0.500000 − 0.866025i 5.67178 − 4.75918i 0
301.2 −0.766044 − 0.642788i −0.476729 + 0.173515i 0.173648 + 0.984808i 0 0.476729 + 0.173515i 0.753583 + 1.30524i 0.500000 − 0.866025i −2.10097 + 1.76292i 0
301.3 −0.766044 − 0.642788i −0.0808150 + 0.0294142i 0.173648 + 0.984808i 0 0.0808150 + 0.0294142i −1.91879 − 3.32344i 0.500000 − 0.866025i −2.29247 + 1.92361i 0
301.4 −0.766044 − 0.642788i 0.845354 − 0.307684i 0.173648 + 0.984808i 0 −0.845354 − 0.307684i 1.06731 + 1.84863i 0.500000 − 0.866025i −1.67818 + 1.40816i 0
301.5 −0.766044 − 0.642788i 2.74319 − 0.998438i 0.173648 + 0.984808i 0 −2.74319 − 0.998438i −0.366794 − 0.635305i 0.500000 − 0.866025i 4.23006 − 3.54944i 0
351.1 −0.173648 − 0.984808i −2.12694 + 1.78472i −0.939693 + 0.342020i 0 2.12694 + 1.78472i −0.303737 + 0.526088i 0.500000 + 0.866025i 0.817727 − 4.63756i 0
351.2 −0.173648 − 0.984808i −1.28288 + 1.07646i −0.939693 + 0.342020i 0 1.28288 + 1.07646i −1.16183 + 2.01234i 0.500000 + 0.866025i −0.0339381 + 0.192472i 0
351.3 −0.173648 − 0.984808i 0.0864812 − 0.0725664i −0.939693 + 0.342020i 0 −0.0864812 − 0.0725664i 0.772138 − 1.33738i 0.500000 + 0.866025i −0.518731 + 2.94187i 0
351.4 −0.173648 − 0.984808i 1.52559 − 1.28013i −0.939693 + 0.342020i 0 −1.52559 − 1.28013i −1.97239 + 3.41629i 0.500000 + 0.866025i 0.167771 − 0.951479i 0
351.5 −0.173648 − 0.984808i 1.79775 − 1.50849i −0.939693 + 0.342020i 0 −1.79775 − 1.50849i −0.273873 + 0.474362i 0.500000 + 0.866025i 0.435412 − 2.46935i 0
See all 30 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 101.5
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
19.e even 9 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 950.2.l.l 30
5.b even 2 1 950.2.l.m 30
5.c odd 4 2 190.2.p.a ✓ 60
19.e even 9 1 inner 950.2.l.l 30
95.p even 18 1 950.2.l.m 30
95.q odd 36 2 190.2.p.a ✓ 60
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.2.p.a ✓ 60 5.c odd 4 2
190.2.p.a ✓ 60 95.q odd 36 2
950.2.l.l 30 1.a even 1 1 trivial
950.2.l.l 30 19.e even 9 1 inner
950.2.l.m 30 5.b even 2 1
950.2.l.m 30 95.p even 18 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{30} + 6 T_{3}^{27} - 15 T_{3}^{26} - 102 T_{3}^{25} + 616 T_{3}^{24} + 186 T_{3}^{23} + 2142 T_{3}^{22} + \cdots + 64 \) acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\). Copy content Toggle raw display