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Properties

Label 950.2.l.k
Level $950$
Weight $2$
Character orbit 950.l
Analytic conductor $7.586$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $2$

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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: \(24\)
Relative dimension: \(4\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 3 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 3 q^{7} - 12 q^{8} - 6 q^{11} - 3 q^{12} + 24 q^{13} - 15 q^{14} - 9 q^{17} + 30 q^{18} - 15 q^{19} - 18 q^{21} + 12 q^{23} - 9 q^{26} - 21 q^{27} + 12 q^{28} - 12 q^{29} + 9 q^{31} - 42 q^{33} - 9 q^{34} + 66 q^{37} + 6 q^{38} + 66 q^{39} + 18 q^{41} + 9 q^{42} - 3 q^{43} - 3 q^{46} - 12 q^{47} - 27 q^{49} - 3 q^{51} - 12 q^{52} - 45 q^{53} + 27 q^{54} - 6 q^{56} - 27 q^{57} - 18 q^{58} + 36 q^{59} + 12 q^{61} - 24 q^{62} - 63 q^{63} - 12 q^{64} + 48 q^{66} - 54 q^{67} + 3 q^{68} + 21 q^{69} - 39 q^{71} + 48 q^{73} + 18 q^{74} + 6 q^{76} + 48 q^{77} - 12 q^{78} - 42 q^{79} - 36 q^{81} + 18 q^{82} - 3 q^{83} + 9 q^{84} - 39 q^{86} - 24 q^{87} - 6 q^{88} - 36 q^{89} + 12 q^{91} - 15 q^{92} - 6 q^{93} + 12 q^{94} + 6 q^{96} - 54 q^{97} + 3 q^{98} + 51 q^{99}+O(q^{100}) \) 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 −2.78771 − 1.01464i 0.173648 − 0.984808i 0 −2.78771 + 1.01464i −0.454865 + 0.787850i −0.500000 − 0.866025i 4.44370 + 3.72870i 0
101.2 0.766044 − 0.642788i −0.799943 − 0.291155i 0.173648 − 0.984808i 0 −0.799943 + 0.291155i 2.52492 − 4.37330i −0.500000 − 0.866025i −1.74300 − 1.46255i 0
101.3 0.766044 − 0.642788i 0.0801377 + 0.0291678i 0.173648 − 0.984808i 0 0.0801377 − 0.0291678i −0.920368 + 1.59412i −0.500000 − 0.866025i −2.29256 − 1.92369i 0
101.4 0.766044 − 0.642788i 2.56782 + 0.934611i 0.173648 − 0.984808i 0 2.56782 − 0.934611i −1.06844 + 1.85059i −0.500000 − 0.866025i 3.42208 + 2.87147i 0
251.1 −0.939693 − 0.342020i −0.443457 − 2.51497i 0.766044 + 0.642788i 0 −0.443457 + 2.51497i 2.28243 − 3.95328i −0.500000 − 0.866025i −3.30934 + 1.20450i 0
251.2 −0.939693 − 0.342020i −0.111946 − 0.634880i 0.766044 + 0.642788i 0 −0.111946 + 0.634880i −0.213557 + 0.369892i −0.500000 − 0.866025i 2.42854 − 0.883915i 0
251.3 −0.939693 − 0.342020i 0.227288 + 1.28901i 0.766044 + 0.642788i 0 0.227288 − 1.28901i −1.11539 + 1.93191i −0.500000 − 0.866025i 1.20918 − 0.440106i 0
251.4 −0.939693 − 0.342020i 0.501764 + 2.84564i 0.766044 + 0.642788i 0 0.501764 − 2.84564i 2.01830 − 3.49580i −0.500000 − 0.866025i −5.02684 + 1.82962i 0
301.1 0.766044 + 0.642788i −2.78771 + 1.01464i 0.173648 + 0.984808i 0 −2.78771 − 1.01464i −0.454865 − 0.787850i −0.500000 + 0.866025i 4.44370 − 3.72870i 0
301.2 0.766044 + 0.642788i −0.799943 + 0.291155i 0.173648 + 0.984808i 0 −0.799943 − 0.291155i 2.52492 + 4.37330i −0.500000 + 0.866025i −1.74300 + 1.46255i 0
301.3 0.766044 + 0.642788i 0.0801377 − 0.0291678i 0.173648 + 0.984808i 0 0.0801377 + 0.0291678i −0.920368 − 1.59412i −0.500000 + 0.866025i −2.29256 + 1.92369i 0
301.4 0.766044 + 0.642788i 2.56782 − 0.934611i 0.173648 + 0.984808i 0 2.56782 + 0.934611i −1.06844 − 1.85059i −0.500000 + 0.866025i 3.42208 − 2.87147i 0
351.1 0.173648 + 0.984808i −1.71131 + 1.43596i −0.939693 + 0.342020i 0 −1.71131 − 1.43596i −1.40802 + 2.43877i −0.500000 − 0.866025i 0.345659 − 1.96033i 0
351.2 0.173648 + 0.984808i −0.654394 + 0.549102i −0.939693 + 0.342020i 0 −0.654394 − 0.549102i 1.39086 − 2.40903i −0.500000 − 0.866025i −0.394226 + 2.23577i 0
351.3 0.173648 + 0.984808i 0.639791 − 0.536848i −0.939693 + 0.342020i 0 0.639791 + 0.536848i −2.09271 + 3.62467i −0.500000 − 0.866025i −0.399818 + 2.26748i 0
351.4 0.173648 + 0.984808i 2.49196 − 2.09100i −0.939693 + 0.342020i 0 2.49196 + 2.09100i 0.556842 − 0.964479i −0.500000 − 0.866025i 1.31663 − 7.46696i 0
651.1 −0.939693 + 0.342020i −0.443457 + 2.51497i 0.766044 − 0.642788i 0 −0.443457 − 2.51497i 2.28243 + 3.95328i −0.500000 + 0.866025i −3.30934 − 1.20450i 0
651.2 −0.939693 + 0.342020i −0.111946 + 0.634880i 0.766044 − 0.642788i 0 −0.111946 − 0.634880i −0.213557 − 0.369892i −0.500000 + 0.866025i 2.42854 + 0.883915i 0
651.3 −0.939693 + 0.342020i 0.227288 − 1.28901i 0.766044 − 0.642788i 0 0.227288 + 1.28901i −1.11539 − 1.93191i −0.500000 + 0.866025i 1.20918 + 0.440106i 0
651.4 −0.939693 + 0.342020i 0.501764 − 2.84564i 0.766044 − 0.642788i 0 0.501764 + 2.84564i 2.01830 + 3.49580i −0.500000 + 0.866025i −5.02684 − 1.82962i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 101.4
Significant digits:
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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.k yes 24
5.b even 2 1 950.2.l.j ✓ 24
5.c odd 4 2 950.2.u.h 48
19.e even 9 1 inner 950.2.l.k yes 24
95.p even 18 1 950.2.l.j ✓ 24
95.q odd 36 2 950.2.u.h 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
950.2.l.j ✓ 24 5.b even 2 1
950.2.l.j ✓ 24 95.p even 18 1
950.2.l.k yes 24 1.a even 1 1 trivial
950.2.l.k yes 24 19.e even 9 1 inner
950.2.u.h 48 5.c odd 4 2
950.2.u.h 48 95.q odd 36 2

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{24} + 13 T_{3}^{21} + 9 T_{3}^{20} + 81 T_{3}^{19} + 630 T_{3}^{18} + 9 T_{3}^{17} + 423 T_{3}^{16} + \cdots + 361 \) acting on \(S_{2}^{\mathrm{new}}(950, [\chi])\). Copy content Toggle raw display