Properties

Label 935.2.s.a
Level $935$
Weight $2$
Character orbit 935.s
Analytic conductor $7.466$
Analytic rank $0$
Dimension $176$
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] = [935,2,Mod(89,935)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(935, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("935.89");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.s (of order \(4\), degree \(2\), 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: \(7.46601258899\)
Analytic rank: \(0\)
Dimension: \(176\)
Relative dimension: \(88\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 176 q + 168 q^{4} + 4 q^{5} + 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 176 q + 168 q^{4} + 4 q^{5} + 8 q^{6} - 8 q^{10} - 8 q^{14} + 136 q^{16} + 8 q^{20} - 48 q^{21} + 8 q^{24} - 104 q^{30} - 24 q^{31} - 24 q^{34} - 64 q^{35} - 16 q^{39} - 56 q^{40} - 16 q^{41} - 8 q^{44} + 12 q^{45} + 40 q^{46} + 24 q^{50} - 136 q^{54} - 24 q^{56} + 72 q^{61} + 88 q^{64} - 16 q^{65} + 160 q^{69} + 32 q^{71} + 32 q^{74} - 120 q^{75} + 32 q^{79} - 4 q^{80} - 112 q^{81} - 192 q^{84} + 84 q^{85} - 144 q^{86} - 48 q^{89} + 108 q^{90} + 16 q^{91} + 100 q^{95} - 72 q^{96}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
89.1 −2.78286 1.11291 + 1.11291i 5.74428 −0.780852 2.09530i −3.09707 3.09707i 1.86351 1.86351i −10.4198 0.522851i 2.17300 + 5.83091i
89.2 −2.71389 1.08381 + 1.08381i 5.36518 −0.196718 + 2.22740i −2.94135 2.94135i −0.893035 + 0.893035i −9.13272 0.650695i 0.533870 6.04491i
89.3 −2.68198 −1.48774 1.48774i 5.19303 −1.37789 + 1.76109i 3.99008 + 3.99008i 1.70185 1.70185i −8.56365 1.42672i 3.69547 4.72320i
89.4 −2.60361 −1.03941 1.03941i 4.77880 2.06449 + 0.858995i 2.70623 + 2.70623i −0.436910 + 0.436910i −7.23493 0.839245i −5.37514 2.23649i
89.5 −2.54872 1.00064 + 1.00064i 4.49595 2.21347 + 0.317109i −2.55034 2.55034i −0.462784 + 0.462784i −6.36146 0.997457i −5.64150 0.808221i
89.6 −2.48276 −0.552169 0.552169i 4.16409 1.20456 1.88389i 1.37090 + 1.37090i 2.12488 2.12488i −5.37292 2.39022i −2.99062 + 4.67725i
89.7 −2.46090 1.90829 + 1.90829i 4.05603 1.00606 1.99696i −4.69611 4.69611i −3.35879 + 3.35879i −5.05970 4.28312i −2.47581 + 4.91432i
89.8 −2.43106 −0.953668 0.953668i 3.91005 −2.00582 + 0.988275i 2.31842 + 2.31842i 0.451938 0.451938i −4.64343 1.18103i 4.87627 2.40255i
89.9 −2.31180 −1.72601 1.72601i 3.34442 1.14866 + 1.91848i 3.99019 + 3.99019i −2.78193 + 2.78193i −3.10803 2.95821i −2.65547 4.43515i
89.10 −2.29290 −2.27659 2.27659i 3.25738 2.12692 0.690070i 5.21999 + 5.21999i 2.42710 2.42710i −2.88306 7.36573i −4.87682 + 1.58226i
89.11 −2.29290 0.332523 + 0.332523i 3.25737 −1.86965 1.22655i −0.762439 0.762439i −1.52018 + 1.52018i −2.88302 2.77886i 4.28691 + 2.81234i
89.12 −2.23685 −1.31033 1.31033i 3.00350 −1.16908 1.90611i 2.93101 + 2.93101i −0.128790 + 0.128790i −2.24467 0.433933i 2.61505 + 4.26368i
89.13 −2.11924 0.710313 + 0.710313i 2.49120 −2.21657 + 0.294649i −1.50533 1.50533i 3.33492 3.33492i −1.04097 1.99091i 4.69745 0.624434i
89.14 −2.08344 0.210181 + 0.210181i 2.34072 0.240850 + 2.22306i −0.437899 0.437899i −2.18770 + 2.18770i −0.709863 2.91165i −0.501797 4.63161i
89.15 −2.07859 2.16490 + 2.16490i 2.32052 1.59023 + 1.57199i −4.49994 4.49994i 1.14367 1.14367i −0.666239 6.37360i −3.30544 3.26753i
89.16 −2.07526 1.11341 + 1.11341i 2.30670 1.95717 1.08142i −2.31061 2.31061i 2.29464 2.29464i −0.636478 0.520652i −4.06164 + 2.24423i
89.17 −1.99798 −2.26187 2.26187i 1.99192 −2.15822 + 0.584891i 4.51917 + 4.51917i −2.62923 + 2.62923i 0.0161446 7.23211i 4.31207 1.16860i
89.18 −1.93920 −0.202137 0.202137i 1.76050 1.09642 1.94881i 0.391984 + 0.391984i −1.63995 + 1.63995i 0.464433 2.91828i −2.12617 + 3.77914i
89.19 −1.71101 0.318077 + 0.318077i 0.927565 −1.48521 + 1.67157i −0.544233 0.544233i 0.619417 0.619417i 1.83495 2.79765i 2.54122 2.86008i
89.20 −1.64074 −1.91660 1.91660i 0.692030 −0.0332711 + 2.23582i 3.14465 + 3.14465i 2.09640 2.09640i 2.14604 4.34672i 0.0545892 3.66840i
See next 80 embeddings (of 176 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 89.88
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
17.c even 4 1 inner
85.j even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 935.2.s.a 176
5.b even 2 1 inner 935.2.s.a 176
17.c even 4 1 inner 935.2.s.a 176
85.j even 4 1 inner 935.2.s.a 176
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.s.a 176 1.a even 1 1 trivial
935.2.s.a 176 5.b even 2 1 inner
935.2.s.a 176 17.c even 4 1 inner
935.2.s.a 176 85.j even 4 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(935, [\chi])\).