Properties

Label 935.2.cq.a
Level $935$
Weight $2$
Character orbit 935.cq
Analytic conductor $7.466$
Analytic rank $0$
Dimension $2304$
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] = [935,2,Mod(6,935)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(935, base_ring=CyclotomicField(80))
 
chi = DirichletCharacter(H, H._module([0, 72, 75]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("935.6");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 935 = 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 935.cq (of order \(80\), degree \(32\), 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: \(2304\)
Relative dimension: \(72\) over \(\Q(\zeta_{80})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{80}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 2304 q+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 2304 q - 96 q^{12} - 80 q^{13} + 64 q^{14} + 32 q^{22} - 32 q^{23} - 240 q^{24} + 32 q^{26} - 144 q^{27} - 64 q^{31} + 64 q^{37} - 208 q^{38} - 240 q^{41} - 192 q^{42} - 64 q^{44} + 64 q^{49} - 32 q^{55} + 128 q^{59} + 128 q^{60} - 240 q^{63} - 848 q^{66} - 384 q^{69} - 384 q^{77} + 128 q^{81} - 80 q^{83} + 64 q^{86} - 128 q^{88} - 144 q^{91} + 128 q^{93} - 960 q^{94} - 160 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
6.1 −2.75247 0.216624i 2.06942 + 0.954014i 5.55378 + 0.879632i 0.619094 + 0.785317i −5.48934 3.07418i 1.32001 3.57803i −9.72667 2.33517i 1.42400 + 1.66729i −1.53392 2.29567i
6.2 −2.74161 0.215769i −2.38115 1.09773i 5.49447 + 0.870239i 0.619094 + 0.785317i 6.29133 + 3.52331i −0.698491 + 1.89334i −9.52771 2.28740i 2.51654 + 2.94649i −1.52786 2.28661i
6.3 −2.71024 0.213300i −0.0605571 0.0279172i 5.32452 + 0.843321i −0.619094 0.785317i 0.158169 + 0.0885791i −1.76341 + 4.77993i −8.96383 2.15202i −1.94546 2.27784i 1.51038 + 2.26045i
6.4 −2.58467 0.203418i 1.02211 + 0.471199i 4.66379 + 0.738671i −0.619094 0.785317i −2.54597 1.42581i 1.33454 3.61742i −6.86205 1.64743i −1.12566 1.31798i 1.44041 + 2.15572i
6.5 −2.44267 0.192243i 2.80452 + 1.29290i 3.95432 + 0.626303i 0.619094 + 0.785317i −6.60198 3.69729i −1.30609 + 3.54031i −4.77366 1.14605i 4.24540 + 4.97073i −1.36127 2.03729i
6.6 −2.38548 0.187741i 1.96792 + 0.907224i 3.67989 + 0.582837i −0.619094 0.785317i −4.52411 2.53362i −0.170398 + 0.461884i −4.01540 0.964011i 1.10131 + 1.28947i 1.32940 + 1.98959i
6.7 −2.34874 0.184849i −0.633787 0.292180i 3.50701 + 0.555456i −0.619094 0.785317i 1.43459 + 0.803408i 0.260599 0.706386i −3.55256 0.852895i −1.63203 1.91086i 1.30892 + 1.95894i
6.8 −2.34721 0.184730i 2.55658 + 1.17860i 3.49991 + 0.554332i −0.619094 0.785317i −5.78311 3.23870i 0.286675 0.777066i −3.53381 0.848392i 3.19865 + 3.74514i 1.30807 + 1.95767i
6.9 −2.28388 0.179745i −1.59650 0.735999i 3.20841 + 0.508162i 0.619094 + 0.785317i 3.51393 + 1.96789i −0.172703 + 0.468131i −2.78099 0.667657i 0.0587886 + 0.0688327i −1.27278 1.90485i
6.10 −2.27895 0.179357i −2.01672 0.929721i 3.18605 + 0.504620i −0.619094 0.785317i 4.42925 + 2.48050i 0.761722 2.06474i −2.72466 0.654133i 1.25444 + 1.46876i 1.27003 + 1.90073i
6.11 −2.23081 0.175569i 1.40132 + 0.646019i 2.97032 + 0.470452i 0.619094 + 0.785317i −3.01267 1.68717i −1.08832 + 2.95002i −2.19186 0.526218i −0.401978 0.470656i −1.24320 1.86059i
6.12 −2.12071 0.166904i −0.539372 0.248654i 2.49418 + 0.395040i 0.619094 + 0.785317i 1.10235 + 0.617346i 1.13191 3.06817i −1.08652 0.260851i −1.71925 2.01298i −1.18185 1.76876i
6.13 −1.87118 0.147265i 1.38650 + 0.639187i 1.50425 + 0.238249i 0.619094 + 0.785317i −2.50026 1.40022i 0.00615221 0.0166763i 0.870581 + 0.209008i −0.434513 0.508750i −1.04279 1.56064i
6.14 −1.83460 0.144386i −1.63655 0.754461i 1.36952 + 0.216911i 0.619094 + 0.785317i 2.89348 + 1.62043i −1.71992 + 4.66204i 1.09765 + 0.263522i 0.160748 + 0.188212i −1.02240 1.53013i
6.15 −1.80742 0.142247i −0.928595 0.428088i 1.27116 + 0.201333i 0.619094 + 0.785317i 1.61747 + 0.905826i 1.66255 4.50654i 1.25694 + 0.301766i −1.26932 1.48618i −1.00725 1.50746i
6.16 −1.79039 0.140907i −3.04749 1.40491i 1.21028 + 0.191689i 0.619094 + 0.785317i 5.25824 + 2.94476i 0.451335 1.22340i 1.35276 + 0.324768i 5.36507 + 6.28168i −0.997765 1.49326i
6.17 −1.74796 0.137567i −0.786637 0.362645i 1.06106 + 0.168056i −0.619094 0.785317i 1.32512 + 0.742104i −0.688996 + 1.86760i 1.57826 + 0.378907i −1.46106 1.71068i 0.974118 + 1.45787i
6.18 −1.70423 0.134126i −3.09649 1.42750i 0.911048 + 0.144296i −0.619094 0.785317i 5.08568 + 2.84812i −1.01619 + 2.75451i 1.79126 + 0.430043i 5.60215 + 6.55927i 0.949750 + 1.42140i
6.19 −1.66536 0.131067i 2.87013 + 1.32315i 0.780884 + 0.123680i −0.619094 0.785317i −4.60640 2.57971i −0.441550 + 1.19687i 1.96447 + 0.471627i 4.53859 + 5.31401i 0.928088 + 1.38898i
6.20 −1.52246 0.119820i 0.407330 + 0.187782i 0.328144 + 0.0519728i −0.619094 0.785317i −0.597642 0.334696i 1.14264 3.09726i 2.47658 + 0.594575i −1.81769 2.12824i 0.848448 + 1.26979i
See next 80 embeddings (of 2304 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 6.72
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
11.d odd 10 1 inner
17.e odd 16 1 inner
187.t even 80 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 935.2.cq.a 2304
11.d odd 10 1 inner 935.2.cq.a 2304
17.e odd 16 1 inner 935.2.cq.a 2304
187.t even 80 1 inner 935.2.cq.a 2304
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
935.2.cq.a 2304 1.a even 1 1 trivial
935.2.cq.a 2304 11.d odd 10 1 inner
935.2.cq.a 2304 17.e odd 16 1 inner
935.2.cq.a 2304 187.t even 80 1 inner

Hecke kernels

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