↑

Properties

Label 185.2.p.a
Level $185$
Weight $2$
Character orbit 185.p
Analytic conductor $1.477$
Analytic rank $0$
Dimension $68$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [185,2,Mod(82,185)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(185, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("185.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 185 = 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 185.p (of order \(12\), degree \(4\), 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: \(1.47723243739\)
Analytic rank: \(0\)
Dimension: \(68\)
Relative dimension: \(17\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 68 q - 4 q^{2} - 8 q^{3} - 30 q^{4} - 10 q^{5} - 8 q^{6} - 2 q^{7} + 12 q^{8} - 6 q^{10} + 14 q^{12} - 6 q^{13} - 8 q^{15} - 26 q^{16} + 12 q^{17} + 18 q^{18} + 4 q^{19} + 48 q^{20} - 12 q^{21} + 6 q^{22}+ \cdots + 32 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
82.1 −1.37559 − 2.38259i 0.692973 − 0.185681i −2.78450 + 4.82289i −0.638688 + 2.14291i −1.39565 − 1.39565i −1.87540 + 0.502511i 9.81895 −2.15234 + 1.24266i 5.98426 − 1.42604i
82.2 −1.21425 − 2.10315i 0.672498 − 0.180195i −1.94883 + 3.37547i 1.55471 − 1.60713i −1.19556 − 1.19556i 4.47423 − 1.19887i 4.60849 −2.17829 + 1.25764i −5.26786 − 1.31832i
82.3 −1.10225 − 1.90916i −3.05050 + 0.817378i −1.42993 + 2.47671i 1.99367 + 1.01257i 4.92293 + 4.92293i −0.147229 + 0.0394498i 1.89556 6.03934 − 3.48681i −0.264372 − 4.92234i
82.4 −0.993536 − 1.72086i 2.35179 − 0.630160i −0.974229 + 1.68741i −1.49861 − 1.65957i −3.42100 − 3.42100i −2.62941 + 0.704548i −0.102418 2.53574 − 1.46401i −1.36695 + 4.22774i
82.5 −0.892058 − 1.54509i −1.76128 + 0.471934i −0.591534 + 1.02457i −1.38296 − 1.75711i 2.30034 + 2.30034i 0.500724 − 0.134169i −1.45750 0.281310 − 0.162414i −1.48121 + 3.70424i
82.6 −0.723320 − 1.25283i −0.791482 + 0.212077i −0.0463849 + 0.0803411i −1.65059 + 1.50849i 0.838191 + 0.838191i −1.58905 + 0.425785i −2.75908 −2.01661 + 1.16429i 3.08379 + 0.976784i
82.7 −0.412077 − 0.713738i 1.77336 − 0.475172i 0.660386 − 1.14382i 1.99238 − 1.01510i −1.06991 − 1.06991i −1.19739 + 0.320840i −2.73682 0.320958 − 0.185305i −1.54553 − 1.00374i
82.8 −0.354544 − 0.614089i −0.280512 + 0.0751630i 0.748597 − 1.29661i 1.19547 + 1.88967i 0.145611 + 0.145611i 3.64653 − 0.977086i −2.47982 −2.52504 + 1.45783i 0.736577 − 1.40410i
82.9 −0.122725 − 0.212566i −1.83492 + 0.491666i 0.969877 − 1.67988i 1.28977 − 1.82661i 0.329702 + 0.329702i −3.76446 + 1.00868i −0.967013 0.527123 − 0.304334i −0.546561 − 0.0499898i
82.10 −0.0797909 − 0.138202i 2.26850 − 0.607844i 0.987267 − 1.71000i −2.00255 + 0.994886i −0.265011 − 0.265011i 1.28763 − 0.345018i −0.634263 2.17856 − 1.25779i 0.297280 + 0.197373i
82.11 0.235037 + 0.407096i −3.12752 + 0.838017i 0.889515 − 1.54069i −2.22812 + 0.188382i −1.07624 − 1.07624i 3.61347 − 0.968227i 1.77643 6.48105 − 3.74183i −0.600381 − 0.862782i
82.12 0.506716 + 0.877658i 1.71192 − 0.458707i 0.486478 − 0.842604i 0.902808 + 2.04571i 1.27004 + 1.27004i −4.18129 + 1.12037i 3.01289 0.122169 − 0.0705344i −1.33797 + 1.82895i
82.13 0.560713 + 0.971183i 0.628874 − 0.168506i 0.371203 − 0.642942i −0.606686 − 2.15219i 0.516268 + 0.516268i 1.40791 − 0.377247i 3.07540 −2.23099 + 1.28806i 1.75000 − 1.79596i
82.14 0.643846 + 1.11517i −1.31376 + 0.352022i 0.170924 − 0.296050i 2.23601 − 0.0164393i −1.23843 − 1.23843i 1.71395 − 0.459253i 3.01558 −0.996020 + 0.575052i 1.45798 + 2.48295i
82.15 1.04034 + 1.80193i −1.09812 + 0.294240i −1.16463 + 2.01721i −1.05057 + 1.97391i −1.67262 − 1.67262i 0.0769563 − 0.0206204i −0.685107 −1.47879 + 0.853779i −4.64979 + 0.160500i
82.16 1.20502 + 2.08716i −2.76431 + 0.740695i −1.90415 + 3.29809i −0.404091 − 2.19925i −4.87700 − 4.87700i −3.19584 + 0.856324i −4.35808 4.49471 − 2.59502i 4.10325 − 3.49355i
82.17 1.21245 + 2.10002i 2.19044 − 0.586925i −1.94006 + 3.36028i −2.20194 − 0.389154i 3.88834 + 3.88834i 0.492639 − 0.132002i −4.55908 1.85545 − 1.07124i −1.85251 − 5.09596i
88.1 −1.37559 + 2.38259i 0.692973 + 0.185681i −2.78450 − 4.82289i −0.638688 − 2.14291i −1.39565 + 1.39565i −1.87540 − 0.502511i 9.81895 −2.15234 − 1.24266i 5.98426 + 1.42604i
88.2 −1.21425 + 2.10315i 0.672498 + 0.180195i −1.94883 − 3.37547i 1.55471 + 1.60713i −1.19556 + 1.19556i 4.47423 + 1.19887i 4.60849 −2.17829 − 1.25764i −5.26786 + 1.31832i
88.3 −1.10225 + 1.90916i −3.05050 − 0.817378i −1.42993 − 2.47671i 1.99367 − 1.01257i 4.92293 − 4.92293i −0.147229 − 0.0394498i 1.89556 6.03934 + 3.48681i −0.264372 + 4.92234i
See all 68 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 82.17
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
185.p even 12 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 185.2.p.a ✓ 68
5.b even 2 1 925.2.t.b 68
5.c odd 4 1 185.2.u.a yes 68
5.c odd 4 1 925.2.y.b 68
37.g odd 12 1 185.2.u.a yes 68
185.p even 12 1 inner 185.2.p.a ✓ 68
185.q odd 12 1 925.2.y.b 68
185.u even 12 1 925.2.t.b 68
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
185.2.p.a ✓ 68 1.a even 1 1 trivial
185.2.p.a ✓ 68 185.p even 12 1 inner
185.2.u.a yes 68 5.c odd 4 1
185.2.u.a yes 68 37.g odd 12 1
925.2.t.b 68 5.b even 2 1
925.2.t.b 68 185.u even 12 1
925.2.y.b 68 5.c odd 4 1
925.2.y.b 68 185.q odd 12 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(185, [\chi])\).