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Properties

Label 184.2.p.a
Level $184$
Weight $2$
Character orbit 184.p
Analytic conductor $1.469$
Analytic rank $0$
Dimension $220$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [184,2,Mod(13,184)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(184, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 11, 14]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("184.13");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 184 = 2^{3} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 184.p (of order \(22\), degree \(10\), 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: \(1.46924739719\)
Analytic rank: \(0\)
Dimension: \(220\)
Relative dimension: \(22\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 220 q - 11 q^{2} - 11 q^{4} - 14 q^{6} - 22 q^{7} - 14 q^{8} - 9 q^{10} - 12 q^{12} - 3 q^{14} - 22 q^{15} + 5 q^{16} - 18 q^{17} - 4 q^{18} - 27 q^{20} - 42 q^{22} - 16 q^{23} - 22 q^{24} - 4 q^{25} - 16 q^{26}+ \cdots + 109 q^{98}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
13.1 −1.41340 + 0.0480184i 1.16787 − 1.81725i 1.99539 − 0.135738i −0.362199 − 0.165411i −1.56341 + 2.62457i 4.46721 + 1.31169i −2.81376 + 0.287667i −0.692209 − 1.51573i 0.519873 + 0.216399i
13.2 −1.38759 − 0.273122i 0.00705328 − 0.0109751i 1.85081 + 0.757962i 3.12173 + 1.42565i −0.0127846 + 0.0133026i −2.69654 − 0.791776i −2.36115 − 1.55724i 1.24617 + 2.72874i −3.94231 − 2.83083i
13.3 −1.38192 + 0.300513i −1.16603 + 1.81437i 1.81938 − 0.830568i −1.93519 − 0.883774i 1.06611 − 2.85772i −1.41177 − 0.414532i −2.26464 + 1.69452i −0.686086 − 1.50232i 2.93986 + 0.639750i
13.4 −1.15854 − 0.811046i −0.429687 + 0.668606i 0.684409 + 1.87925i −2.58320 − 1.17971i 1.04008 − 0.426108i 2.06173 + 0.605378i 0.731246 − 2.73227i 0.983842 + 2.15431i 2.03593 + 3.46182i
13.5 −1.04742 + 0.950221i −0.510908 + 0.794988i 0.194160 − 1.99055i 1.50887 + 0.689079i −0.220282 − 1.31816i 0.462185 + 0.135710i 1.68810 + 2.26943i 0.875266 + 1.91656i −2.23519 + 0.712010i
13.6 −1.00874 − 0.991179i 1.73543 − 2.70038i 0.0351273 + 1.99969i −0.678074 − 0.309666i −4.42717 + 1.00387i −2.93526 − 0.861871i 1.94662 − 2.05199i −3.03410 − 6.64376i 0.377068 + 0.984467i
13.7 −0.859833 + 1.12280i 1.14322 − 1.77888i −0.521373 − 1.93085i −2.56635 − 1.17201i 1.01436 + 2.81315i −2.17612 − 0.638967i 2.61625 + 1.07481i −0.611228 − 1.33840i 3.52257 − 1.87377i
13.8 −0.837531 − 1.13954i −1.73543 + 2.70038i −0.597083 + 1.90879i 0.678074 + 0.309666i 4.53066 − 0.284070i −2.93526 − 0.861871i 2.67521 − 0.918277i −3.03410 − 6.64376i −0.215033 − 1.03204i
13.9 −0.637914 − 1.26217i 0.429687 − 0.668606i −1.18613 + 1.61031i 2.58320 + 1.17971i −1.11800 − 0.115824i 2.06173 + 0.605378i 2.78913 + 0.469860i 0.983842 + 2.15431i −0.158870 − 4.01298i
13.10 −0.329997 + 1.37517i 0.583943 − 0.908634i −1.78220 − 0.907607i 0.293263 + 0.133929i 1.05683 + 1.10287i 1.64760 + 0.483779i 1.83624 − 2.15133i 0.761620 + 1.66772i −0.280951 + 0.359091i
13.11 −0.0728674 − 1.41234i −0.00705328 + 0.0109751i −1.98938 + 0.205826i −3.12173 − 1.42565i 0.0160145 + 0.00916187i −2.69654 − 0.791776i 0.435657 + 2.79467i 1.24617 + 2.72874i −1.78602 + 4.51282i
13.12 0.248677 − 1.39218i −1.16787 + 1.81725i −1.87632 − 0.692406i 0.362199 + 0.165411i 2.23951 + 2.07779i 4.46721 + 1.31169i −1.43055 + 2.43999i −0.692209 − 1.51573i 0.320351 − 0.463111i
13.13 0.297466 + 1.38258i −1.35779 + 2.11277i −1.82303 + 0.822538i 3.81860 + 1.74390i −3.32496 − 1.24878i 1.23190 + 0.361720i −1.67951 − 2.27580i −1.37394 − 3.00851i −1.27516 + 5.79825i
13.14 0.304232 + 1.38110i −0.603355 + 0.938838i −1.81489 + 0.840351i −1.75955 − 0.803560i −1.48019 − 0.547670i −4.74970 − 1.39464i −1.71276 − 2.25088i 0.728865 + 1.59599i 0.574487 − 2.67459i
13.15 0.494121 − 1.32508i 1.16603 − 1.81437i −1.51169 − 1.30950i 1.93519 + 0.883774i −1.82804 − 2.44160i −1.41177 − 0.414532i −2.48216 + 1.35606i −0.686086 − 1.50232i 2.12729 − 2.12760i
13.16 0.500600 + 1.32265i 1.57562 − 2.45171i −1.49880 + 1.32424i 1.68414 + 0.769120i 4.03151 + 0.856663i 0.338518 + 0.0993980i −2.50180 − 1.31947i −2.28207 − 4.99704i −0.174195 + 2.61254i
13.17 1.08961 − 0.901524i 0.510908 − 0.794988i 0.374509 − 1.96462i −1.50887 − 0.689079i −0.160010 − 1.32682i 0.462185 + 0.135710i −1.36309 − 2.47831i 0.875266 + 1.91656i −2.26531 + 0.609456i
13.18 1.23374 − 0.691290i −1.14322 + 1.77888i 1.04424 − 1.70575i 2.56635 + 1.17201i −0.180712 + 2.98498i −2.17612 − 0.638967i 0.109152 − 2.82632i −0.611228 − 1.33840i 3.97641 − 0.328131i
13.19 1.23794 + 0.683738i −1.57562 + 2.45171i 1.06501 + 1.69286i −1.68414 − 0.769120i −3.62686 + 1.95777i 0.338518 + 0.0993980i 0.160947 + 2.82384i −2.28207 − 4.99704i −1.55899 − 2.10363i
13.20 1.32375 + 0.497687i 0.603355 − 0.938838i 1.50462 + 1.31762i 1.75955 + 0.803560i 1.26594 − 0.942503i −4.74970 − 1.39464i 1.33597 + 2.49303i 0.728865 + 1.59599i 1.92928 + 1.93942i
See next 80 embeddings (of 220 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 13.22
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
8.b even 2 1 inner
23.c even 11 1 inner
184.p even 22 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 184.2.p.a ✓ 220
4.b odd 2 1 736.2.x.a 220
8.b even 2 1 inner 184.2.p.a ✓ 220
8.d odd 2 1 736.2.x.a 220
23.c even 11 1 inner 184.2.p.a ✓ 220
92.g odd 22 1 736.2.x.a 220
184.k odd 22 1 736.2.x.a 220
184.p even 22 1 inner 184.2.p.a ✓ 220
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
184.2.p.a ✓ 220 1.a even 1 1 trivial
184.2.p.a ✓ 220 8.b even 2 1 inner
184.2.p.a ✓ 220 23.c even 11 1 inner
184.2.p.a ✓ 220 184.p even 22 1 inner
736.2.x.a 220 4.b odd 2 1
736.2.x.a 220 8.d odd 2 1
736.2.x.a 220 92.g odd 22 1
736.2.x.a 220 184.k odd 22 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(184, [\chi])\).