Properties

Label 165.3.e.a
Level $165$
Weight $3$
Character orbit 165.e
Analytic conductor $4.496$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,3,Mod(56,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.56");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 165.e (of order \(2\), degree \(1\), 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: \(4.49592436194\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 28 q - 60 q^{4} - 4 q^{6} + 24 q^{7} - 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q - 60 q^{4} - 4 q^{6} + 24 q^{7} - 16 q^{9} - 20 q^{10} + 40 q^{12} - 64 q^{13} + 172 q^{16} + 16 q^{18} + 56 q^{19} + 56 q^{21} - 140 q^{24} - 140 q^{25} - 96 q^{27} - 128 q^{28} - 40 q^{30} + 80 q^{31} - 32 q^{34} + 208 q^{36} + 72 q^{37} + 232 q^{39} - 60 q^{40} + 224 q^{42} - 360 q^{43} - 80 q^{45} + 264 q^{46} - 456 q^{48} + 332 q^{49} - 232 q^{51} + 488 q^{52} + 36 q^{54} - 16 q^{57} - 408 q^{58} - 360 q^{61} - 32 q^{63} - 300 q^{64} + 220 q^{66} - 16 q^{67} + 384 q^{69} + 240 q^{70} - 120 q^{72} + 464 q^{73} - 152 q^{76} + 16 q^{78} + 136 q^{79} + 48 q^{81} - 840 q^{82} - 392 q^{84} + 160 q^{85} + 32 q^{87} + 180 q^{90} - 32 q^{91} - 96 q^{93} + 520 q^{94} + 44 q^{96} - 136 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
56.1 3.91781i −2.98166 + 0.331216i −11.3492 2.23607i 1.29764 + 11.6816i 1.80014 28.7928i 8.78059 1.97515i 8.76048
56.2 3.60682i 0.198737 + 2.99341i −9.00917 2.23607i 10.7967 0.716809i −9.02564 18.0672i −8.92101 + 1.18980i −8.06510
56.3 3.53441i −0.569949 2.94536i −8.49206 2.23607i −10.4101 + 2.01443i 0.0644394 15.8768i −8.35032 + 3.35741i −7.90318
56.4 3.30976i 1.46910 + 2.61567i −6.95453 2.23607i 8.65725 4.86238i 13.2372 9.77881i −4.68347 + 7.68538i 7.40086
56.5 3.05080i 2.70308 1.30130i −5.30736 2.23607i −3.97000 8.24653i 8.10434 3.98849i 5.61324 7.03502i −6.82179
56.6 2.73142i −1.09395 2.79343i −3.46068 2.23607i −7.63005 + 2.98805i −7.40152 1.47311i −6.60653 + 6.11177i 6.10765
56.7 2.57595i −2.05309 + 2.18743i −2.63553 2.23607i 5.63470 + 5.28865i 8.07832 3.51481i −0.569667 8.98195i −5.76000
56.8 1.85137i 1.43262 2.63583i 0.572437 2.23607i −4.87989 2.65231i 5.32431 8.46526i −4.89519 7.55229i 4.13978
56.9 1.66350i 2.17775 + 2.06335i 1.23276 2.23607i 3.43238 3.62269i 1.72484 8.70471i 0.485191 + 8.98691i −3.71971
56.10 1.38379i −2.86837 0.878884i 2.08514 2.23607i −1.21619 + 3.96921i −9.90208 8.42053i 7.45513 + 5.04193i −3.09424
56.11 1.32767i 1.89125 2.32877i 2.23729 2.23607i −3.09184 2.51095i −13.0586 8.28106i −1.84637 8.80857i −2.96876
56.12 0.880395i 2.93851 + 0.604290i 3.22491 2.23607i 0.532014 2.58705i 0.198790 6.36077i 8.26967 + 3.55142i 1.96862
56.13 0.278106i −0.532850 2.95230i 3.92266 2.23607i −0.821052 + 0.148189i 9.87562 2.20334i −8.43214 + 3.14626i −0.621864
56.14 0.258153i −2.71117 1.28435i 3.93336 2.23607i −0.331558 + 0.699896i 2.97982 2.04802i 5.70089 + 6.96418i 0.577247
56.15 0.258153i −2.71117 + 1.28435i 3.93336 2.23607i −0.331558 0.699896i 2.97982 2.04802i 5.70089 6.96418i 0.577247
56.16 0.278106i −0.532850 + 2.95230i 3.92266 2.23607i −0.821052 0.148189i 9.87562 2.20334i −8.43214 3.14626i −0.621864
56.17 0.880395i 2.93851 0.604290i 3.22491 2.23607i 0.532014 + 2.58705i 0.198790 6.36077i 8.26967 3.55142i 1.96862
56.18 1.32767i 1.89125 + 2.32877i 2.23729 2.23607i −3.09184 + 2.51095i −13.0586 8.28106i −1.84637 + 8.80857i −2.96876
56.19 1.38379i −2.86837 + 0.878884i 2.08514 2.23607i −1.21619 3.96921i −9.90208 8.42053i 7.45513 5.04193i −3.09424
56.20 1.66350i 2.17775 2.06335i 1.23276 2.23607i 3.43238 + 3.62269i 1.72484 8.70471i 0.485191 8.98691i −3.71971
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 56.28
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 165.3.e.a 28
3.b odd 2 1 inner 165.3.e.a 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
165.3.e.a 28 1.a even 1 1 trivial
165.3.e.a 28 3.b odd 2 1 inner

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(165, [\chi])\).