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Properties

Label 465.2.w.c
Level $465$
Weight $2$
Character orbit 465.w
Analytic conductor $3.713$
Analytic rank $0$
Dimension $224$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [465,2,Mod(29,465)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(465, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("465.29");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 465.w (of order \(10\), 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: \(3.71304369399\)
Analytic rank: \(0\)
Dimension: \(224\)
Relative dimension: \(56\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 224 q - 52 q^{4} - 14 q^{9} - 2 q^{10} - 15 q^{15} - 76 q^{16} + 32 q^{19} - 10 q^{21} + 90 q^{24} - 80 q^{25} + 56 q^{31} - 40 q^{34} + 68 q^{36} + 2 q^{39} - 74 q^{40} - 42 q^{45} - 40 q^{46} + 8 q^{49}+ \cdots - 90 q^{96}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
29.1 −2.17476 − 1.58006i −1.39076 + 1.03236i 1.61497 + 4.97038i 1.84413 + 1.26459i 4.65577 − 0.0476579i −2.62331 + 0.852364i 2.67993 − 8.24797i 0.868451 − 2.87155i −2.01243 − 5.66400i
29.2 −2.17476 − 1.58006i 1.41161 − 1.00368i 1.61497 + 4.97038i 1.84413 − 1.26459i −4.65577 − 0.0476579i 2.62331 − 0.852364i 2.67993 − 8.24797i 0.985262 − 2.83359i −6.00866 − 0.163662i
29.3 −2.13783 − 1.55322i −0.825661 + 1.52259i 1.53977 + 4.73893i −1.91718 − 1.15084i 4.13004 − 1.97260i 2.83245 − 0.920319i 2.43569 − 7.49628i −1.63657 − 2.51429i 2.31108 + 5.43810i
29.4 −2.13783 − 1.55322i 1.70321 − 0.314743i 1.53977 + 4.73893i −1.91718 + 1.15084i −4.13004 − 1.97260i −2.83245 + 0.920319i 2.43569 − 7.49628i 2.80187 − 1.07215i 5.88610 + 0.517500i
29.5 −1.93988 − 1.40940i 0.843084 + 1.51301i 1.15867 + 3.56602i 0.953695 − 2.02249i 0.496966 − 4.12330i −3.08879 + 1.00361i 1.29635 − 3.98976i −1.57842 + 2.55119i −4.70055 + 2.57924i
29.6 −1.93988 − 1.40940i 1.17843 + 1.26937i 1.15867 + 3.56602i 0.953695 + 2.02249i −0.496966 − 4.12330i 3.08879 − 1.00361i 1.29635 − 3.98976i −0.222587 + 2.99173i 1.00045 − 5.26752i
29.7 −1.80416 − 1.31080i −1.70077 − 0.327670i 0.918771 + 2.82769i 0.118368 − 2.23293i 2.63896 + 2.82055i 0.687565 − 0.223404i 0.670664 − 2.06409i 2.78527 + 1.11458i −3.14049 + 3.87342i
29.8 −1.80416 − 1.31080i 0.213936 − 1.71879i 0.918771 + 2.82769i 0.118368 + 2.23293i −2.63896 + 2.82055i −0.687565 + 0.223404i 0.670664 − 2.06409i −2.90846 − 0.735420i 2.71338 − 4.18373i
29.9 −1.67717 − 1.21854i −1.66147 − 0.489400i 0.710043 + 2.18529i −1.68652 + 1.46821i 2.19022 + 2.84538i 2.98458 − 0.969747i 0.190744 − 0.587051i 2.52098 + 1.62625i 4.61766 − 0.407353i
29.10 −1.67717 − 1.21854i 0.0479758 − 1.73139i 0.710043 + 2.18529i −1.68652 − 1.46821i −2.19022 + 2.84538i −2.98458 + 0.969747i 0.190744 − 0.587051i −2.99540 − 0.166129i 1.03952 + 4.51754i
29.11 −1.34617 − 0.978049i 0.106881 + 1.72875i 0.237556 + 0.731123i −2.22111 − 0.258232i 1.54692 − 2.43172i −1.69392 + 0.550387i −0.633098 + 1.94848i −2.97715 + 0.369541i 2.73742 + 2.51997i
29.12 −1.34617 − 0.978049i 1.61111 + 0.635863i 0.237556 + 0.731123i −2.22111 + 0.258232i −1.54692 − 2.43172i 1.69392 − 0.550387i −0.633098 + 1.94848i 2.19136 + 2.04889i 3.24255 + 1.82473i
29.13 −1.34382 − 0.976344i −1.21881 + 1.23065i 0.234577 + 0.721954i −0.451941 + 2.18992i 2.83941 − 0.463789i −0.178840 + 0.0581085i −0.636943 + 1.96031i −0.0289842 − 2.99986i 2.74544 − 2.50161i
29.14 −1.34382 − 0.976344i 1.54705 − 0.778870i 0.234577 + 0.721954i −0.451941 − 2.18992i −2.83941 − 0.463789i 0.178840 − 0.0581085i −0.636943 + 1.96031i 1.78672 − 2.40990i −1.53079 + 3.38411i
29.15 −1.32909 − 0.965643i −0.519304 + 1.65237i 0.215989 + 0.664746i 2.05145 − 0.889701i 2.28580 − 1.69469i 4.85968 − 1.57900i −0.660500 + 2.03281i −2.46065 − 1.71616i −3.58570 − 0.798468i
29.16 −1.32909 − 0.965643i 1.73197 + 0.0167223i 0.215989 + 0.664746i 2.05145 + 0.889701i −2.28580 − 1.69469i −4.85968 + 1.57900i −0.660500 + 2.03281i 2.99944 + 0.0579251i −1.86743 − 3.16346i
29.17 −0.947381 − 0.688313i −1.72341 + 0.172753i −0.194277 − 0.597924i 2.20604 − 0.365200i 1.75164 + 1.02259i −1.47965 + 0.480767i −0.951239 + 2.92761i 2.94031 − 0.595450i −2.34134 − 1.17246i
29.18 −0.947381 − 0.688313i 0.696862 − 1.58568i −0.194277 − 0.597924i 2.20604 + 0.365200i −1.75164 + 1.02259i 1.47965 − 0.480767i −0.951239 + 2.92761i −2.02877 − 2.21000i −1.83859 − 1.86443i
29.19 −0.871945 − 0.633505i 0.564951 + 1.63732i −0.259075 − 0.797351i 0.965755 + 2.01676i 0.544647 − 1.78555i −2.06777 + 0.671858i −0.945333 + 2.90944i −2.36166 + 1.85002i 0.435542 − 2.37031i
29.20 −0.871945 − 0.633505i 1.38261 + 1.04326i −0.259075 − 0.797351i 0.965755 − 2.01676i −0.544647 − 1.78555i 2.06777 − 0.671858i −0.945333 + 2.90944i 0.823212 + 2.88484i −2.11971 + 1.14669i
See next 80 embeddings (of 224 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 29.56
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.b even 2 1 inner
15.d odd 2 1 inner
31.f odd 10 1 inner
93.k even 10 1 inner
155.m odd 10 1 inner
465.w even 10 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 465.2.w.c ✓ 224
3.b odd 2 1 inner 465.2.w.c ✓ 224
5.b even 2 1 inner 465.2.w.c ✓ 224
15.d odd 2 1 inner 465.2.w.c ✓ 224
31.f odd 10 1 inner 465.2.w.c ✓ 224
93.k even 10 1 inner 465.2.w.c ✓ 224
155.m odd 10 1 inner 465.2.w.c ✓ 224
465.w even 10 1 inner 465.2.w.c ✓ 224
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
465.2.w.c ✓ 224 1.a even 1 1 trivial
465.2.w.c ✓ 224 3.b odd 2 1 inner
465.2.w.c ✓ 224 5.b even 2 1 inner
465.2.w.c ✓ 224 15.d odd 2 1 inner
465.2.w.c ✓ 224 31.f odd 10 1 inner
465.2.w.c ✓ 224 93.k even 10 1 inner
465.2.w.c ✓ 224 155.m odd 10 1 inner
465.2.w.c ✓ 224 465.w even 10 1 inner

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{112} + 41 T_{2}^{110} + 945 T_{2}^{108} + 16187 T_{2}^{106} + 229461 T_{2}^{104} + 2805068 T_{2}^{102} + \cdots + 390625 \) acting on \(S_{2}^{\mathrm{new}}(465, [\chi])\). Copy content Toggle raw display