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Properties

Label 105.3.k.d
Level $105$
Weight $3$
Character orbit 105.k
Analytic conductor $2.861$
Analytic rank $0$
Dimension $32$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(62,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.62");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.k (of order \(4\), degree \(2\), 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: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q - 48 q^{15} - 24 q^{16} - 92 q^{18} - 60 q^{21} + 112 q^{22} - 72 q^{25} + 88 q^{28} - 108 q^{30} + 416 q^{36} + 72 q^{37} + 300 q^{42} - 328 q^{43} + 32 q^{46} + 148 q^{51} - 748 q^{57} - 392 q^{58}+ \cdots + 292 q^{93}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
62.1 −2.63482 + 2.63482i −2.54097 − 1.59482i − 9.88460i −4.15332 − 2.78387i 10.8971 − 2.49295i 2.39850 + 6.57626i 15.5049 + 15.5049i 3.91310 + 8.10479i 18.2783 − 3.60824i
62.2 −2.63482 + 2.63482i 2.54097 + 1.59482i − 9.88460i 4.15332 + 2.78387i −10.8971 + 2.49295i 6.57626 + 2.39850i 15.5049 + 15.5049i 3.91310 + 8.10479i −18.2783 + 3.60824i
62.3 −2.28094 + 2.28094i −1.07458 + 2.80094i − 6.40541i 1.80941 − 4.66112i −3.93772 − 8.83986i −6.22100 − 3.20922i 5.48661 + 5.48661i −6.69054 − 6.01969i 6.50460 + 14.7589i
62.4 −2.28094 + 2.28094i 1.07458 − 2.80094i − 6.40541i −1.80941 + 4.66112i 3.93772 + 8.83986i −3.20922 − 6.22100i 5.48661 + 5.48661i −6.69054 − 6.01969i −6.50460 − 14.7589i
62.5 −1.88692 + 1.88692i −2.65373 − 1.39918i − 3.12092i 4.96950 + 0.551428i 7.64751 − 2.36725i 2.09055 − 6.68054i −1.65875 − 1.65875i 5.08462 + 7.42608i −10.4175 + 8.33654i
62.6 −1.88692 + 1.88692i 2.65373 + 1.39918i − 3.12092i −4.96950 − 0.551428i −7.64751 + 2.36725i −6.68054 + 2.09055i −1.65875 − 1.65875i 5.08462 + 7.42608i 10.4175 − 8.33654i
62.7 −1.67168 + 1.67168i −2.55943 + 1.56503i − 1.58906i 0.529219 + 4.97191i 1.66231 − 6.89480i −1.73590 + 6.78135i −4.03033 − 4.03033i 4.10134 − 8.01118i −9.19616 − 7.42678i
62.8 −1.67168 + 1.67168i 2.55943 − 1.56503i − 1.58906i −0.529219 − 4.97191i −1.66231 + 6.89480i 6.78135 − 1.73590i −4.03033 − 4.03033i 4.10134 − 8.01118i 9.19616 + 7.42678i
62.9 1.67168 − 1.67168i −1.56503 + 2.55943i − 1.58906i 0.529219 + 4.97191i 1.66231 + 6.89480i 6.78135 − 1.73590i 4.03033 + 4.03033i −4.10134 − 8.01118i 9.19616 + 7.42678i
62.10 1.67168 − 1.67168i 1.56503 − 2.55943i − 1.58906i −0.529219 − 4.97191i −1.66231 − 6.89480i −1.73590 + 6.78135i 4.03033 + 4.03033i −4.10134 − 8.01118i −9.19616 − 7.42678i
62.11 1.88692 − 1.88692i −1.39918 − 2.65373i − 3.12092i −4.96950 − 0.551428i −7.64751 − 2.36725i 2.09055 − 6.68054i 1.65875 + 1.65875i −5.08462 + 7.42608i −10.4175 + 8.33654i
62.12 1.88692 − 1.88692i 1.39918 + 2.65373i − 3.12092i 4.96950 + 0.551428i 7.64751 + 2.36725i −6.68054 + 2.09055i 1.65875 + 1.65875i −5.08462 + 7.42608i 10.4175 − 8.33654i
62.13 2.28094 − 2.28094i −2.80094 + 1.07458i − 6.40541i 1.80941 − 4.66112i −3.93772 + 8.83986i −3.20922 − 6.22100i −5.48661 − 5.48661i 6.69054 − 6.01969i −6.50460 − 14.7589i
62.14 2.28094 − 2.28094i 2.80094 − 1.07458i − 6.40541i −1.80941 + 4.66112i 3.93772 − 8.83986i −6.22100 − 3.20922i −5.48661 − 5.48661i 6.69054 − 6.01969i 6.50460 + 14.7589i
62.15 2.63482 − 2.63482i −1.59482 − 2.54097i − 9.88460i 4.15332 + 2.78387i −10.8971 − 2.49295i 2.39850 + 6.57626i −15.5049 − 15.5049i −3.91310 + 8.10479i 18.2783 − 3.60824i
62.16 2.63482 − 2.63482i 1.59482 + 2.54097i − 9.88460i −4.15332 − 2.78387i 10.8971 + 2.49295i 6.57626 + 2.39850i −15.5049 − 15.5049i −3.91310 + 8.10479i −18.2783 + 3.60824i
83.1 −2.63482 − 2.63482i −2.54097 + 1.59482i 9.88460i −4.15332 + 2.78387i 10.8971 + 2.49295i 2.39850 − 6.57626i 15.5049 − 15.5049i 3.91310 − 8.10479i 18.2783 + 3.60824i
83.2 −2.63482 − 2.63482i 2.54097 − 1.59482i 9.88460i 4.15332 − 2.78387i −10.8971 − 2.49295i 6.57626 − 2.39850i 15.5049 − 15.5049i 3.91310 − 8.10479i −18.2783 − 3.60824i
83.3 −2.28094 − 2.28094i −1.07458 − 2.80094i 6.40541i 1.80941 + 4.66112i −3.93772 + 8.83986i −6.22100 + 3.20922i 5.48661 − 5.48661i −6.69054 + 6.01969i 6.50460 − 14.7589i
83.4 −2.28094 − 2.28094i 1.07458 + 2.80094i 6.40541i −1.80941 − 4.66112i 3.93772 − 8.83986i −3.20922 + 6.22100i 5.48661 − 5.48661i −6.69054 + 6.01969i −6.50460 + 14.7589i
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 62.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
3.b odd 2 1 inner
5.c odd 4 1 inner
7.b odd 2 1 inner
15.e even 4 1 inner
21.c even 2 1 inner
35.f even 4 1 inner
105.k odd 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.3.k.d ✓ 32
3.b odd 2 1 inner 105.3.k.d ✓ 32
5.c odd 4 1 inner 105.3.k.d ✓ 32
7.b odd 2 1 inner 105.3.k.d ✓ 32
15.e even 4 1 inner 105.3.k.d ✓ 32
21.c even 2 1 inner 105.3.k.d ✓ 32
35.f even 4 1 inner 105.3.k.d ✓ 32
105.k odd 4 1 inner 105.3.k.d ✓ 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.k.d ✓ 32 1.a even 1 1 trivial
105.3.k.d ✓ 32 3.b odd 2 1 inner
105.3.k.d ✓ 32 5.c odd 4 1 inner
105.3.k.d ✓ 32 7.b odd 2 1 inner
105.3.k.d ✓ 32 15.e even 4 1 inner
105.3.k.d ✓ 32 21.c even 2 1 inner
105.3.k.d ✓ 32 35.f even 4 1 inner
105.3.k.d ✓ 32 105.k odd 4 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(105, [\chi])\):

\( T_{2}^{16} + 383T_{2}^{12} + 47127T_{2}^{8} + 2187309T_{2}^{4} + 33062500 \) Copy content Toggle raw display
\( T_{11}^{8} + 497T_{11}^{6} + 63614T_{11}^{4} + 2343020T_{11}^{2} + 25047000 \) Copy content Toggle raw display
\( T_{13}^{16} + 66241T_{13}^{12} + 288088400T_{13}^{8} + 17091165504T_{13}^{4} + 253806379264 \) Copy content Toggle raw display