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Properties

Label 105.3.f.a
Level $105$
Weight $3$
Character orbit 105.f
Analytic conductor $2.861$
Analytic rank $0$
Dimension $24$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,3,Mod(29,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 105.f (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: \(2.86104277578\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 52 q^{4} - 22 q^{9} - 24 q^{10} + 26 q^{15} + 4 q^{16} + 72 q^{19} + 14 q^{21} - 156 q^{24} - 64 q^{25} - 32 q^{30} - 40 q^{31} - 144 q^{34} + 36 q^{36} + 62 q^{39} - 40 q^{40} + 120 q^{45} - 104 q^{46}+ \cdots + 582 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
29.1 −3.57140 2.50375 − 1.65264i 8.75491 −0.280149 + 4.99215i −8.94190 + 5.90225i 2.64575i −16.9817 3.53755 − 8.27561i 1.00052 − 17.8290i
29.2 −3.57140 2.50375 + 1.65264i 8.75491 −0.280149 − 4.99215i −8.94190 − 5.90225i − 2.64575i −16.9817 3.53755 + 8.27561i 1.00052 + 17.8290i
29.3 −3.21327 −1.93400 − 2.29339i 6.32511 4.77035 − 1.49792i 6.21446 + 7.36929i 2.64575i −7.47120 −1.51929 + 8.87084i −15.3284 + 4.81322i
29.4 −3.21327 −1.93400 + 2.29339i 6.32511 4.77035 + 1.49792i 6.21446 − 7.36929i − 2.64575i −7.47120 −1.51929 − 8.87084i −15.3284 − 4.81322i
29.5 −2.80814 0.0756962 − 2.99904i 3.88565 −4.04610 − 2.93753i −0.212566 + 8.42174i − 2.64575i 0.321110 −8.98854 − 0.454033i 11.3620 + 8.24901i
29.6 −2.80814 0.0756962 + 2.99904i 3.88565 −4.04610 + 2.93753i −0.212566 − 8.42174i 2.64575i 0.321110 −8.98854 + 0.454033i 11.3620 − 8.24901i
29.7 −1.87229 −2.98471 − 0.302541i −0.494516 −2.18081 + 4.49934i 5.58825 + 0.566446i − 2.64575i 8.41505 8.81694 + 1.80599i 4.08312 − 8.42408i
29.8 −1.87229 −2.98471 + 0.302541i −0.494516 −2.18081 − 4.49934i 5.58825 − 0.566446i 2.64575i 8.41505 8.81694 − 1.80599i 4.08312 + 8.42408i
29.9 −1.50770 2.08699 − 2.15510i −1.72685 4.79474 + 1.41790i −3.14656 + 3.24924i − 2.64575i 8.63435 −0.288904 − 8.99536i −7.22902 − 2.13777i
29.10 −1.50770 2.08699 + 2.15510i −1.72685 4.79474 − 1.41790i −3.14656 − 3.24924i 2.64575i 8.63435 −0.288904 + 8.99536i −7.22902 + 2.13777i
29.11 −0.505667 −0.985457 − 2.83353i −3.74430 −0.221081 + 4.99511i 0.498313 + 1.43282i 2.64575i 3.91604 −7.05775 + 5.58464i 0.111793 − 2.52586i
29.12 −0.505667 −0.985457 + 2.83353i −3.74430 −0.221081 − 4.99511i 0.498313 − 1.43282i − 2.64575i 3.91604 −7.05775 − 5.58464i 0.111793 + 2.52586i
29.13 0.505667 0.985457 − 2.83353i −3.74430 0.221081 − 4.99511i 0.498313 − 1.43282i 2.64575i −3.91604 −7.05775 − 5.58464i 0.111793 − 2.52586i
29.14 0.505667 0.985457 + 2.83353i −3.74430 0.221081 + 4.99511i 0.498313 + 1.43282i − 2.64575i −3.91604 −7.05775 + 5.58464i 0.111793 + 2.52586i
29.15 1.50770 −2.08699 − 2.15510i −1.72685 −4.79474 − 1.41790i −3.14656 − 3.24924i − 2.64575i −8.63435 −0.288904 + 8.99536i −7.22902 − 2.13777i
29.16 1.50770 −2.08699 + 2.15510i −1.72685 −4.79474 + 1.41790i −3.14656 + 3.24924i 2.64575i −8.63435 −0.288904 − 8.99536i −7.22902 + 2.13777i
29.17 1.87229 2.98471 − 0.302541i −0.494516 2.18081 − 4.49934i 5.58825 − 0.566446i − 2.64575i −8.41505 8.81694 − 1.80599i 4.08312 − 8.42408i
29.18 1.87229 2.98471 + 0.302541i −0.494516 2.18081 + 4.49934i 5.58825 + 0.566446i 2.64575i −8.41505 8.81694 + 1.80599i 4.08312 + 8.42408i
29.19 2.80814 −0.0756962 − 2.99904i 3.88565 4.04610 + 2.93753i −0.212566 − 8.42174i − 2.64575i −0.321110 −8.98854 + 0.454033i 11.3620 + 8.24901i
29.20 2.80814 −0.0756962 + 2.99904i 3.88565 4.04610 − 2.93753i −0.212566 + 8.42174i 2.64575i −0.321110 −8.98854 − 0.454033i 11.3620 − 8.24901i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 29.24
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

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.3.f.a ✓ 24
3.b odd 2 1 inner 105.3.f.a ✓ 24
5.b even 2 1 inner 105.3.f.a ✓ 24
5.c odd 4 2 525.3.c.e 24
15.d odd 2 1 inner 105.3.f.a ✓ 24
15.e even 4 2 525.3.c.e 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.3.f.a ✓ 24 1.a even 1 1 trivial
105.3.f.a ✓ 24 3.b odd 2 1 inner
105.3.f.a ✓ 24 5.b even 2 1 inner
105.3.f.a ✓ 24 15.d odd 2 1 inner
525.3.c.e 24 5.c odd 4 2
525.3.c.e 24 15.e even 4 2

Hecke kernels

This newform subspace is the entire newspace \(S_{3}^{\mathrm{new}}(105, [\chi])\).