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Properties

Label 105.2.p.a
Level $105$
Weight $2$
Character orbit 105.p
Analytic conductor $0.838$
Analytic rank $0$
Dimension $24$
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,2,Mod(59,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.59");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.p (of order \(6\), 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: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 6 q^{21} + 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} - 72 q^{40} - 18 q^{45} + 36 q^{46} - 12 q^{49} - 12 q^{51} - 36 q^{54} + 12 q^{60}+ \cdots - 48 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
59.1 −1.25399 − 2.17197i 0.0401158 + 1.73159i −2.14497 + 3.71520i 0.00874528 + 2.23605i 3.71065 − 2.25852i 1.65993 + 2.06025i 5.74313 −2.99678 + 0.138928i 4.84567 − 2.82298i
59.2 −1.25399 − 2.17197i 1.51966 − 0.831052i −2.14497 + 3.71520i −1.93210 − 1.12560i −3.71065 − 2.25852i −1.65993 − 2.06025i 5.74313 1.61871 − 2.52582i −0.0219329 + 5.60796i
59.3 −0.757344 − 1.31176i −1.24551 + 1.20362i −0.147140 + 0.254854i 1.42830 − 1.72046i 2.52214 + 0.722254i −0.0753638 − 2.64468i −2.58363 0.102593 − 2.99825i −3.33853 − 0.570605i
59.4 −0.757344 − 1.31176i 0.419611 − 1.68045i −0.147140 + 0.254854i 2.20411 − 0.376714i −2.52214 + 0.722254i 0.0753638 + 2.64468i −2.58363 −2.64785 − 1.41027i −2.16343 − 2.60595i
59.5 −0.322403 − 0.558418i 1.15761 + 1.28838i 0.792113 − 1.37198i −1.60193 − 1.56008i 0.346239 − 1.06181i 2.64366 + 0.105130i −2.31113 −0.319861 + 2.98290i −0.354709 + 1.39752i
59.6 −0.322403 − 0.558418i 1.69458 + 0.358331i 0.792113 − 1.37198i 0.550103 + 2.16735i −0.346239 − 1.06181i −2.64366 − 0.105130i −2.31113 2.74320 + 1.21444i 1.03293 − 1.00595i
59.7 0.322403 + 0.558418i −1.69458 − 0.358331i 0.792113 − 1.37198i 1.60193 + 1.56008i −0.346239 − 1.06181i 2.64366 + 0.105130i 2.31113 2.74320 + 1.21444i −0.354709 + 1.39752i
59.8 0.322403 + 0.558418i −1.15761 − 1.28838i 0.792113 − 1.37198i −0.550103 − 2.16735i 0.346239 − 1.06181i −2.64366 − 0.105130i 2.31113 −0.319861 + 2.98290i 1.03293 − 1.00595i
59.9 0.757344 + 1.31176i −0.419611 + 1.68045i −0.147140 + 0.254854i −1.42830 + 1.72046i −2.52214 + 0.722254i −0.0753638 − 2.64468i 2.58363 −2.64785 − 1.41027i −3.33853 − 0.570605i
59.10 0.757344 + 1.31176i 1.24551 − 1.20362i −0.147140 + 0.254854i −2.20411 + 0.376714i 2.52214 + 0.722254i 0.0753638 + 2.64468i 2.58363 0.102593 − 2.99825i −2.16343 − 2.60595i
59.11 1.25399 + 2.17197i −1.51966 + 0.831052i −2.14497 + 3.71520i −0.00874528 − 2.23605i −3.71065 − 2.25852i 1.65993 + 2.06025i −5.74313 1.61871 − 2.52582i 4.84567 − 2.82298i
59.12 1.25399 + 2.17197i −0.0401158 − 1.73159i −2.14497 + 3.71520i 1.93210 + 1.12560i 3.71065 − 2.25852i −1.65993 − 2.06025i −5.74313 −2.99678 + 0.138928i −0.0219329 + 5.60796i
89.1 −1.25399 + 2.17197i 0.0401158 − 1.73159i −2.14497 − 3.71520i 0.00874528 − 2.23605i 3.71065 + 2.25852i 1.65993 − 2.06025i 5.74313 −2.99678 − 0.138928i 4.84567 + 2.82298i
89.2 −1.25399 + 2.17197i 1.51966 + 0.831052i −2.14497 − 3.71520i −1.93210 + 1.12560i −3.71065 + 2.25852i −1.65993 + 2.06025i 5.74313 1.61871 + 2.52582i −0.0219329 − 5.60796i
89.3 −0.757344 + 1.31176i −1.24551 − 1.20362i −0.147140 − 0.254854i 1.42830 + 1.72046i 2.52214 − 0.722254i −0.0753638 + 2.64468i −2.58363 0.102593 + 2.99825i −3.33853 + 0.570605i
89.4 −0.757344 + 1.31176i 0.419611 + 1.68045i −0.147140 − 0.254854i 2.20411 + 0.376714i −2.52214 − 0.722254i 0.0753638 − 2.64468i −2.58363 −2.64785 + 1.41027i −2.16343 + 2.60595i
89.5 −0.322403 + 0.558418i 1.15761 − 1.28838i 0.792113 + 1.37198i −1.60193 + 1.56008i 0.346239 + 1.06181i 2.64366 − 0.105130i −2.31113 −0.319861 − 2.98290i −0.354709 − 1.39752i
89.6 −0.322403 + 0.558418i 1.69458 − 0.358331i 0.792113 + 1.37198i 0.550103 − 2.16735i −0.346239 + 1.06181i −2.64366 + 0.105130i −2.31113 2.74320 − 1.21444i 1.03293 + 1.00595i
89.7 0.322403 − 0.558418i −1.69458 + 0.358331i 0.792113 + 1.37198i 1.60193 − 1.56008i −0.346239 + 1.06181i 2.64366 − 0.105130i 2.31113 2.74320 − 1.21444i −0.354709 − 1.39752i
89.8 0.322403 − 0.558418i −1.15761 + 1.28838i 0.792113 + 1.37198i −0.550103 + 2.16735i 0.346239 + 1.06181i −2.64366 + 0.105130i 2.31113 −0.319861 − 2.98290i 1.03293 + 1.00595i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 59.12
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
7.d odd 6 1 inner
15.d odd 2 1 inner
21.g even 6 1 inner
35.i odd 6 1 inner
105.p even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.2.p.a ✓ 24
3.b odd 2 1 inner 105.2.p.a ✓ 24
5.b even 2 1 inner 105.2.p.a ✓ 24
5.c odd 4 2 525.2.t.j 24
7.b odd 2 1 735.2.p.f 24
7.c even 3 1 735.2.g.b 24
7.c even 3 1 735.2.p.f 24
7.d odd 6 1 inner 105.2.p.a ✓ 24
7.d odd 6 1 735.2.g.b 24
15.d odd 2 1 inner 105.2.p.a ✓ 24
15.e even 4 2 525.2.t.j 24
21.c even 2 1 735.2.p.f 24
21.g even 6 1 inner 105.2.p.a ✓ 24
21.g even 6 1 735.2.g.b 24
21.h odd 6 1 735.2.g.b 24
21.h odd 6 1 735.2.p.f 24
35.c odd 2 1 735.2.p.f 24
35.i odd 6 1 inner 105.2.p.a ✓ 24
35.i odd 6 1 735.2.g.b 24
35.j even 6 1 735.2.g.b 24
35.j even 6 1 735.2.p.f 24
35.k even 12 2 525.2.t.j 24
105.g even 2 1 735.2.p.f 24
105.o odd 6 1 735.2.g.b 24
105.o odd 6 1 735.2.p.f 24
105.p even 6 1 inner 105.2.p.a ✓ 24
105.p even 6 1 735.2.g.b 24
105.w odd 12 2 525.2.t.j 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.2.p.a ✓ 24 1.a even 1 1 trivial
105.2.p.a ✓ 24 3.b odd 2 1 inner
105.2.p.a ✓ 24 5.b even 2 1 inner
105.2.p.a ✓ 24 7.d odd 6 1 inner
105.2.p.a ✓ 24 15.d odd 2 1 inner
105.2.p.a ✓ 24 21.g even 6 1 inner
105.2.p.a ✓ 24 35.i odd 6 1 inner
105.2.p.a ✓ 24 105.p even 6 1 inner
525.2.t.j 24 5.c odd 4 2
525.2.t.j 24 15.e even 4 2
525.2.t.j 24 35.k even 12 2
525.2.t.j 24 105.w odd 12 2
735.2.g.b 24 7.c even 3 1
735.2.g.b 24 7.d odd 6 1
735.2.g.b 24 21.g even 6 1
735.2.g.b 24 21.h odd 6 1
735.2.g.b 24 35.i odd 6 1
735.2.g.b 24 35.j even 6 1
735.2.g.b 24 105.o odd 6 1
735.2.g.b 24 105.p even 6 1
735.2.p.f 24 7.b odd 2 1
735.2.p.f 24 7.c even 3 1
735.2.p.f 24 21.c even 2 1
735.2.p.f 24 21.h odd 6 1
735.2.p.f 24 35.c odd 2 1
735.2.p.f 24 35.j even 6 1
735.2.p.f 24 105.g even 2 1
735.2.p.f 24 105.o odd 6 1

Hecke kernels

This newform subspace is the entire newspace \(S_{2}^{\mathrm{new}}(105, [\chi])\).