Properties

Label 105.2.j.a
Level $105$
Weight $2$
Character orbit 105.j
Analytic conductor $0.838$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,2,Mod(8,105)]
 
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, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.j (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: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 4 q^{3} - 16 q^{10} + 16 q^{12} - 8 q^{13} - 16 q^{15} - 16 q^{16} - 20 q^{18} + 4 q^{21} + 8 q^{22} - 16 q^{25} - 16 q^{27} + 20 q^{30} + 28 q^{33} + 16 q^{36} - 16 q^{37} + 64 q^{40} - 20 q^{42} - 40 q^{43} + 20 q^{45} - 64 q^{46} + 16 q^{48} - 20 q^{51} + 40 q^{55} + 4 q^{57} + 40 q^{58} + 32 q^{60} + 32 q^{61} - 8 q^{63} - 16 q^{66} + 24 q^{67} - 8 q^{70} - 8 q^{72} + 32 q^{73} - 60 q^{75} + 32 q^{76} + 60 q^{78} + 52 q^{81} - 80 q^{82} + 24 q^{85} + 4 q^{87} + 96 q^{88} - 24 q^{90} - 24 q^{91} - 76 q^{93} - 96 q^{96} + 24 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
8.1 −1.79963 1.79963i −1.66094 + 0.491204i 4.47734i 1.87996 + 1.21069i 3.87306 + 2.10509i −0.707107 + 0.707107i 4.45829 4.45829i 2.51744 1.63172i −1.20443 5.56202i
8.2 −1.54414 1.54414i −0.00622252 1.73204i 2.76875i 0.252500 2.22177i −2.66491 + 2.68412i 0.707107 0.707107i 1.18705 1.18705i −2.99992 + 0.0215553i −3.82062 + 3.04083i
8.3 −1.24414 1.24414i 1.66575 + 0.474620i 1.09578i 1.67522 + 1.48109i −1.48194 2.66293i 0.707107 0.707107i −1.12498 + 1.12498i 2.54947 + 1.58120i −0.241524 3.92690i
8.4 −0.800553 0.800553i −1.34285 1.09397i 0.718229i −2.10480 + 0.754855i 0.199242 + 1.95080i −0.707107 + 0.707107i −2.17609 + 2.17609i 0.606476 + 2.93806i 2.28931 + 1.08070i
8.5 −0.347054 0.347054i 1.72305 + 0.176396i 1.75911i −1.16790 1.90683i −0.536770 0.659208i −0.707107 + 0.707107i −1.30461 + 1.30461i 2.93777 + 0.607876i −0.256447 + 1.06710i
8.6 −0.260263 0.260263i −1.52191 + 0.826909i 1.86453i 0.895238 2.04904i 0.611312 + 0.180884i 0.707107 0.707107i −1.00579 + 1.00579i 1.63244 2.51697i −0.766286 + 0.300291i
8.7 0.260263 + 0.260263i 0.826909 1.52191i 1.86453i −0.895238 + 2.04904i 0.611312 0.180884i 0.707107 0.707107i 1.00579 1.00579i −1.63244 2.51697i −0.766286 + 0.300291i
8.8 0.347054 + 0.347054i 0.176396 + 1.72305i 1.75911i 1.16790 + 1.90683i −0.536770 + 0.659208i −0.707107 + 0.707107i 1.30461 1.30461i −2.93777 + 0.607876i −0.256447 + 1.06710i
8.9 0.800553 + 0.800553i −1.09397 1.34285i 0.718229i 2.10480 0.754855i 0.199242 1.95080i −0.707107 + 0.707107i 2.17609 2.17609i −0.606476 + 2.93806i 2.28931 + 1.08070i
8.10 1.24414 + 1.24414i 0.474620 + 1.66575i 1.09578i −1.67522 1.48109i −1.48194 + 2.66293i 0.707107 0.707107i 1.12498 1.12498i −2.54947 + 1.58120i −0.241524 3.92690i
8.11 1.54414 + 1.54414i −1.73204 0.00622252i 2.76875i −0.252500 + 2.22177i −2.66491 2.68412i 0.707107 0.707107i −1.18705 + 1.18705i 2.99992 + 0.0215553i −3.82062 + 3.04083i
8.12 1.79963 + 1.79963i 0.491204 1.66094i 4.47734i −1.87996 1.21069i 3.87306 2.10509i −0.707107 + 0.707107i −4.45829 + 4.45829i −2.51744 1.63172i −1.20443 5.56202i
92.1 −1.79963 + 1.79963i −1.66094 0.491204i 4.47734i 1.87996 1.21069i 3.87306 2.10509i −0.707107 0.707107i 4.45829 + 4.45829i 2.51744 + 1.63172i −1.20443 + 5.56202i
92.2 −1.54414 + 1.54414i −0.00622252 + 1.73204i 2.76875i 0.252500 + 2.22177i −2.66491 2.68412i 0.707107 + 0.707107i 1.18705 + 1.18705i −2.99992 0.0215553i −3.82062 3.04083i
92.3 −1.24414 + 1.24414i 1.66575 0.474620i 1.09578i 1.67522 1.48109i −1.48194 + 2.66293i 0.707107 + 0.707107i −1.12498 1.12498i 2.54947 1.58120i −0.241524 + 3.92690i
92.4 −0.800553 + 0.800553i −1.34285 + 1.09397i 0.718229i −2.10480 0.754855i 0.199242 1.95080i −0.707107 0.707107i −2.17609 2.17609i 0.606476 2.93806i 2.28931 1.08070i
92.5 −0.347054 + 0.347054i 1.72305 0.176396i 1.75911i −1.16790 + 1.90683i −0.536770 + 0.659208i −0.707107 0.707107i −1.30461 1.30461i 2.93777 0.607876i −0.256447 1.06710i
92.6 −0.260263 + 0.260263i −1.52191 0.826909i 1.86453i 0.895238 + 2.04904i 0.611312 0.180884i 0.707107 + 0.707107i −1.00579 1.00579i 1.63244 + 2.51697i −0.766286 0.300291i
92.7 0.260263 0.260263i 0.826909 + 1.52191i 1.86453i −0.895238 2.04904i 0.611312 + 0.180884i 0.707107 + 0.707107i 1.00579 + 1.00579i −1.63244 + 2.51697i −0.766286 0.300291i
92.8 0.347054 0.347054i 0.176396 1.72305i 1.75911i 1.16790 1.90683i −0.536770 0.659208i −0.707107 0.707107i 1.30461 + 1.30461i −2.93777 0.607876i −0.256447 1.06710i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 8.12
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
15.e even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 105.2.j.a 24
3.b odd 2 1 inner 105.2.j.a 24
5.b even 2 1 525.2.j.b 24
5.c odd 4 1 inner 105.2.j.a 24
5.c odd 4 1 525.2.j.b 24
7.b odd 2 1 735.2.j.h 24
7.c even 3 2 735.2.y.j 48
7.d odd 6 2 735.2.y.g 48
15.d odd 2 1 525.2.j.b 24
15.e even 4 1 inner 105.2.j.a 24
15.e even 4 1 525.2.j.b 24
21.c even 2 1 735.2.j.h 24
21.g even 6 2 735.2.y.g 48
21.h odd 6 2 735.2.y.j 48
35.f even 4 1 735.2.j.h 24
35.k even 12 2 735.2.y.g 48
35.l odd 12 2 735.2.y.j 48
105.k odd 4 1 735.2.j.h 24
105.w odd 12 2 735.2.y.g 48
105.x even 12 2 735.2.y.j 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
105.2.j.a 24 1.a even 1 1 trivial
105.2.j.a 24 3.b odd 2 1 inner
105.2.j.a 24 5.c odd 4 1 inner
105.2.j.a 24 15.e even 4 1 inner
525.2.j.b 24 5.b even 2 1
525.2.j.b 24 5.c odd 4 1
525.2.j.b 24 15.d odd 2 1
525.2.j.b 24 15.e even 4 1
735.2.j.h 24 7.b odd 2 1
735.2.j.h 24 21.c even 2 1
735.2.j.h 24 35.f even 4 1
735.2.j.h 24 105.k odd 4 1
735.2.y.g 48 7.d odd 6 2
735.2.y.g 48 21.g even 6 2
735.2.y.g 48 35.k even 12 2
735.2.y.g 48 105.w odd 12 2
735.2.y.j 48 7.c even 3 2
735.2.y.j 48 21.h odd 6 2
735.2.y.j 48 35.l odd 12 2
735.2.y.j 48 105.x even 12 2

Hecke kernels

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