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Properties

Label 2760.2.p.a
Level $2760$
Weight $2$
Character orbit 2760.p
Analytic conductor $22.039$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2760,2,Mod(1241,2760)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2760, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2760.1241");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2760 = 2^{3} \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2760.p (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: \(22.0387109579\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 48 q - 48 q^{5} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 48 q - 48 q^{5} - 2 q^{9} + 4 q^{11} - 4 q^{21} - 8 q^{23} + 48 q^{25} - 4 q^{31} + 8 q^{33} + 12 q^{39} + 2 q^{45} - 68 q^{49} + 34 q^{51} - 4 q^{55} + 24 q^{57} - 20 q^{63} - 2 q^{69} + 8 q^{73} - 22 q^{81} + 16 q^{83} + 48 q^{87} - 8 q^{89} - 24 q^{93} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1241.1 0 −1.73131 − 0.0505586i 0 −1.00000 0 2.89850i 0 2.99489 + 0.175066i 0
1241.2 0 −1.73131 + 0.0505586i 0 −1.00000 0 − 2.89850i 0 2.99489 − 0.175066i 0
1241.3 0 −1.72135 − 0.192263i 0 −1.00000 0 2.41479i 0 2.92607 + 0.661902i 0
1241.4 0 −1.72135 + 0.192263i 0 −1.00000 0 − 2.41479i 0 2.92607 − 0.661902i 0
1241.5 0 −1.70911 − 0.280952i 0 −1.00000 0 2.69510i 0 2.84213 + 0.960358i 0
1241.6 0 −1.70911 + 0.280952i 0 −1.00000 0 − 2.69510i 0 2.84213 − 0.960358i 0
1241.7 0 −1.37850 − 1.04868i 0 −1.00000 0 4.66363i 0 0.800541 + 2.89122i 0
1241.8 0 −1.37850 + 1.04868i 0 −1.00000 0 − 4.66363i 0 0.800541 − 2.89122i 0
1241.9 0 −1.33966 − 1.09786i 0 −1.00000 0 − 3.79178i 0 0.589396 + 2.94153i 0
1241.10 0 −1.33966 + 1.09786i 0 −1.00000 0 3.79178i 0 0.589396 − 2.94153i 0
1241.11 0 −1.27593 − 1.17132i 0 −1.00000 0 − 4.49556i 0 0.256020 + 2.98906i 0
1241.12 0 −1.27593 + 1.17132i 0 −1.00000 0 4.49556i 0 0.256020 − 2.98906i 0
1241.13 0 −1.27150 − 1.17613i 0 −1.00000 0 − 1.32290i 0 0.233436 + 2.99090i 0
1241.14 0 −1.27150 + 1.17613i 0 −1.00000 0 1.32290i 0 0.233436 − 2.99090i 0
1241.15 0 −0.891707 − 1.48488i 0 −1.00000 0 0.626160i 0 −1.40972 + 2.64815i 0
1241.16 0 −0.891707 + 1.48488i 0 −1.00000 0 − 0.626160i 0 −1.40972 − 2.64815i 0
1241.17 0 −0.779214 − 1.54688i 0 −1.00000 0 − 1.13322i 0 −1.78565 + 2.41070i 0
1241.18 0 −0.779214 + 1.54688i 0 −1.00000 0 1.13322i 0 −1.78565 − 2.41070i 0
1241.19 0 −0.491879 − 1.66074i 0 −1.00000 0 1.55251i 0 −2.51611 + 1.63377i 0
1241.20 0 −0.491879 + 1.66074i 0 −1.00000 0 − 1.55251i 0 −2.51611 − 1.63377i 0
See all 48 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1241.48
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
69.c even 2 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2760.2.p.a ✓ 48
3.b odd 2 1 2760.2.p.b yes 48
23.b odd 2 1 2760.2.p.b yes 48
69.c even 2 1 inner 2760.2.p.a ✓ 48
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2760.2.p.a ✓ 48 1.a even 1 1 trivial
2760.2.p.a ✓ 48 69.c even 2 1 inner
2760.2.p.b yes 48 3.b odd 2 1
2760.2.p.b yes 48 23.b odd 2 1