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Properties

Label 2940.2.x.b
Level $2940$
Weight $2$
Character orbit 2940.x
Analytic conductor $23.476$
Analytic rank $0$
Dimension $24$
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] = [2940,2,Mod(97,2940)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2940, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2940.97");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2940.x (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: \(23.4760181943\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{5} - 16 q^{13} - 32 q^{19} + 16 q^{23} - 16 q^{25} + 16 q^{37} - 16 q^{43} - 8 q^{45} + 16 q^{47} + 24 q^{53} + 16 q^{57} - 64 q^{59} - 32 q^{65} + 32 q^{67} + 32 q^{71} + 16 q^{73} - 24 q^{81} + 48 q^{85} + 40 q^{87} - 144 q^{89} + 16 q^{93} - 64 q^{95} - 16 q^{97}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
97.1 0 −0.707107 − 0.707107i 0 0.754578 + 2.10490i 0 0 0 1.00000i 0
97.2 0 −0.707107 − 0.707107i 0 −0.329802 + 2.21161i 0 0 0 1.00000i 0
97.3 0 −0.707107 − 0.707107i 0 2.23574 + 0.0384920i 0 0 0 1.00000i 0
97.4 0 −0.707107 − 0.707107i 0 −0.523252 − 2.17398i 0 0 0 1.00000i 0
97.5 0 −0.707107 − 0.707107i 0 −1.84810 + 1.25878i 0 0 0 1.00000i 0
97.6 0 −0.707107 − 0.707107i 0 1.71084 − 1.43981i 0 0 0 1.00000i 0
97.7 0 0.707107 + 0.707107i 0 0.0980241 + 2.23392i 0 0 0 1.00000i 0
97.8 0 0.707107 + 0.707107i 0 −0.875368 + 2.05760i 0 0 0 1.00000i 0
97.9 0 0.707107 + 0.707107i 0 1.80064 + 1.32578i 0 0 0 1.00000i 0
97.10 0 0.707107 + 0.707107i 0 −2.09559 − 0.780056i 0 0 0 1.00000i 0
97.11 0 0.707107 + 0.707107i 0 2.07369 − 0.836546i 0 0 0 1.00000i 0
97.12 0 0.707107 + 0.707107i 0 0.998605 − 2.00070i 0 0 0 1.00000i 0
1273.1 0 −0.707107 + 0.707107i 0 0.754578 − 2.10490i 0 0 0 − 1.00000i 0
1273.2 0 −0.707107 + 0.707107i 0 −0.329802 − 2.21161i 0 0 0 − 1.00000i 0
1273.3 0 −0.707107 + 0.707107i 0 2.23574 − 0.0384920i 0 0 0 − 1.00000i 0
1273.4 0 −0.707107 + 0.707107i 0 −0.523252 + 2.17398i 0 0 0 − 1.00000i 0
1273.5 0 −0.707107 + 0.707107i 0 −1.84810 − 1.25878i 0 0 0 − 1.00000i 0
1273.6 0 −0.707107 + 0.707107i 0 1.71084 + 1.43981i 0 0 0 − 1.00000i 0
1273.7 0 0.707107 − 0.707107i 0 0.0980241 − 2.23392i 0 0 0 − 1.00000i 0
1273.8 0 0.707107 − 0.707107i 0 −0.875368 − 2.05760i 0 0 0 − 1.00000i 0
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 97.12
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
35.f even 4 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2940.2.x.b yes 24
5.c odd 4 1 2940.2.x.a ✓ 24
7.b odd 2 1 2940.2.x.a ✓ 24
35.f even 4 1 inner 2940.2.x.b yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2940.2.x.a ✓ 24 5.c odd 4 1
2940.2.x.a ✓ 24 7.b odd 2 1
2940.2.x.b yes 24 1.a even 1 1 trivial
2940.2.x.b yes 24 35.f even 4 1 inner