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Properties

Label 2898.2.h.b
Level $2898$
Weight $2$
Character orbit 2898.h
Analytic conductor $23.141$
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] = [2898,2,Mod(827,2898)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2898, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("2898.827");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2898 = 2 \cdot 3^{2} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2898.h (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: \(23.1406465058\)
Analytic rank: \(0\)
Dimension: \(24\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{4} + 8 q^{5}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q - 24 q^{4} + 8 q^{5} - 16 q^{13} + 24 q^{14} + 24 q^{16} - 16 q^{17} - 8 q^{20} - 8 q^{23} + 48 q^{25} - 16 q^{31} + 8 q^{46} - 24 q^{49} + 16 q^{52} - 48 q^{53} + 16 q^{55} - 24 q^{56} - 8 q^{58} - 24 q^{64} + 48 q^{65} + 16 q^{68} + 8 q^{70} + 64 q^{73} + 32 q^{74} + 8 q^{80} + 16 q^{82} + 16 q^{83} + 32 q^{85} - 32 q^{86} - 48 q^{89} + 8 q^{92} - 16 q^{94}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
827.1 − 1.00000i 0 −1.00000 −3.15091 0 1.00000i 1.00000i 0 3.15091i
827.2 1.00000i 0 −1.00000 −3.15091 0 − 1.00000i − 1.00000i 0 − 3.15091i
827.3 − 1.00000i 0 −1.00000 −4.19040 0 1.00000i 1.00000i 0 4.19040i
827.4 1.00000i 0 −1.00000 −4.19040 0 − 1.00000i − 1.00000i 0 − 4.19040i
827.5 − 1.00000i 0 −1.00000 −2.08832 0 1.00000i 1.00000i 0 2.08832i
827.6 1.00000i 0 −1.00000 −2.08832 0 − 1.00000i − 1.00000i 0 − 2.08832i
827.7 − 1.00000i 0 −1.00000 3.88566 0 1.00000i 1.00000i 0 − 3.88566i
827.8 1.00000i 0 −1.00000 3.88566 0 − 1.00000i − 1.00000i 0 3.88566i
827.9 − 1.00000i 0 −1.00000 −0.526990 0 1.00000i 1.00000i 0 0.526990i
827.10 1.00000i 0 −1.00000 −0.526990 0 − 1.00000i − 1.00000i 0 − 0.526990i
827.11 − 1.00000i 0 −1.00000 −0.390260 0 1.00000i 1.00000i 0 0.390260i
827.12 1.00000i 0 −1.00000 −0.390260 0 − 1.00000i − 1.00000i 0 − 0.390260i
827.13 − 1.00000i 0 −1.00000 2.77683 0 1.00000i 1.00000i 0 − 2.77683i
827.14 1.00000i 0 −1.00000 2.77683 0 − 1.00000i − 1.00000i 0 2.77683i
827.15 − 1.00000i 0 −1.00000 −0.588858 0 1.00000i 1.00000i 0 0.588858i
827.16 1.00000i 0 −1.00000 −0.588858 0 − 1.00000i − 1.00000i 0 − 0.588858i
827.17 − 1.00000i 0 −1.00000 −0.814586 0 1.00000i 1.00000i 0 0.814586i
827.18 1.00000i 0 −1.00000 −0.814586 0 − 1.00000i − 1.00000i 0 − 0.814586i
827.19 − 1.00000i 0 −1.00000 2.89581 0 1.00000i 1.00000i 0 − 2.89581i
827.20 1.00000i 0 −1.00000 2.89581 0 − 1.00000i − 1.00000i 0 2.89581i
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 827.24
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 2898.2.h.b yes 24
3.b odd 2 1 2898.2.h.a ✓ 24
23.b odd 2 1 2898.2.h.a ✓ 24
69.c even 2 1 inner 2898.2.h.b yes 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2898.2.h.a ✓ 24 3.b odd 2 1
2898.2.h.a ✓ 24 23.b odd 2 1
2898.2.h.b yes 24 1.a even 1 1 trivial
2898.2.h.b yes 24 69.c even 2 1 inner