↑

Properties

Label 2940.2.bb.j
Level $2940$
Weight $2$
Character orbit 2940.bb
Analytic conductor $23.476$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2940,2,Mod(949,2940)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2940, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2940.949");
 
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.bb (of order \(6\), degree \(2\), not 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: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 32 q + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 32 q + 16 q^{9} - 8 q^{25} - 32 q^{29} - 16 q^{51} + 40 q^{65} + 128 q^{71} + 16 q^{79} - 16 q^{81} - 80 q^{85} + 48 q^{95}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
949.1 0 −0.866025 − 0.500000i 0 −1.16836 + 1.90655i 0 0 0 0.500000 + 0.866025i 0
949.2 0 −0.866025 − 0.500000i 0 −2.23530 + 0.0585577i 0 0 0 0.500000 + 0.866025i 0
949.3 0 −0.866025 − 0.500000i 0 −1.50668 − 1.65224i 0 0 0 0.500000 + 0.866025i 0
949.4 0 −0.866025 − 0.500000i 0 −0.902511 − 2.04584i 0 0 0 0.500000 + 0.866025i 0
949.5 0 −0.866025 − 0.500000i 0 2.10044 − 0.766909i 0 0 0 0.500000 + 0.866025i 0
949.6 0 −0.866025 − 0.500000i 0 0.677540 + 2.13095i 0 0 0 0.500000 + 0.866025i 0
949.7 0 −0.866025 − 0.500000i 0 1.71438 − 1.43558i 0 0 0 0.500000 + 0.866025i 0
949.8 0 −0.866025 − 0.500000i 0 1.32050 + 1.80452i 0 0 0 0.500000 + 0.866025i 0
949.9 0 0.866025 + 0.500000i 0 −1.71438 + 1.43558i 0 0 0 0.500000 + 0.866025i 0
949.10 0 0.866025 + 0.500000i 0 0.902511 + 2.04584i 0 0 0 0.500000 + 0.866025i 0
949.11 0 0.866025 + 0.500000i 0 −2.10044 + 0.766909i 0 0 0 0.500000 + 0.866025i 0
949.12 0 0.866025 + 0.500000i 0 −0.677540 − 2.13095i 0 0 0 0.500000 + 0.866025i 0
949.13 0 0.866025 + 0.500000i 0 1.50668 + 1.65224i 0 0 0 0.500000 + 0.866025i 0
949.14 0 0.866025 + 0.500000i 0 1.16836 − 1.90655i 0 0 0 0.500000 + 0.866025i 0
949.15 0 0.866025 + 0.500000i 0 2.23530 − 0.0585577i 0 0 0 0.500000 + 0.866025i 0
949.16 0 0.866025 + 0.500000i 0 −1.32050 − 1.80452i 0 0 0 0.500000 + 0.866025i 0
1549.1 0 −0.866025 + 0.500000i 0 −1.16836 − 1.90655i 0 0 0 0.500000 − 0.866025i 0
1549.2 0 −0.866025 + 0.500000i 0 −2.23530 − 0.0585577i 0 0 0 0.500000 − 0.866025i 0
1549.3 0 −0.866025 + 0.500000i 0 −1.50668 + 1.65224i 0 0 0 0.500000 − 0.866025i 0
1549.4 0 −0.866025 + 0.500000i 0 −0.902511 + 2.04584i 0 0 0 0.500000 − 0.866025i 0
See all 32 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 949.16
Significant digits:
Format:

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
5.b even 2 1 inner
7.b odd 2 1 inner
7.c even 3 1 inner
7.d odd 6 1 inner
35.c odd 2 1 inner
35.i odd 6 1 inner
35.j even 6 1 inner

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 2940.2.bb.j 32
5.b even 2 1 inner 2940.2.bb.j 32
7.b odd 2 1 inner 2940.2.bb.j 32
7.c even 3 1 2940.2.k.h ✓ 16
7.c even 3 1 inner 2940.2.bb.j 32
7.d odd 6 1 2940.2.k.h ✓ 16
7.d odd 6 1 inner 2940.2.bb.j 32
35.c odd 2 1 inner 2940.2.bb.j 32
35.i odd 6 1 2940.2.k.h ✓ 16
35.i odd 6 1 inner 2940.2.bb.j 32
35.j even 6 1 2940.2.k.h ✓ 16
35.j even 6 1 inner 2940.2.bb.j 32
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2940.2.k.h ✓ 16 7.c even 3 1
2940.2.k.h ✓ 16 7.d odd 6 1
2940.2.k.h ✓ 16 35.i odd 6 1
2940.2.k.h ✓ 16 35.j even 6 1
2940.2.bb.j 32 1.a even 1 1 trivial
2940.2.bb.j 32 5.b even 2 1 inner
2940.2.bb.j 32 7.b odd 2 1 inner
2940.2.bb.j 32 7.c even 3 1 inner
2940.2.bb.j 32 7.d odd 6 1 inner
2940.2.bb.j 32 35.c odd 2 1 inner
2940.2.bb.j 32 35.i odd 6 1 inner
2940.2.bb.j 32 35.j even 6 1 inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(2940, [\chi])\):

\( T_{11}^{8} + 36T_{11}^{6} - 32T_{11}^{5} + 1264T_{11}^{4} - 576T_{11}^{3} + 1408T_{11}^{2} + 512T_{11} + 1024 \) Copy content Toggle raw display
\( T_{13}^{8} + 76T_{13}^{6} + 1556T_{13}^{4} + 6560T_{13}^{2} + 3136 \) Copy content Toggle raw display
\( T_{19}^{16} + 84 T_{19}^{14} + 4652 T_{19}^{12} + 151504 T_{19}^{10} + 3610896 T_{19}^{8} + \cdots + 2517630976 \) Copy content Toggle raw display
\( T_{31}^{16} + 148 T_{31}^{14} + 13932 T_{31}^{12} + 813776 T_{31}^{10} + 34984208 T_{31}^{8} + \cdots + 2186423566336 \) Copy content Toggle raw display