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Properties

Label 6027.2.a.bo
Level $6027$
Weight $2$
Character orbit 6027.a
Self dual yes
Analytic conductor $48.126$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6027,2,Mod(1,6027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6027, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("6027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6027.a (trivial)

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: yes
Analytic conductor: \(48.1258372982\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) \) 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   \( a_{2} \) \( a_{3} \) \( a_{4} \) \( a_{5} \) \( a_{6} \) \( a_{7} \) \( a_{8} \) \( a_{9} \) \( a_{10} \)
1.1 −2.69245 1.00000 5.24930 3.40876 −2.69245 0 −8.74860 1.00000 −9.17792
1.2 −2.37986 1.00000 3.66372 3.68734 −2.37986 0 −3.95941 1.00000 −8.77534
1.3 −2.22021 1.00000 2.92934 0.165927 −2.22021 0 −2.06334 1.00000 −0.368393
1.4 −1.96907 1.00000 1.87725 −4.10878 −1.96907 0 0.241710 1.00000 8.09048
1.5 −1.80081 1.00000 1.24292 −2.17778 −1.80081 0 1.36336 1.00000 3.92176
1.6 −1.32413 1.00000 −0.246682 4.03355 −1.32413 0 2.97490 1.00000 −5.34094
1.7 −1.25316 1.00000 −0.429590 −1.76265 −1.25316 0 3.04466 1.00000 2.20889
1.8 −0.844195 1.00000 −1.28734 −1.91229 −0.844195 0 2.77515 1.00000 1.61434
1.9 −0.423828 1.00000 −1.82037 3.41632 −0.423828 0 1.61918 1.00000 −1.44793
1.10 −0.308797 1.00000 −1.90464 −0.898648 −0.308797 0 1.20574 1.00000 0.277499
1.11 −0.0650408 1.00000 −1.99577 −2.65358 −0.0650408 0 0.259888 1.00000 0.172591
1.12 0.154130 1.00000 −1.97624 1.29015 0.154130 0 −0.612860 1.00000 0.198852
1.13 0.368135 1.00000 −1.86448 −0.572097 0.368135 0 −1.42265 1.00000 −0.210609
1.14 1.11646 1.00000 −0.753512 −0.900581 1.11646 0 −3.07419 1.00000 −1.00546
1.15 1.33013 1.00000 −0.230742 −3.44355 1.33013 0 −2.96719 1.00000 −4.58038
1.16 1.50751 1.00000 0.272577 1.10903 1.50751 0 −2.60410 1.00000 1.67187
1.17 1.64420 1.00000 0.703405 3.28206 1.64420 0 −2.13187 1.00000 5.39638
1.18 1.95065 1.00000 1.80504 2.46699 1.95065 0 −0.380308 1.00000 4.81223
1.19 2.26259 1.00000 3.11931 3.51535 2.26259 0 2.53253 1.00000 7.95379
1.20 2.37367 1.00000 3.63432 −3.47491 2.37367 0 3.87933 1.00000 −8.24830
See all 24 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.24
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(3\) \(-1\)
\(7\) \(1\)
\(41\) \(1\)

Inner twists

This newform does not admit any (nontrivial) inner twists.

Twists

       By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 6027.2.a.bo yes 24
7.b odd 2 1 6027.2.a.bn ✓ 24
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6027.2.a.bn ✓ 24 7.b odd 2 1
6027.2.a.bo yes 24 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6027))\):

\( T_{2}^{24} - 8 T_{2}^{23} - 8 T_{2}^{22} + 216 T_{2}^{21} - 267 T_{2}^{20} - 2332 T_{2}^{19} + 5308 T_{2}^{18} + \cdots - 64 \) Copy content Toggle raw display
\( T_{5}^{24} - 4 T_{5}^{23} - 76 T_{5}^{22} + 308 T_{5}^{21} + 2446 T_{5}^{20} - 10044 T_{5}^{19} + \cdots - 1116416 \) Copy content Toggle raw display
\( T_{13}^{24} - 156 T_{13}^{22} - 88 T_{13}^{21} + 10172 T_{13}^{20} + 9908 T_{13}^{19} + \cdots + 3175599616 \) Copy content Toggle raw display