↑

Properties

Label 6014.2.a.f
Level $6014$
Weight $2$
Character orbit 6014.a
Self dual yes
Analytic conductor $48.022$
Analytic rank $1$
Dimension $22$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.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: \(48.0220317756\)
Analytic rank: \(1\)
Dimension: \(22\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 22 q - 22 q^{2} + 22 q^{4} - 11 q^{7} - 22 q^{8} + 8 q^{9} - 8 q^{13} + 11 q^{14} + q^{15} + 22 q^{16} - 4 q^{17} - 8 q^{18} - 23 q^{19} - 12 q^{21} + 2 q^{23} - 12 q^{25} + 8 q^{26} + 3 q^{27} - 11 q^{28} + 9 q^{29} - q^{30} + 22 q^{31} - 22 q^{32} + 4 q^{34} + 4 q^{35} + 8 q^{36} - 17 q^{37} + 23 q^{38} + 8 q^{39} - 21 q^{41} + 12 q^{42} - 7 q^{43} + 9 q^{45} - 2 q^{46} - 10 q^{47} - 27 q^{49} + 12 q^{50} - q^{51} - 8 q^{52} + 9 q^{53} - 3 q^{54} - 6 q^{55} + 11 q^{56} - q^{57} - 9 q^{58} - 12 q^{59} + q^{60} - 34 q^{61} - 22 q^{62} - 5 q^{63} + 22 q^{64} + 4 q^{65} - 31 q^{67} - 4 q^{68} - 51 q^{69} - 4 q^{70} - 15 q^{71} - 8 q^{72} + 3 q^{73} + 17 q^{74} - 24 q^{75} - 23 q^{76} + 24 q^{77} - 8 q^{78} - 23 q^{79} - 26 q^{81} + 21 q^{82} + 22 q^{83} - 12 q^{84} - 42 q^{85} + 7 q^{86} - 9 q^{87} - 36 q^{89} - 9 q^{90} - 6 q^{91} + 2 q^{92} + 10 q^{94} + 2 q^{95} + 22 q^{97} + 27 q^{98} - 25 q^{99}+O(q^{100}) \) 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 −1.00000 −2.92127 1.00000 −1.99624 2.92127 −0.468229 −1.00000 5.53384 1.99624
1.2 −1.00000 −2.80047 1.00000 0.364133 2.80047 1.53058 −1.00000 4.84261 −0.364133
1.3 −1.00000 −2.51447 1.00000 3.35437 2.51447 0.494792 −1.00000 3.32256 −3.35437
1.4 −1.00000 −2.06526 1.00000 1.84106 2.06526 0.807248 −1.00000 1.26528 −1.84106
1.5 −1.00000 −1.79599 1.00000 −3.70171 1.79599 −3.49561 −1.00000 0.225587 3.70171
1.6 −1.00000 −1.60979 1.00000 1.84866 1.60979 −2.27059 −1.00000 −0.408562 −1.84866
1.7 −1.00000 −1.34015 1.00000 0.146848 1.34015 4.48511 −1.00000 −1.20399 −0.146848
1.8 −1.00000 −1.04488 1.00000 −0.722746 1.04488 −0.912399 −1.00000 −1.90823 0.722746
1.9 −1.00000 −0.916242 1.00000 −2.81390 0.916242 0.508180 −1.00000 −2.16050 2.81390
1.10 −1.00000 −0.531212 1.00000 1.86385 0.531212 −4.06404 −1.00000 −2.71781 −1.86385
1.11 −1.00000 0.0685928 1.00000 −2.24786 −0.0685928 −4.29331 −1.00000 −2.99530 2.24786
1.12 −1.00000 0.191955 1.00000 −1.50666 −0.191955 −2.08203 −1.00000 −2.96315 1.50666
1.13 −1.00000 0.253397 1.00000 −0.480250 −0.253397 2.09789 −1.00000 −2.93579 0.480250
1.14 −1.00000 0.813553 1.00000 3.21035 −0.813553 −2.44817 −1.00000 −2.33813 −3.21035
1.15 −1.00000 1.04707 1.00000 1.01417 −1.04707 3.78577 −1.00000 −1.90364 −1.01417
1.16 −1.00000 1.29017 1.00000 3.44095 −1.29017 −0.471801 −1.00000 −1.33547 −3.44095
1.17 −1.00000 1.47323 1.00000 −3.13161 −1.47323 0.874706 −1.00000 −0.829602 3.13161
1.18 −1.00000 2.07834 1.00000 −0.312935 −2.07834 0.578926 −1.00000 1.31950 0.312935
1.19 −1.00000 2.17019 1.00000 1.18841 −2.17019 −1.11869 −1.00000 1.70972 −1.18841
1.20 −1.00000 2.25454 1.00000 −2.47204 −2.25454 0.953481 −1.00000 2.08293 2.47204
See all 22 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.22
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(1\)
\(31\) \(-1\)
\(97\) \(-1\)

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 6014.2.a.f ✓ 22
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6014.2.a.f ✓ 22 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{22} - 37 T_{3}^{20} - T_{3}^{19} + 574 T_{3}^{18} + 28 T_{3}^{17} - 4877 T_{3}^{16} - 318 T_{3}^{15} + \cdots + 40 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\). Copy content Toggle raw display