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Properties

Label 6014.2.a.e
Level $6014$
Weight $2$
Character orbit 6014.a
Self dual yes
Analytic conductor $48.022$
Analytic rank $1$
Dimension $21$
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] = [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: \(21\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 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 −3.14785 1.00000 1.07577 −3.14785 −0.384133 1.00000 6.90896 1.07577
1.2 1.00000 −3.05317 1.00000 0.104652 −3.05317 −2.07086 1.00000 6.32187 0.104652
1.3 1.00000 −2.57113 1.00000 3.16346 −2.57113 −4.41426 1.00000 3.61072 3.16346
1.4 1.00000 −2.42118 1.00000 −1.30859 −2.42118 3.90591 1.00000 2.86213 −1.30859
1.5 1.00000 −2.40239 1.00000 −4.08857 −2.40239 0.438180 1.00000 2.77149 −4.08857
1.6 1.00000 −1.86116 1.00000 −3.25735 −1.86116 −2.35478 1.00000 0.463919 −3.25735
1.7 1.00000 −1.32252 1.00000 −0.257676 −1.32252 −2.07296 1.00000 −1.25095 −0.257676
1.8 1.00000 −1.27481 1.00000 1.77282 −1.27481 1.20773 1.00000 −1.37487 1.77282
1.9 1.00000 −1.26246 1.00000 2.97735 −1.26246 1.38275 1.00000 −1.40619 2.97735
1.10 1.00000 −1.09484 1.00000 −2.95477 −1.09484 4.52432 1.00000 −1.80131 −2.95477
1.11 1.00000 −1.07052 1.00000 −1.71120 −1.07052 −0.903944 1.00000 −1.85399 −1.71120
1.12 1.00000 −0.343301 1.00000 1.80151 −0.343301 0.627271 1.00000 −2.88214 1.80151
1.13 1.00000 −0.333415 1.00000 −2.81042 −0.333415 −3.40902 1.00000 −2.88883 −2.81042
1.14 1.00000 0.436625 1.00000 −0.0518544 0.436625 0.167384 1.00000 −2.80936 −0.0518544
1.15 1.00000 0.761502 1.00000 −0.855697 0.761502 0.402181 1.00000 −2.42012 −0.855697
1.16 1.00000 1.37186 1.00000 −2.00517 1.37186 2.66469 1.00000 −1.11799 −2.00517
1.17 1.00000 1.56192 1.00000 −3.75184 1.56192 −2.39374 1.00000 −0.560398 −3.75184
1.18 1.00000 1.71445 1.00000 2.08645 1.71445 −3.84728 1.00000 −0.0606696 2.08645
1.19 1.00000 1.74046 1.00000 0.258024 1.74046 −2.13023 1.00000 0.0291912 0.258024
1.20 1.00000 2.22590 1.00000 1.86093 2.22590 −2.90456 1.00000 1.95462 1.86093
See all 21 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.21
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.e ✓ 21
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6014.2.a.e ✓ 21 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{21} + 10 T_{3}^{20} + 15 T_{3}^{19} - 157 T_{3}^{18} - 558 T_{3}^{17} + 658 T_{3}^{16} + \cdots + 848 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\). Copy content Toggle raw display