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Properties

Label 6014.2.a.i
Level $6014$
Weight $2$
Character orbit 6014.a
Self dual yes
Analytic conductor $48.022$
Analytic rank $0$
Dimension $28$
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: \(0\)
Dimension: \(28\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 28 q + 28 q^{2} + 12 q^{3} + 28 q^{4} + 10 q^{5} + 12 q^{6} + 13 q^{7} + 28 q^{8} + 38 q^{9} + 10 q^{10} + 12 q^{11} + 12 q^{12} + 20 q^{13} + 13 q^{14} + 19 q^{15} + 28 q^{16} - 4 q^{17} + 38 q^{18} + 35 q^{19} + 10 q^{20} + 30 q^{21} + 12 q^{22} + 20 q^{23} + 12 q^{24} + 46 q^{25} + 20 q^{26} + 39 q^{27} + 13 q^{28} + 5 q^{29} + 19 q^{30} - 28 q^{31} + 28 q^{32} + 12 q^{33} - 4 q^{34} + 36 q^{35} + 38 q^{36} + 11 q^{37} + 35 q^{38} - 4 q^{39} + 10 q^{40} - 5 q^{41} + 30 q^{42} + 43 q^{43} + 12 q^{44} + 11 q^{45} + 20 q^{46} + 18 q^{47} + 12 q^{48} + 99 q^{49} + 46 q^{50} - 43 q^{51} + 20 q^{52} + 11 q^{53} + 39 q^{54} + 66 q^{55} + 13 q^{56} - 15 q^{57} + 5 q^{58} + 34 q^{59} + 19 q^{60} + 66 q^{61} - 28 q^{62} + 65 q^{63} + 28 q^{64} - 16 q^{65} + 12 q^{66} + 5 q^{67} - 4 q^{68} - 33 q^{69} + 36 q^{70} + 25 q^{71} + 38 q^{72} - 9 q^{73} + 11 q^{74} + 92 q^{75} + 35 q^{76} + 4 q^{77} - 4 q^{78} + 15 q^{79} + 10 q^{80} - 5 q^{82} - 12 q^{83} + 30 q^{84} + 88 q^{85} + 43 q^{86} + 31 q^{87} + 12 q^{88} + 8 q^{89} + 11 q^{90} + 34 q^{91} + 20 q^{92} - 12 q^{93} + 18 q^{94} + 32 q^{95} + 12 q^{96} - 28 q^{97} + 99 q^{98} + 51 q^{99}+O(q^{100}) \) 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 −3.13670 1.00000 −0.941618 −3.13670 −2.29539 1.00000 6.83889 −0.941618
1.2 1.00000 −2.70233 1.00000 1.19953 −2.70233 4.06202 1.00000 4.30256 1.19953
1.3 1.00000 −2.39276 1.00000 −2.51232 −2.39276 −0.441417 1.00000 2.72531 −2.51232
1.4 1.00000 −2.30582 1.00000 −2.66329 −2.30582 3.25823 1.00000 2.31680 −2.66329
1.5 1.00000 −2.09814 1.00000 3.98650 −2.09814 1.58307 1.00000 1.40217 3.98650
1.6 1.00000 −2.00278 1.00000 3.09460 −2.00278 −1.28060 1.00000 1.01112 3.09460
1.7 1.00000 −1.45310 1.00000 1.69777 −1.45310 −3.88385 1.00000 −0.888510 1.69777
1.8 1.00000 −1.17518 1.00000 −3.11669 −1.17518 −1.35191 1.00000 −1.61895 −3.11669
1.9 1.00000 −1.17506 1.00000 −0.398275 −1.17506 −4.80253 1.00000 −1.61923 −0.398275
1.10 1.00000 −0.706567 1.00000 0.802206 −0.706567 5.13557 1.00000 −2.50076 0.802206
1.11 1.00000 −0.492368 1.00000 −0.547220 −0.492368 4.87929 1.00000 −2.75757 −0.547220
1.12 1.00000 −0.370415 1.00000 2.36567 −0.370415 1.74646 1.00000 −2.86279 2.36567
1.13 1.00000 −0.289255 1.00000 −1.50320 −0.289255 −2.57965 1.00000 −2.91633 −1.50320
1.14 1.00000 0.680504 1.00000 −3.85980 0.680504 −5.17023 1.00000 −2.53691 −3.85980
1.15 1.00000 0.739140 1.00000 −1.50686 0.739140 −3.35387 1.00000 −2.45367 −1.50686
1.16 1.00000 1.28193 1.00000 1.29778 1.28193 1.61746 1.00000 −1.35667 1.29778
1.17 1.00000 1.56730 1.00000 4.16992 1.56730 1.53618 1.00000 −0.543558 4.16992
1.18 1.00000 1.69964 1.00000 3.58462 1.69964 3.25191 1.00000 −0.111231 3.58462
1.19 1.00000 1.97781 1.00000 3.20639 1.97781 −4.54964 1.00000 0.911724 3.20639
1.20 1.00000 2.05494 1.00000 −3.09222 2.05494 3.17288 1.00000 1.22280 −3.09222
See all 28 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.28
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.i ✓ 28
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6014.2.a.i ✓ 28 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{28} - 12 T_{3}^{27} + 11 T_{3}^{26} + 407 T_{3}^{25} - 1435 T_{3}^{24} - 4906 T_{3}^{23} + \cdots - 342400 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\). Copy content Toggle raw display