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Properties

Label 6014.2.a.l
Level $6014$
Weight $2$
Character orbit 6014.a
Self dual yes
Analytic conductor $48.022$
Analytic rank $0$
Dimension $38$
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: \(38\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 38 q - 38 q^{2} - 2 q^{3} + 38 q^{4} + 2 q^{5} + 2 q^{6} + 3 q^{7} - 38 q^{8} + 54 q^{9} - 2 q^{10} + 6 q^{11} - 2 q^{12} + 12 q^{13} - 3 q^{14} + 19 q^{15} + 38 q^{16} + 16 q^{17} - 54 q^{18} + 37 q^{19} + 2 q^{20} + 8 q^{21} - 6 q^{22} - 12 q^{23} + 2 q^{24} + 66 q^{25} - 12 q^{26} - 5 q^{27} + 3 q^{28} + 3 q^{29} - 19 q^{30} + 38 q^{31} - 38 q^{32} + 12 q^{33} - 16 q^{34} - 16 q^{35} + 54 q^{36} + 5 q^{37} - 37 q^{38} + 36 q^{39} - 2 q^{40} + 7 q^{41} - 8 q^{42} + 7 q^{43} + 6 q^{44} + 45 q^{45} + 12 q^{46} - 10 q^{47} - 2 q^{48} + 111 q^{49} - 66 q^{50} - 13 q^{51} + 12 q^{52} + 5 q^{53} + 5 q^{54} + 56 q^{55} - 3 q^{56} - 5 q^{57} - 3 q^{58} + 14 q^{59} + 19 q^{60} + 54 q^{61} - 38 q^{62} - 3 q^{63} + 38 q^{64} + 8 q^{65} - 12 q^{66} - 9 q^{67} + 16 q^{68} + 45 q^{69} + 16 q^{70} + 13 q^{71} - 54 q^{72} + 65 q^{73} - 5 q^{74} - 14 q^{75} + 37 q^{76} - 22 q^{77} - 36 q^{78} - 11 q^{79} + 2 q^{80} + 46 q^{81} - 7 q^{82} - 42 q^{83} + 8 q^{84} + 18 q^{85} - 7 q^{86} - 19 q^{87} - 6 q^{88} + 74 q^{89} - 45 q^{90} + 14 q^{91} - 12 q^{92} - 2 q^{93} + 10 q^{94} - 10 q^{95} + 2 q^{96} - 38 q^{97} - 111 q^{98} + 15 q^{99}+O(q^{100}) \) 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 −3.36850 1.00000 3.93449 3.36850 −2.34410 −1.00000 8.34681 −3.93449
1.2 −1.00000 −3.27880 1.00000 0.401675 3.27880 −4.68111 −1.00000 7.75051 −0.401675
1.3 −1.00000 −3.21269 1.00000 −0.168256 3.21269 2.46391 −1.00000 7.32140 0.168256
1.4 −1.00000 −3.06494 1.00000 −3.85153 3.06494 4.92968 −1.00000 6.39384 3.85153
1.5 −1.00000 −2.46616 1.00000 −2.24161 2.46616 4.72952 −1.00000 3.08193 2.24161
1.6 −1.00000 −2.41930 1.00000 0.0104516 2.41930 −3.11450 −1.00000 2.85300 −0.0104516
1.7 −1.00000 −2.33846 1.00000 2.68670 2.33846 5.16448 −1.00000 2.46841 −2.68670
1.8 −1.00000 −2.25991 1.00000 3.07445 2.25991 −1.73147 −1.00000 2.10720 −3.07445
1.9 −1.00000 −2.22677 1.00000 −4.13450 2.22677 −4.78775 −1.00000 1.95850 4.13450
1.10 −1.00000 −2.20978 1.00000 −2.38189 2.20978 −2.04649 −1.00000 1.88314 2.38189
1.11 −1.00000 −1.71746 1.00000 −1.04814 1.71746 0.0655046 −1.00000 −0.0503220 1.04814
1.12 −1.00000 −1.56405 1.00000 2.83927 1.56405 2.44268 −1.00000 −0.553753 −2.83927
1.13 −1.00000 −1.31913 1.00000 1.08741 1.31913 −0.837035 −1.00000 −1.25989 −1.08741
1.14 −1.00000 −1.26759 1.00000 −3.06753 1.26759 1.65725 −1.00000 −1.39322 3.06753
1.15 −1.00000 −1.26563 1.00000 1.94989 1.26563 −2.66768 −1.00000 −1.39817 −1.94989
1.16 −1.00000 −0.885413 1.00000 −0.534430 0.885413 1.09138 −1.00000 −2.21604 0.534430
1.17 −1.00000 −0.717443 1.00000 3.51838 0.717443 −3.26736 −1.00000 −2.48528 −3.51838
1.18 −1.00000 −0.679880 1.00000 −4.32143 0.679880 1.08152 −1.00000 −2.53776 4.32143
1.19 −1.00000 −0.181456 1.00000 3.41962 0.181456 3.19929 −1.00000 −2.96707 −3.41962
1.20 −1.00000 −0.173832 1.00000 −1.31890 0.173832 −4.23696 −1.00000 −2.96978 1.31890
See all 38 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.38
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.l ✓ 38
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6014.2.a.l ✓ 38 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3}^{38} + 2 T_{3}^{37} - 82 T_{3}^{36} - 161 T_{3}^{35} + 3068 T_{3}^{34} + 5915 T_{3}^{33} + \cdots - 8280704 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(6014))\). Copy content Toggle raw display