↑

Properties

Label 6034.2.a.q
Level $6034$
Weight $2$
Character orbit 6034.a
Self dual yes
Analytic conductor $48.182$
Analytic rank $0$
Dimension $31$
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] = [6034,2,Mod(1,6034)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6034, 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("6034.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6034 = 2 \cdot 7 \cdot 431 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6034.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: \(48.1817325796\)
Analytic rank: \(0\)
Dimension: \(31\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 31 q + 31 q^{2} + 2 q^{3} + 31 q^{4} + 13 q^{5} + 2 q^{6} + 31 q^{7} + 31 q^{8} + 43 q^{9} + 13 q^{10} + 28 q^{11} + 2 q^{12} + 23 q^{13} + 31 q^{14} + 12 q^{15} + 31 q^{16} + 15 q^{17} + 43 q^{18} + 5 q^{19} + 13 q^{20} + 2 q^{21} + 28 q^{22} + 16 q^{23} + 2 q^{24} + 66 q^{25} + 23 q^{26} + 29 q^{27} + 31 q^{28} + 30 q^{29} + 12 q^{30} + 7 q^{31} + 31 q^{32} - 7 q^{33} + 15 q^{34} + 13 q^{35} + 43 q^{36} + 26 q^{37} + 5 q^{38} + 25 q^{39} + 13 q^{40} + 23 q^{41} + 2 q^{42} + 29 q^{43} + 28 q^{44} + 13 q^{45} + 16 q^{46} + q^{47} + 2 q^{48} + 31 q^{49} + 66 q^{50} + 15 q^{51} + 23 q^{52} + 47 q^{53} + 29 q^{54} - 21 q^{55} + 31 q^{56} - 4 q^{57} + 30 q^{58} + 12 q^{59} + 12 q^{60} + q^{61} + 7 q^{62} + 43 q^{63} + 31 q^{64} + 42 q^{65} - 7 q^{66} + 40 q^{67} + 15 q^{68} - 25 q^{69} + 13 q^{70} + 32 q^{71} + 43 q^{72} + 9 q^{73} + 26 q^{74} + 13 q^{75} + 5 q^{76} + 28 q^{77} + 25 q^{78} - 9 q^{79} + 13 q^{80} + 63 q^{81} + 23 q^{82} + 7 q^{83} + 2 q^{84} + 32 q^{85} + 29 q^{86} - 53 q^{87} + 28 q^{88} + 61 q^{89} + 13 q^{90} + 23 q^{91} + 16 q^{92} + 3 q^{93} + q^{94} + 17 q^{95} + 2 q^{96} + 28 q^{97} + 31 q^{98} + 54 q^{99}+O(q^{100}) \) 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 −3.16461 1.00000 3.38179 −3.16461 1.00000 1.00000 7.01477 3.38179
1.2 1.00000 −2.89830 1.00000 −2.40071 −2.89830 1.00000 1.00000 5.40017 −2.40071
1.3 1.00000 −2.89657 1.00000 −0.704468 −2.89657 1.00000 1.00000 5.39012 −0.704468
1.4 1.00000 −2.80916 1.00000 1.77691 −2.80916 1.00000 1.00000 4.89139 1.77691
1.5 1.00000 −2.64787 1.00000 −3.70858 −2.64787 1.00000 1.00000 4.01123 −3.70858
1.6 1.00000 −2.45055 1.00000 −1.39178 −2.45055 1.00000 1.00000 3.00517 −1.39178
1.7 1.00000 −2.05592 1.00000 0.0511127 −2.05592 1.00000 1.00000 1.22679 0.0511127
1.8 1.00000 −1.92779 1.00000 4.40026 −1.92779 1.00000 1.00000 0.716369 4.40026
1.9 1.00000 −1.44788 1.00000 2.75672 −1.44788 1.00000 1.00000 −0.903639 2.75672
1.10 1.00000 −1.34024 1.00000 2.37980 −1.34024 1.00000 1.00000 −1.20375 2.37980
1.11 1.00000 −1.32232 1.00000 −1.62109 −1.32232 1.00000 1.00000 −1.25146 −1.62109
1.12 1.00000 −0.827780 1.00000 −4.23980 −0.827780 1.00000 1.00000 −2.31478 −4.23980
1.13 1.00000 −0.676569 1.00000 1.60949 −0.676569 1.00000 1.00000 −2.54225 1.60949
1.14 1.00000 −0.368112 1.00000 1.13454 −0.368112 1.00000 1.00000 −2.86449 1.13454
1.15 1.00000 −0.120971 1.00000 3.54943 −0.120971 1.00000 1.00000 −2.98537 3.54943
1.16 1.00000 −0.111656 1.00000 −1.58993 −0.111656 1.00000 1.00000 −2.98753 −1.58993
1.17 1.00000 −0.0841654 1.00000 3.03532 −0.0841654 1.00000 1.00000 −2.99292 3.03532
1.18 1.00000 0.510622 1.00000 −1.22941 0.510622 1.00000 1.00000 −2.73927 −1.22941
1.19 1.00000 0.603112 1.00000 −3.65115 0.603112 1.00000 1.00000 −2.63626 −3.65115
1.20 1.00000 0.913939 1.00000 −2.72754 0.913939 1.00000 1.00000 −2.16472 −2.72754
See all 31 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.31
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(2\) \(-1\)
\(7\) \(-1\)
\(431\) \(-1\)

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 6034.2.a.q ✓ 31
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6034.2.a.q ✓ 31 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(6034))\):

\( T_{3}^{31} - 2 T_{3}^{30} - 66 T_{3}^{29} + 121 T_{3}^{28} + 1952 T_{3}^{27} - 3226 T_{3}^{26} + \cdots + 4000 \) Copy content Toggle raw display
\( T_{5}^{31} - 13 T_{5}^{30} - 26 T_{5}^{29} + 1021 T_{5}^{28} - 2041 T_{5}^{27} - 32817 T_{5}^{26} + \cdots + 1373520896 \) Copy content Toggle raw display
\( T_{11}^{31} - 28 T_{11}^{30} + 205 T_{11}^{29} + 1402 T_{11}^{28} - 27400 T_{11}^{27} + \cdots - 154646665216 \) Copy content Toggle raw display