Properties

Label 2563.2.a.j
Level $2563$
Weight $2$
Character orbit 2563.a
Self dual yes
Analytic conductor $20.466$
Analytic rank $0$
Dimension $45$
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] = [2563,2,Mod(1,2563)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2563, 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("2563.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2563 = 11 \cdot 233 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2563.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: \(20.4656580381\)
Analytic rank: \(0\)
Dimension: \(45\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 45 q + 12 q^{2} + 5 q^{3} + 54 q^{4} + 29 q^{5} - 2 q^{6} - 22 q^{7} + 36 q^{8} + 52 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 45 q + 12 q^{2} + 5 q^{3} + 54 q^{4} + 29 q^{5} - 2 q^{6} - 22 q^{7} + 36 q^{8} + 52 q^{9} + 10 q^{10} - 45 q^{11} + 39 q^{12} + 8 q^{13} + 24 q^{14} + 42 q^{15} + 64 q^{16} + 20 q^{17} + 27 q^{18} - 20 q^{19} + 66 q^{20} - 8 q^{21} - 12 q^{22} + 22 q^{23} - 2 q^{24} + 80 q^{25} + 26 q^{26} + 32 q^{27} - 39 q^{28} + 12 q^{29} + 16 q^{30} + 32 q^{31} + 79 q^{32} - 5 q^{33} + 47 q^{34} + 24 q^{35} + 70 q^{36} + 33 q^{37} + 46 q^{38} + 17 q^{40} + 9 q^{41} + 6 q^{42} - 22 q^{43} - 54 q^{44} + 83 q^{45} + 13 q^{46} + 85 q^{47} + 62 q^{48} + 67 q^{49} + 27 q^{50} + 8 q^{51} + 9 q^{52} + 56 q^{53} - 35 q^{54} - 29 q^{55} + 6 q^{56} + 14 q^{57} + 42 q^{58} + 28 q^{59} + 115 q^{60} + 6 q^{61} + 57 q^{62} - 52 q^{63} + 152 q^{64} + 31 q^{65} + 2 q^{66} + 23 q^{67} - 2 q^{68} + 28 q^{69} + 85 q^{70} + 6 q^{71} + 45 q^{72} + 17 q^{73} - 14 q^{74} + 76 q^{75} + 19 q^{76} + 22 q^{77} - 106 q^{78} - 75 q^{79} + 41 q^{80} + 101 q^{81} + 69 q^{82} + 43 q^{83} + 5 q^{84} + 42 q^{85} + 57 q^{86} + 19 q^{87} - 36 q^{88} + 5 q^{89} + 52 q^{90} - 7 q^{91} + 64 q^{92} + 81 q^{93} - 40 q^{94} + 9 q^{95} + 39 q^{96} + 58 q^{97} + 90 q^{98} - 52 q^{99}+O(q^{100}) \) Copy content Toggle raw display

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 −2.70718 1.46397 5.32882 0.250551 −3.96323 −0.994047 −9.01171 −0.856791 −0.678287
1.2 −2.58654 2.77304 4.69019 4.02297 −7.17259 −0.351276 −6.95830 4.68977 −10.4056
1.3 −2.52909 −0.770947 4.39628 3.50476 1.94979 −4.50615 −6.06041 −2.40564 −8.86386
1.4 −2.34189 −1.85027 3.48444 −1.38150 4.33312 −0.582255 −3.47639 0.423486 3.23532
1.5 −2.30257 0.482027 3.30185 −2.32678 −1.10990 −2.51327 −2.99761 −2.76765 5.35759
1.6 −1.89466 2.99980 1.58973 2.28311 −5.68360 −3.69382 0.777328 5.99881 −4.32571
1.7 −1.82664 −0.0402198 1.33663 0.447996 0.0734673 1.52619 1.21174 −2.99838 −0.818330
1.8 −1.79218 −2.15949 1.21192 −0.344282 3.87021 2.09531 1.41238 1.66341 0.617016
1.9 −1.75979 3.40508 1.09688 −2.18301 −5.99224 −0.895247 1.58931 8.59457 3.84165
1.10 −1.57507 2.56434 0.480842 3.68930 −4.03901 4.54649 2.39278 3.57582 −5.81090
1.11 −1.44485 −1.97476 0.0875777 0.813719 2.85322 −3.62864 2.76315 0.899659 −1.17570
1.12 −1.25993 −2.65835 −0.412587 4.38316 3.34933 −2.39478 3.03968 4.06685 −5.52246
1.13 −1.23616 0.970298 −0.471908 0.266522 −1.19944 −1.54832 3.05567 −2.05852 −0.329464
1.14 −1.12952 −2.93696 −0.724192 −2.56654 3.31735 0.444238 3.07702 5.62575 2.89895
1.15 −1.02056 −0.462786 −0.958455 1.71072 0.472301 −4.72321 3.01928 −2.78583 −1.74589
1.16 −0.957968 0.934427 −1.08230 3.06265 −0.895151 1.67167 2.95274 −2.12685 −2.93392
1.17 −0.827030 −1.01201 −1.31602 −2.77734 0.836966 2.14903 2.74245 −1.97583 2.29695
1.18 −0.617158 1.85866 −1.61912 −2.84817 −1.14709 −4.80487 2.23357 0.454614 1.75777
1.19 −0.0567764 −1.29238 −1.99678 3.37731 0.0733764 2.30084 0.226923 −1.32977 −0.191751
1.20 0.0394839 0.213929 −1.99844 −1.33992 0.00844676 −3.36689 −0.157874 −2.95423 −0.0529053
See all 45 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.45
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(11\) \(1\)
\(233\) \(-1\)

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 2563.2.a.j 45
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
2563.2.a.j 45 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(2563))\):

\( T_{2}^{45} - 12 T_{2}^{44} + 548 T_{2}^{42} - 1579 T_{2}^{41} - 10319 T_{2}^{40} + 51320 T_{2}^{39} + 91836 T_{2}^{38} - 844192 T_{2}^{37} - 99019 T_{2}^{36} + 8784896 T_{2}^{35} - 7305788 T_{2}^{34} - 62516652 T_{2}^{33} + \cdots + 11304 \) Copy content Toggle raw display
\( T_{3}^{45} - 5 T_{3}^{44} - 81 T_{3}^{43} + 426 T_{3}^{42} + 2987 T_{3}^{41} - 16680 T_{3}^{40} - 66403 T_{3}^{39} + 398477 T_{3}^{38} + 992611 T_{3}^{37} - 6503200 T_{3}^{36} - 10523931 T_{3}^{35} + 76931054 T_{3}^{34} + \cdots - 8192 \) Copy content Toggle raw display