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Properties

Label 8027.2.a.c
Level $8027$
Weight $2$
Character orbit 8027.a
Self dual yes
Analytic conductor $64.096$
Analytic rank $1$
Dimension $143$
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] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, 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("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.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: \(64.0959177025\)
Analytic rank: \(1\)
Dimension: \(143\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 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 −2.81318 −2.25224 5.91397 2.72187 6.33595 −2.92129 −11.0107 2.07257 −7.65711
1.2 −2.73897 −2.10858 5.50198 −1.32967 5.77534 4.16128 −9.59184 1.44610 3.64193
1.3 −2.72223 2.61290 5.41054 −3.36664 −7.11292 −3.38304 −9.28427 3.82726 9.16478
1.4 −2.70535 −0.945977 5.31892 2.14258 2.55920 −0.218411 −8.97883 −2.10513 −5.79642
1.5 −2.66984 −0.755713 5.12803 0.937284 2.01763 2.29767 −8.35133 −2.42890 −2.50240
1.6 −2.65785 2.82218 5.06415 0.881121 −7.50092 1.80840 −8.14403 4.96471 −2.34188
1.7 −2.62887 1.58844 4.91095 0.705653 −4.17581 −0.559393 −7.65249 −0.476845 −1.85507
1.8 −2.59213 0.439138 4.71916 1.76571 −1.13830 3.87571 −7.04843 −2.80716 −4.57697
1.9 −2.56363 3.26823 4.57221 −1.87479 −8.37854 −1.87590 −6.59421 7.68132 4.80627
1.10 −2.54714 −2.88541 4.48790 −0.694174 7.34952 −2.36870 −6.33703 5.32557 1.76816
1.11 −2.53949 −2.72406 4.44903 −2.80223 6.91773 −4.07042 −6.21931 4.42048 7.11625
1.12 −2.53769 0.0556295 4.43986 2.89276 −0.141170 −5.18186 −6.19160 −2.99691 −7.34093
1.13 −2.48946 −0.455224 4.19741 −1.13104 1.13326 −1.16006 −5.47036 −2.79277 2.81568
1.14 −2.42374 0.415987 3.87452 −3.49995 −1.00824 −1.51919 −4.54334 −2.82696 8.48296
1.15 −2.40779 2.53147 3.79745 0.438044 −6.09525 1.85360 −4.32788 3.40834 −1.05472
1.16 −2.40357 1.04878 3.77713 −2.29703 −2.52082 −0.387376 −4.27144 −1.90005 5.52106
1.17 −2.32772 −2.91674 3.41827 2.71745 6.78934 4.37081 −3.30132 5.50736 −6.32547
1.18 −2.31697 −3.13483 3.36836 −3.69960 7.26332 1.63548 −3.17044 6.82718 8.57187
1.19 −2.31347 1.92997 3.35213 3.01701 −4.46493 −2.82894 −3.12810 0.724803 −6.97976
1.20 −2.30190 0.450462 3.29874 −0.676454 −1.03692 2.59801 −2.98957 −2.79708 1.55713
See next 80 embeddings (of 143 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.143
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(23\) \(-1\)
\(349\) \(-1\)

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 8027.2.a.c ✓ 143
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8027.2.a.c ✓ 143 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{143} + 17 T_{2}^{142} - 59 T_{2}^{141} - 2603 T_{2}^{140} - 5067 T_{2}^{139} + \cdots + 167871723280 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\). Copy content Toggle raw display