↑

Properties

Label 8027.2.a.e
Level $8027$
Weight $2$
Character orbit 8027.a
Self dual yes
Analytic conductor $64.096$
Analytic rank $0$
Dimension $169$
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] = [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: \(0\)
Dimension: \(169\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 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 −2.75446 1.69224 5.58704 1.99190 −4.66119 −2.92850 −9.88036 −0.136337 −5.48661
1.2 −2.75254 −1.96907 5.57647 −0.0473576 5.41994 2.07710 −9.84438 0.877234 0.130354
1.3 −2.71035 −1.96664 5.34597 2.92225 5.33028 3.98832 −9.06874 0.867686 −7.92031
1.4 −2.70848 3.38397 5.33587 −0.801714 −9.16542 2.62162 −9.03513 8.45127 2.17143
1.5 −2.70691 1.62616 5.32735 −1.60888 −4.40186 −2.81542 −9.00682 −0.355610 4.35510
1.6 −2.69664 −0.711836 5.27186 2.29086 1.91957 3.32005 −8.82303 −2.49329 −6.17762
1.7 −2.69608 1.22457 5.26883 −1.75306 −3.30153 4.29034 −8.81301 −1.50043 4.72638
1.8 −2.66018 0.0465626 5.07657 −3.78943 −0.123865 2.50882 −8.18425 −2.99783 10.0806
1.9 −2.60952 −0.136825 4.80961 −0.260304 0.357049 −0.298256 −7.33174 −2.98128 0.679270
1.10 −2.60584 −2.87607 4.79042 −4.02377 7.49460 0.529095 −7.27140 5.27181 10.4853
1.11 −2.57271 0.131094 4.61881 4.05012 −0.337267 −4.42802 −6.73744 −2.98281 −10.4198
1.12 −2.50053 2.23425 4.25264 −3.72100 −5.58681 −1.83421 −5.63280 1.99189 9.30447
1.13 −2.48779 −1.56706 4.18912 −0.470974 3.89852 −0.335999 −5.44607 −0.544327 1.17169
1.14 −2.47925 −2.94109 4.14669 −0.477027 7.29170 −3.55930 −5.32218 5.65002 1.18267
1.15 −2.47225 −1.54593 4.11203 3.04029 3.82192 −2.57940 −5.22147 −0.610108 −7.51637
1.16 −2.43156 2.09261 3.91247 2.37281 −5.08829 3.03145 −4.65029 1.37900 −5.76963
1.17 −2.35712 0.851105 3.55600 1.53859 −2.00615 0.407410 −3.66768 −2.27562 −3.62663
1.18 −2.35439 −0.664496 3.54317 −2.57609 1.56449 5.27951 −3.63324 −2.55844 6.06514
1.19 −2.32136 −1.73102 3.38869 −3.82853 4.01832 −3.14873 −3.22365 −0.00355516 8.88737
1.20 −2.31715 2.98534 3.36921 4.10060 −6.91750 4.34971 −3.17266 5.91228 −9.50172
See next 80 embeddings (of 169 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.169
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.e ✓ 169
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8027.2.a.e ✓ 169 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{169} - 6 T_{2}^{168} - 244 T_{2}^{167} + 1522 T_{2}^{166} + 29077 T_{2}^{165} + \cdots - 90567403569152 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8027))\). Copy content Toggle raw display