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Properties

Label 8035.2.a.c
Level $8035$
Weight $2$
Character orbit 8035.a
Self dual yes
Analytic conductor $64.160$
Analytic rank $0$
Dimension $127$
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] = [8035,2,Mod(1,8035)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8035, 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("8035.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8035 = 5 \cdot 1607 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8035.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: \(64.1597980241\)
Analytic rank: \(0\)
Dimension: \(127\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 127 q + 19 q^{2} + 10 q^{3} + 125 q^{4} - 127 q^{5} + 13 q^{7} + 54 q^{8} + 123 q^{9} - 19 q^{10} + 30 q^{11} + 35 q^{12} + 30 q^{13} + 39 q^{14} - 10 q^{15} + 121 q^{16} + 63 q^{17} + 53 q^{18} - 35 q^{19} - 125 q^{20} + 33 q^{21} + 49 q^{22} + 61 q^{23} - 5 q^{24} + 127 q^{25} + 10 q^{26} + 40 q^{27} + 32 q^{28} + 134 q^{29} - 25 q^{31} + 122 q^{32} + 48 q^{33} - 21 q^{34} - 13 q^{35} + 133 q^{36} + 60 q^{37} + 33 q^{38} + 26 q^{39} - 54 q^{40} + 9 q^{41} + 45 q^{42} + 48 q^{43} + 85 q^{44} - 123 q^{45} - 11 q^{46} + 57 q^{47} + 71 q^{48} + 70 q^{49} + 19 q^{50} + 45 q^{51} + 68 q^{52} + 182 q^{53} - 29 q^{54} - 30 q^{55} + 96 q^{56} + 74 q^{57} + 47 q^{58} + 19 q^{59} - 35 q^{60} + 16 q^{61} + 43 q^{62} + 73 q^{63} + 110 q^{64} - 30 q^{65} + 8 q^{66} + 40 q^{67} + 129 q^{68} + 2 q^{69} - 39 q^{70} + 48 q^{71} + 151 q^{72} + 30 q^{73} + 117 q^{74} + 10 q^{75} - 98 q^{76} + 134 q^{77} + 54 q^{78} + 23 q^{79} - 121 q^{80} + 111 q^{81} + 4 q^{82} + 92 q^{83} + 48 q^{84} - 63 q^{85} + 42 q^{86} + 69 q^{87} + 121 q^{88} + 12 q^{89} - 53 q^{90} - 30 q^{91} + 175 q^{92} + 82 q^{93} - 23 q^{94} + 35 q^{95} + 6 q^{96} + 67 q^{97} + 122 q^{98} + 73 q^{99}+O(q^{100}) \) 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 −2.73873 0.672106 5.50064 −1.00000 −1.84072 −4.04942 −9.58729 −2.54827 2.73873
1.2 −2.68442 −1.35317 5.20611 −1.00000 3.63248 −0.554981 −8.60654 −1.16892 2.68442
1.3 −2.65256 2.52646 5.03608 −1.00000 −6.70158 −1.65453 −8.05337 3.38299 2.65256
1.4 −2.61836 3.26899 4.85584 −1.00000 −8.55940 1.91983 −7.47762 7.68627 2.61836
1.5 −2.47063 −2.44892 4.10400 −1.00000 6.05037 0.863350 −5.19820 2.99721 2.47063
1.6 −2.46463 −1.44696 4.07438 −1.00000 3.56623 3.47016 −5.11258 −0.906295 2.46463
1.7 −2.44893 0.721523 3.99726 −1.00000 −1.76696 −0.931483 −4.89116 −2.47940 2.44893
1.8 −2.44268 2.17434 3.96666 −1.00000 −5.31121 1.92177 −4.80392 1.72777 2.44268
1.9 −2.42672 −1.34880 3.88897 −1.00000 3.27316 −0.627259 −4.58399 −1.18074 2.42672
1.10 −2.38169 0.502549 3.67242 −1.00000 −1.19691 1.76739 −3.98319 −2.74744 2.38169
1.11 −2.33324 −1.40461 3.44401 −1.00000 3.27730 −3.84799 −3.36922 −1.02706 2.33324
1.12 −2.32831 1.94155 3.42102 −1.00000 −4.52053 0.423460 −3.30857 0.769626 2.32831
1.13 −2.25182 0.156734 3.07069 −1.00000 −0.352938 4.92465 −2.41100 −2.97543 2.25182
1.14 −2.23096 0.376155 2.97717 −1.00000 −0.839185 −1.46614 −2.18003 −2.85851 2.23096
1.15 −2.19837 −2.82193 2.83283 −1.00000 6.20363 2.67326 −1.83086 4.96326 2.19837
1.16 −2.17325 2.30276 2.72303 −1.00000 −5.00447 −1.58489 −1.57132 2.30268 2.17325
1.17 −2.09243 −1.43223 2.37828 −1.00000 2.99685 −1.24970 −0.791531 −0.948714 2.09243
1.18 −2.07647 −1.16893 2.31172 −1.00000 2.42725 −0.555409 −0.647270 −1.63360 2.07647
1.19 −2.04769 1.24838 2.19303 −1.00000 −2.55629 −4.80946 −0.395268 −1.44156 2.04769
1.20 −1.99934 −2.20170 1.99734 −1.00000 4.40194 0.230566 0.00531235 1.84749 1.99934
See next 80 embeddings (of 127 total)
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.127
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(1\)
\(1607\) \(-1\)

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 8035.2.a.c ✓ 127
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8035.2.a.c ✓ 127 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{127} - 19 T_{2}^{126} - 9 T_{2}^{125} + 2414 T_{2}^{124} - 10468 T_{2}^{123} - 135985 T_{2}^{122} + \cdots - 28908672 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(8035))\). Copy content Toggle raw display