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Properties

Label 8015.2.a.m
Level $8015$
Weight $2$
Character orbit 8015.a
Self dual yes
Analytic conductor $64.000$
Analytic rank $0$
Dimension $67$
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] = [8015,2,Mod(1,8015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8015, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("8015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8015.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: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(67\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 67 q + 3 q^{2} + 73 q^{4} + 67 q^{5} + 17 q^{6} - 67 q^{7} + 12 q^{8} + 97 q^{9} + 3 q^{10} + 11 q^{11} + 9 q^{12} + 19 q^{13} - 3 q^{14} + 93 q^{16} + 7 q^{17} + 9 q^{18} + 36 q^{19} + 73 q^{20} - 8 q^{22} - 2 q^{23} + 37 q^{24} + 67 q^{25} + 39 q^{26} + 6 q^{27} - 73 q^{28} + 56 q^{29} + 17 q^{30} + 63 q^{31} + 27 q^{32} + 51 q^{33} + 55 q^{34} - 67 q^{35} + 148 q^{36} + 28 q^{37} + 10 q^{38} + 7 q^{39} + 12 q^{40} + 84 q^{41} - 17 q^{42} - 11 q^{43} + 41 q^{44} + 97 q^{45} + 17 q^{46} - 10 q^{47} + 10 q^{48} + 67 q^{49} + 3 q^{50} - q^{51} + 49 q^{52} + 3 q^{53} + 20 q^{54} + 11 q^{55} - 12 q^{56} + 45 q^{57} + 22 q^{58} + 80 q^{59} + 9 q^{60} + 64 q^{61} - 37 q^{62} - 97 q^{63} + 110 q^{64} + 19 q^{65} + 75 q^{66} + 22 q^{67} + 7 q^{68} + 107 q^{69} - 3 q^{70} + 24 q^{71} + 72 q^{72} + 83 q^{73} + 52 q^{74} + 115 q^{76} - 11 q^{77} - 70 q^{78} - 32 q^{79} + 93 q^{80} + 183 q^{81} + 56 q^{82} - 58 q^{83} - 9 q^{84} + 7 q^{85} + 51 q^{86} + 20 q^{87} - 5 q^{88} + 129 q^{89} + 9 q^{90} - 19 q^{91} - 37 q^{92} + 33 q^{93} + 89 q^{94} + 36 q^{95} + 129 q^{96} + 126 q^{97} + 3 q^{98} - 27 q^{99}+O(q^{100}) \) 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 −2.79998 −2.08197 5.83989 1.00000 5.82947 −1.00000 −10.7516 1.33460 −2.79998
1.2 −2.72902 1.60790 5.44753 1.00000 −4.38799 −1.00000 −9.40835 −0.414653 −2.72902
1.3 −2.66598 2.60914 5.10744 1.00000 −6.95591 −1.00000 −8.28438 3.80761 −2.66598
1.4 −2.55168 −1.07267 4.51109 1.00000 2.73711 −1.00000 −6.40752 −1.84938 −2.55168
1.5 −2.54658 −2.85949 4.48508 1.00000 7.28192 −1.00000 −6.32845 5.17667 −2.54658
1.6 −2.53656 −2.78475 4.43415 1.00000 7.06368 −1.00000 −6.17438 4.75481 −2.53656
1.7 −2.40339 −1.71467 3.77630 1.00000 4.12102 −1.00000 −4.26915 −0.0599106 −2.40339
1.8 −2.30662 1.34001 3.32049 1.00000 −3.09089 −1.00000 −3.04587 −1.20437 −2.30662
1.9 −2.25277 3.29965 3.07495 1.00000 −7.43334 −1.00000 −2.42162 7.88769 −2.25277
1.10 −2.05677 1.58909 2.23031 1.00000 −3.26839 −1.00000 −0.473688 −0.474802 −2.05677
1.11 −1.94503 2.18285 1.78313 1.00000 −4.24571 −1.00000 0.421811 1.76484 −1.94503
1.12 −1.89706 −1.32001 1.59885 1.00000 2.50414 −1.00000 0.761013 −1.25758 −1.89706
1.13 −1.83785 1.36680 1.37770 1.00000 −2.51199 −1.00000 1.14369 −1.13184 −1.83785
1.14 −1.82956 −1.24341 1.34731 1.00000 2.27489 −1.00000 1.19414 −1.45394 −1.82956
1.15 −1.80341 0.567965 1.25230 1.00000 −1.02428 −1.00000 1.34841 −2.67742 −1.80341
1.16 −1.76232 −3.28691 1.10578 1.00000 5.79259 −1.00000 1.57590 7.80377 −1.76232
1.17 −1.76209 −0.304110 1.10496 1.00000 0.535869 −1.00000 1.57714 −2.90752 −1.76209
1.18 −1.50021 0.266806 0.250644 1.00000 −0.400267 −1.00000 2.62441 −2.92881 −1.50021
1.19 −1.44039 2.88342 0.0747197 1.00000 −4.15325 −1.00000 2.77315 5.31413 −1.44039
1.20 −1.42994 −3.33526 0.0447232 1.00000 4.76921 −1.00000 2.79592 8.12394 −1.42994
See all 67 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.67
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(5\) \(-1\)
\(7\) \(1\)
\(229\) \(1\)

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 8015.2.a.m ✓ 67
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8015.2.a.m ✓ 67 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 \(S_{2}^{\mathrm{new}}(\Gamma_0(8015))\):

\( T_{2}^{67} - 3 T_{2}^{66} - 99 T_{2}^{65} + 298 T_{2}^{64} + 4651 T_{2}^{63} - 14049 T_{2}^{62} + \cdots - 2440 \) Copy content Toggle raw display
\( T_{3}^{67} - 149 T_{3}^{65} - 2 T_{3}^{64} + 10535 T_{3}^{63} + 281 T_{3}^{62} - 470399 T_{3}^{61} + \cdots + 4713433856 \) Copy content Toggle raw display