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Properties

Label 667.4.a.b
Level $667$
Weight $4$
Character orbit 667.a
Self dual yes
Analytic conductor $39.354$
Analytic rank $1$
Dimension $38$
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] = [667,4,Mod(1,667)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(667, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("667.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 667 = 23 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 667.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: \(39.3542739738\)
Analytic rank: \(1\)
Dimension: \(38\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 38 q - 8 q^{2} - 16 q^{3} + 152 q^{4} - 80 q^{5} - 16 q^{6} - 38 q^{7} - 138 q^{8} + 312 q^{9} + 30 q^{10} - 100 q^{11} - 173 q^{12} - 160 q^{13} - 304 q^{14} - 208 q^{15} + 552 q^{16} - 666 q^{17} - 315 q^{18} - 252 q^{19} - 747 q^{20} - 470 q^{21} - 323 q^{22} - 874 q^{23} - 114 q^{24} + 910 q^{25} - 119 q^{26} - 526 q^{27} - 619 q^{28} + 1102 q^{29} - 533 q^{30} + 358 q^{31} - 1272 q^{32} - 604 q^{33} - 553 q^{34} + 16 q^{35} + 1230 q^{36} - 1206 q^{37} - 2010 q^{38} - 240 q^{39} - 418 q^{40} - 1094 q^{41} - 1184 q^{42} - 936 q^{43} - 2153 q^{44} - 3654 q^{45} + 184 q^{46} - 1702 q^{47} - 1319 q^{48} + 1920 q^{49} - 1255 q^{50} - 270 q^{51} - 2202 q^{52} - 4640 q^{53} - 1529 q^{54} - 318 q^{55} - 2435 q^{56} - 1980 q^{57} - 232 q^{58} + 318 q^{59} - 3279 q^{60} - 2212 q^{61} - 541 q^{62} - 1044 q^{63} + 1186 q^{64} - 2438 q^{65} - 3503 q^{66} - 496 q^{67} - 6099 q^{68} + 368 q^{69} + 4068 q^{70} + 870 q^{71} - 3869 q^{72} - 2810 q^{73} - 2793 q^{74} - 3638 q^{75} + 1548 q^{76} - 6072 q^{77} + 2170 q^{78} - 3084 q^{79} - 6702 q^{80} + 362 q^{81} - 1183 q^{82} - 5566 q^{83} - 6518 q^{84} - 120 q^{85} - 2095 q^{86} - 464 q^{87} - 1220 q^{88} - 6506 q^{89} + 165 q^{90} + 44 q^{91} - 3496 q^{92} - 5928 q^{93} + 135 q^{94} - 2024 q^{95} - 3164 q^{96} - 7472 q^{97} - 6422 q^{98} - 944 q^{99}+O(q^{100}) \) 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 −5.54069 7.25408 22.6992 −1.00273 −40.1926 21.1757 −81.4436 25.6216 5.55579
1.2 −5.43173 −4.78736 21.5037 −12.1368 26.0036 −29.3395 −73.3484 −4.08118 65.9237
1.3 −5.35786 −0.00570496 20.7066 9.87535 0.0305663 −29.9798 −68.0802 −27.0000 −52.9107
1.4 −4.91998 −9.49828 16.2062 −7.62709 46.7314 33.3863 −40.3745 63.2173 37.5252
1.5 −4.44148 −3.45670 11.7268 −19.6259 15.3529 26.9979 −16.5525 −15.0512 87.1682
1.6 −4.37266 7.78228 11.1201 −21.2612 −34.0292 6.24212 −13.6432 33.5639 92.9680
1.7 −4.30484 0.114361 10.5317 −5.91462 −0.492305 1.39837 −10.8985 −26.9869 25.4615
1.8 −4.18330 −8.85462 9.49996 14.6844 37.0415 14.9595 −6.27477 51.4042 −61.4293
1.9 −4.06003 6.74784 8.48386 12.9697 −27.3964 −17.1781 −1.96449 18.5333 −52.6574
1.10 −3.44620 −6.39529 3.87626 0.297471 22.0394 −23.6794 14.2112 13.8998 −1.02514
1.11 −3.00363 3.71540 1.02177 −0.444975 −11.1597 3.04181 20.9600 −13.1958 1.33654
1.12 −2.76563 −5.36353 −0.351302 13.3111 14.8335 8.21355 23.0966 1.76742 −36.8135
1.13 −2.59207 8.27541 −1.28115 −19.7193 −21.4505 −8.50543 24.0574 41.4824 51.1140
1.14 −2.57414 1.72681 −1.37379 7.29105 −4.44507 28.8124 24.1295 −24.0181 −18.7682
1.15 −1.41094 9.12946 −6.00925 3.29678 −12.8811 −5.15545 19.7662 56.3470 −4.65156
1.16 −1.24608 −4.40724 −6.44729 −15.1310 5.49176 −22.0117 18.0024 −7.57625 18.8544
1.17 −0.977530 −4.09937 −7.04444 −14.8883 4.00725 19.8759 14.7064 −10.1952 14.5538
1.18 −0.460454 1.16842 −7.78798 16.4926 −0.538005 −29.6525 7.26964 −25.6348 −7.59408
1.19 −0.422470 −3.15773 −7.82152 15.9122 1.33405 10.1538 6.68412 −17.0287 −6.72244
1.20 −0.110439 4.20263 −7.98780 −3.45054 −0.464136 −7.85612 1.76568 −9.33789 0.381076
See all 38 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.38
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(23\) \(1\)
\(29\) \(-1\)

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 667.4.a.b ✓ 38
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
667.4.a.b ✓ 38 1.a even 1 1 trivial