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Properties

Label 667.4.a.d
Level $667$
Weight $4$
Character orbit 667.a
Self dual yes
Analytic conductor $39.354$
Analytic rank $0$
Dimension $42$
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: \(0\)
Dimension: \(42\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 42 q + 12 q^{2} + 32 q^{3} + 192 q^{4} + 80 q^{5} + 32 q^{6} + 18 q^{7} + 102 q^{8} + 492 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 42 q + 12 q^{2} + 32 q^{3} + 192 q^{4} + 80 q^{5} + 32 q^{6} + 18 q^{7} + 102 q^{8} + 492 q^{9} + 48 q^{10} + 50 q^{11} + 403 q^{12} + 236 q^{13} + 32 q^{14} + 12 q^{15} + 792 q^{16} + 456 q^{17} + 297 q^{18} + 166 q^{19} + 533 q^{20} + 258 q^{21} + 73 q^{22} + 966 q^{23} + 514 q^{24} + 1358 q^{25} + 497 q^{26} + 1250 q^{27} + 143 q^{28} + 1218 q^{29} + 593 q^{30} + 558 q^{31} + 1328 q^{32} - 464 q^{33} + 157 q^{34} + 48 q^{35} + 3030 q^{36} + 352 q^{37} + 218 q^{38} + 1080 q^{39} + 900 q^{40} + 182 q^{41} + 272 q^{42} + 870 q^{43} + 925 q^{44} + 1238 q^{45} + 276 q^{46} + 2058 q^{47} + 4057 q^{48} + 3340 q^{49} + 981 q^{50} + 750 q^{51} + 1850 q^{52} + 2412 q^{53} + 1643 q^{54} + 1506 q^{55} + 671 q^{56} + 516 q^{57} + 348 q^{58} + 2958 q^{59} + 2445 q^{60} + 902 q^{61} + 1123 q^{62} + 296 q^{63} + 3234 q^{64} + 682 q^{65} - 1007 q^{66} - 612 q^{67} + 6445 q^{68} + 736 q^{69} - 608 q^{70} + 1358 q^{71} + 3475 q^{72} + 3102 q^{73} + 777 q^{74} + 2362 q^{75} - 1034 q^{76} + 6440 q^{77} - 430 q^{78} + 614 q^{79} - 272 q^{80} + 6622 q^{81} + 3749 q^{82} + 1910 q^{83} - 582 q^{84} + 4156 q^{85} + 3071 q^{86} + 928 q^{87} + 2584 q^{88} + 3768 q^{89} + 6545 q^{90} - 844 q^{91} + 4416 q^{92} + 3032 q^{93} + 1671 q^{94} + 2432 q^{95} - 1812 q^{96} + 4086 q^{97} + 4714 q^{98} + 3490 q^{99}+O(q^{100}) \) 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 −5.34818 10.0634 20.6030 −5.23098 −53.8209 −13.7162 −67.4031 74.2721 27.9762
1.2 −5.18703 −0.346340 18.9052 7.82679 1.79647 8.42383 −56.5658 −26.8800 −40.5978
1.3 −5.06294 −6.04876 17.6334 −11.8574 30.6245 −3.12117 −48.7732 9.58753 60.0335
1.4 −4.69994 4.13115 14.0895 −11.4333 −19.4162 −6.53014 −28.6202 −9.93361 53.7360
1.5 −4.56359 −0.269361 12.8263 21.6794 1.22925 25.3254 −22.0254 −26.9274 −98.9360
1.6 −4.51172 −7.43675 12.3557 9.90904 33.5526 −10.9332 −19.6515 28.3053 −44.7069
1.7 −4.47663 8.88487 12.0402 10.8211 −39.7743 21.9631 −18.0867 51.9409 −48.4421
1.8 −3.74432 2.41513 6.01991 −5.13945 −9.04301 −16.2081 7.41408 −21.1672 19.2437
1.9 −3.62930 −1.61098 5.17183 16.8422 5.84675 −35.7633 10.2643 −24.4047 −61.1254
1.10 −3.10621 −8.58801 1.64852 −13.6382 26.6761 9.12594 19.7290 46.7540 42.3630
1.11 −2.97874 −2.22945 0.872874 −6.21372 6.64095 28.7287 21.2298 −22.0295 18.5090
1.12 −2.75458 7.67140 −0.412264 13.7387 −21.1315 11.6713 23.1723 31.8504 −37.8443
1.13 −2.59031 4.49667 −1.29030 −11.5048 −11.6477 11.5655 24.0647 −6.78000 29.8009
1.14 −2.01617 7.16294 −3.93505 10.4747 −14.4417 −27.1602 24.0631 24.3077 −21.1187
1.15 −1.43574 −3.02468 −5.93866 6.36146 4.34265 4.92463 20.0123 −17.8513 −9.13340
1.16 −1.41233 −8.74257 −6.00533 19.8782 12.3474 −23.0508 19.7801 49.4326 −28.0745
1.17 −1.17094 −9.30199 −6.62890 −0.0203671 10.8920 9.72814 17.1295 59.5270 0.0238486
1.18 −0.870037 8.00646 −7.24304 −12.7085 −6.96592 33.2612 13.2620 37.1034 11.0569
1.19 −0.606522 7.43273 −7.63213 −17.7976 −4.50812 −35.8438 9.48124 28.2455 10.7946
1.20 −0.322838 0.518190 −7.89578 11.3656 −0.167291 11.7064 5.13176 −26.7315 −3.66926
See all 42 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.42
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.d ✓ 42
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
667.4.a.d ✓ 42 1.a even 1 1 trivial