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Properties

Label 667.4.a.a
Level $667$
Weight $4$
Character orbit 667.a
Self dual yes
Analytic conductor $39.354$
Analytic rank $1$
Dimension $35$
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: \(35\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 35 q - 6 q^{2} - 22 q^{3} + 116 q^{4} - 80 q^{5} - 52 q^{6} - 38 q^{7} + 12 q^{8} + 231 q^{9} - 52 q^{10} - 126 q^{11} - 173 q^{12} - 252 q^{13} + 112 q^{14} - 32 q^{15} + 312 q^{16} - 332 q^{17} - 225 q^{18} - 2 q^{19} - 747 q^{20} - 202 q^{21} - 127 q^{22} + 805 q^{23} - 494 q^{24} + 315 q^{25} - 677 q^{26} - 694 q^{27} - 529 q^{28} - 1015 q^{29} + 389 q^{30} - 652 q^{31} + 320 q^{32} - 290 q^{33} - 455 q^{34} - 940 q^{35} + 34 q^{36} - 528 q^{37} - 1218 q^{38} - 268 q^{39} - 806 q^{40} - 68 q^{41} - 1484 q^{42} - 162 q^{43} - 1817 q^{44} - 356 q^{45} - 138 q^{46} - 1200 q^{47} - 2153 q^{48} + 93 q^{49} - 1369 q^{50} - 270 q^{51} - 3134 q^{52} - 1892 q^{53} - 1221 q^{54} - 794 q^{55} + 191 q^{56} - 1764 q^{57} + 174 q^{58} - 1354 q^{59} + 159 q^{60} - 1274 q^{61} - 5413 q^{62} - 2904 q^{63} - 926 q^{64} - 548 q^{65} - 2477 q^{66} - 3212 q^{67} - 3901 q^{68} - 506 q^{69} - 2768 q^{70} - 2342 q^{71} - 2381 q^{72} + 916 q^{73} + 661 q^{74} - 4708 q^{75} - 2810 q^{76} - 5536 q^{77} - 2434 q^{78} + 2622 q^{79} - 5444 q^{80} + 607 q^{81} - 3687 q^{82} - 2702 q^{83} + 346 q^{84} - 3304 q^{85} - 5789 q^{86} + 638 q^{87} - 2252 q^{88} - 1620 q^{89} - 3933 q^{90} - 4016 q^{91} + 2668 q^{92} - 4942 q^{93} - 1413 q^{94} - 4528 q^{95} - 7920 q^{96} + 682 q^{97} + 152 q^{98} - 582 q^{99}+O(q^{100}) \) 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 −5.41821 0.781110 21.3570 −16.7774 −4.23222 14.7777 −72.3710 −26.3899 90.9037
1.2 −5.24031 4.66607 19.4609 9.98386 −24.4516 −16.6714 −60.0584 −5.22782 −52.3185
1.3 −4.91438 −10.0131 16.1511 −1.41280 49.2080 −21.8421 −40.0578 73.2613 6.94303
1.4 −4.19907 −3.86594 9.63220 12.3104 16.2333 −16.9484 −6.85372 −12.0545 −51.6921
1.5 −4.07352 −4.02776 8.59356 −4.16183 16.4072 24.6022 −2.41789 −10.7772 16.9533
1.6 −4.01219 7.50590 8.09767 −10.1837 −30.1151 25.8615 −0.391885 29.3385 40.8590
1.7 −3.92831 −0.211164 7.43163 −18.5732 0.829519 −32.9860 2.23274 −26.9554 72.9614
1.8 −3.82659 3.57847 6.64282 6.65081 −13.6933 1.73304 5.19338 −14.1946 −25.4500
1.9 −3.67556 10.1827 5.50978 −4.25672 −37.4273 −16.2530 9.15298 76.6884 15.6459
1.10 −3.39262 −6.34305 3.50985 8.60238 21.5195 26.6361 15.2334 13.2343 −29.1846
1.11 −3.16960 −6.32576 2.04637 −18.5438 20.0502 −11.5664 18.8706 13.0153 58.7765
1.12 −2.14069 0.495740 −3.41746 6.11352 −1.06122 −17.2027 24.4412 −26.7542 −13.0871
1.13 −1.53325 −8.54252 −5.64914 18.6586 13.0978 1.14332 20.9276 45.9746 −28.6084
1.14 −1.41885 2.17728 −5.98688 −20.3045 −3.08922 3.99179 19.8452 −22.2595 28.8089
1.15 −1.31602 6.47981 −6.26810 −5.97518 −8.52753 −2.56970 18.7770 14.9879 7.86343
1.16 −1.22695 5.07416 −6.49460 17.3553 −6.22572 −4.17288 17.7841 −1.25295 −21.2940
1.17 −0.421717 −6.03501 −7.82215 −0.362549 2.54506 −27.0061 6.67247 9.42130 0.152893
1.18 −0.356870 0.508952 −7.87264 −0.0507065 −0.181630 30.7062 5.66448 −26.7410 0.0180956
1.19 0.00139515 −3.25434 −8.00000 −15.5862 −0.00454029 11.5101 −0.0223224 −16.4093 −0.0217450
1.20 0.282966 8.03408 −7.91993 −4.50118 2.27337 −16.5936 −4.50481 37.5464 −1.27368
See all 35 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.35
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.a ✓ 35
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
667.4.a.a ✓ 35 1.a even 1 1 trivial