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Properties

Label 583.6.a.b
Level $583$
Weight $6$
Character orbit 583.a
Self dual yes
Analytic conductor $93.504$
Analytic rank $1$
Dimension $54$
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] = [583,6,Mod(1,583)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(583, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("583.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 583 = 11 \cdot 53 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 583.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: \(93.5037669510\)
Analytic rank: \(1\)
Dimension: \(54\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 54 q - 16 q^{2} + 906 q^{4} - 225 q^{5} - 197 q^{6} - 341 q^{7} - 1152 q^{8} + 4240 q^{9} - 233 q^{10} - 6534 q^{11} - 327 q^{12} - 1455 q^{13} + 2254 q^{14} - 694 q^{15} + 16610 q^{16} - 9275 q^{17} - 6797 q^{18} - 2515 q^{19} - 6840 q^{20} - 4744 q^{21} + 1936 q^{22} - 6307 q^{23} - 5681 q^{24} + 26923 q^{25} - 5196 q^{26} - 5190 q^{27} - 36405 q^{28} - 8356 q^{29} - 28719 q^{30} - 4357 q^{31} - 68580 q^{32} + 9406 q^{34} - 3747 q^{35} + 38059 q^{36} - 25798 q^{37} - 32169 q^{38} - 28347 q^{39} - 15014 q^{40} - 89685 q^{41} - 103207 q^{42} - 26640 q^{43} - 109626 q^{44} - 66786 q^{45} - 28271 q^{46} - 26237 q^{47} - 20371 q^{48} + 132327 q^{49} - 189646 q^{50} + 10856 q^{51} - 179789 q^{52} - 151686 q^{53} - 167182 q^{54} + 27225 q^{55} + 24845 q^{56} - 33857 q^{57} - 31384 q^{58} - 49035 q^{59} - 183481 q^{60} - 101718 q^{61} - 103315 q^{62} - 214794 q^{63} + 154912 q^{64} - 55703 q^{65} + 23837 q^{66} + 105905 q^{67} - 267681 q^{68} - 56033 q^{69} - 90034 q^{70} - 107016 q^{71} - 580829 q^{72} - 161641 q^{73} - 259552 q^{74} - 69519 q^{75} - 240846 q^{76} + 41261 q^{77} - 65716 q^{78} - 35649 q^{79} - 279887 q^{80} + 316682 q^{81} + 206196 q^{82} - 326347 q^{83} - 29955 q^{84} - 189486 q^{85} - 444656 q^{86} - 222331 q^{87} + 139392 q^{88} - 633400 q^{89} + 110940 q^{90} - 25954 q^{91} + 18304 q^{92} - 191747 q^{93} - 62405 q^{94} - 515756 q^{95} - 527591 q^{96} - 405641 q^{97} - 919621 q^{98} - 513040 q^{99}+O(q^{100}) \) 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 −11.1510 −28.0585 92.3451 −15.3290 312.881 −236.386 −672.909 544.281 170.934
1.2 −10.9473 10.7847 87.8440 102.528 −118.063 88.8850 −611.342 −126.691 −1122.41
1.3 −10.8429 29.3089 85.5693 −85.2940 −317.795 −75.1971 −580.848 616.014 924.838
1.4 −10.8269 −2.30005 85.2213 −14.6338 24.9024 179.554 −576.220 −237.710 158.438
1.5 −10.0399 −1.70053 68.8000 76.1717 17.0732 −193.816 −369.469 −240.108 −764.758
1.6 −9.75552 −19.3288 63.1702 −88.6690 188.563 16.0758 −304.081 130.603 865.013
1.7 −9.31377 −9.06870 54.7463 10.0233 84.4638 −45.5598 −211.854 −160.759 −93.3543
1.8 −9.07236 16.4473 50.3077 −94.9733 −149.216 75.8752 −166.094 27.5150 861.632
1.9 −8.95335 28.4271 48.1625 56.4574 −254.518 −39.3035 −144.709 565.100 −505.483
1.10 −8.25706 16.4110 36.1790 8.27809 −135.506 −11.5539 −34.5060 26.3207 −68.3526
1.11 −8.20203 −11.3835 35.2733 78.6161 93.3679 −96.6496 −26.8479 −113.416 −644.812
1.12 −8.02958 −0.934504 32.4742 −106.766 7.50368 −253.610 −3.80766 −242.127 857.288
1.13 −7.19367 −24.0942 19.7489 −16.6774 173.325 149.539 88.1305 337.528 119.972
1.14 −6.32810 −2.26638 8.04485 −43.9146 14.3419 −108.041 151.591 −237.864 277.896
1.15 −6.06944 17.7568 4.83813 11.0579 −107.774 200.557 164.857 72.3041 −67.1153
1.16 −6.05423 8.23240 4.65375 45.2787 −49.8409 110.010 165.561 −175.228 −274.128
1.17 −5.24076 −25.1927 −4.53448 −25.4096 132.029 241.738 191.468 391.672 133.166
1.18 −4.66731 −18.5097 −10.2162 −17.6120 86.3904 −165.879 197.036 99.6077 82.2008
1.19 −4.63641 −28.8079 −10.5037 68.1073 133.565 −18.6218 197.065 586.896 −315.773
1.20 −3.78553 −3.58914 −17.6698 −77.1552 13.5868 193.576 188.026 −230.118 292.073
See all 54 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.54
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(11\) \(1\)
\(53\) \(1\)

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 583.6.a.b ✓ 54
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
583.6.a.b ✓ 54 1.a even 1 1 trivial