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Properties

Label 1011.4.a.b
Level $1011$
Weight $4$
Character orbit 1011.a
Self dual yes
Analytic conductor $59.651$
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] = [1011,4,Mod(1,1011)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1011, 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("1011.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1011 = 3 \cdot 337 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1011.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: \(59.6509310158\)
Analytic rank: \(1\)
Dimension: \(38\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 38 q - 5 q^{2} - 114 q^{3} + 135 q^{4} - 48 q^{5} + 15 q^{6} + 68 q^{7} - 39 q^{8} + 342 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 38 q - 5 q^{2} - 114 q^{3} + 135 q^{4} - 48 q^{5} + 15 q^{6} + 68 q^{7} - 39 q^{8} + 342 q^{9} + 8 q^{10} - 116 q^{11} - 405 q^{12} - 94 q^{13} - 225 q^{14} + 144 q^{15} + 307 q^{16} - 186 q^{17} - 45 q^{18} - 18 q^{19} - 467 q^{20} - 204 q^{21} + 71 q^{22} - 258 q^{23} + 117 q^{24} + 478 q^{25} - 542 q^{26} - 1026 q^{27} + 116 q^{28} - 1280 q^{29} - 24 q^{30} + 438 q^{31} - 237 q^{32} + 348 q^{33} - 196 q^{34} - 420 q^{35} + 1215 q^{36} - 194 q^{37} - 272 q^{38} + 282 q^{39} + 171 q^{40} - 520 q^{41} + 675 q^{42} + 86 q^{43} - 812 q^{44} - 432 q^{45} - 475 q^{46} - 870 q^{47} - 921 q^{48} + 1138 q^{49} - 537 q^{50} + 558 q^{51} - 16 q^{52} - 2550 q^{53} + 135 q^{54} + 1064 q^{55} - 2037 q^{56} + 54 q^{57} + 450 q^{58} - 1588 q^{59} + 1401 q^{60} - 684 q^{61} - 234 q^{62} + 612 q^{63} - 89 q^{64} - 1880 q^{65} - 213 q^{66} + 194 q^{67} - 1239 q^{68} + 774 q^{69} + 214 q^{70} - 2502 q^{71} - 351 q^{72} + 818 q^{73} - 2203 q^{74} - 1434 q^{75} - 251 q^{76} - 1974 q^{77} + 1626 q^{78} - 980 q^{79} - 5601 q^{80} + 3078 q^{81} + 2073 q^{82} - 2516 q^{83} - 348 q^{84} - 2738 q^{85} - 6471 q^{86} + 3840 q^{87} - 940 q^{88} - 4998 q^{89} + 72 q^{90} - 2818 q^{91} - 8057 q^{92} - 1314 q^{93} - 3224 q^{94} - 7544 q^{95} + 711 q^{96} - 664 q^{97} - 11457 q^{98} - 1044 q^{99}+O(q^{100}) \) 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 −5.37744 −3.00000 20.9168 −11.0721 16.1323 33.8733 −69.4595 9.00000 59.5395
1.2 −5.35147 −3.00000 20.6382 −1.69721 16.0544 −3.48004 −67.6332 9.00000 9.08260
1.3 −5.17206 −3.00000 18.7502 17.0790 15.5162 −8.75961 −55.6005 9.00000 −88.3336
1.4 −4.84646 −3.00000 15.4881 −18.5463 14.5394 3.21351 −36.2909 9.00000 89.8838
1.5 −4.24180 −3.00000 9.99285 −1.43338 12.7254 25.7436 −8.45327 9.00000 6.08011
1.6 −4.23055 −3.00000 9.89758 −14.8428 12.6917 −35.9428 −8.02781 9.00000 62.7933
1.7 −3.90169 −3.00000 7.22315 −1.25112 11.7051 7.40933 3.03104 9.00000 4.88148
1.8 −3.67715 −3.00000 5.52140 6.56814 11.0314 −26.5606 9.11419 9.00000 −24.1520
1.9 −3.54714 −3.00000 4.58223 8.85506 10.6414 −7.32489 12.1233 9.00000 −31.4102
1.10 −3.20610 −3.00000 2.27905 −8.97002 9.61829 21.6852 18.3419 9.00000 28.7587
1.11 −2.90376 −3.00000 0.431826 11.8648 8.71128 −11.4366 21.9762 9.00000 −34.4527
1.12 −2.78605 −3.00000 −0.237906 −16.4991 8.35816 33.5310 22.9512 9.00000 45.9673
1.13 −2.70153 −3.00000 −0.701738 8.84505 8.10459 17.3814 23.5080 9.00000 −23.8952
1.14 −2.53916 −3.00000 −1.55266 11.2053 7.61748 30.8788 24.2557 9.00000 −28.4520
1.15 −2.16750 −3.00000 −3.30195 −7.73653 6.50249 −19.9706 24.4970 9.00000 16.7689
1.16 −1.13034 −3.00000 −6.72233 10.7041 3.39102 23.3161 16.6412 9.00000 −12.0993
1.17 −0.827474 −3.00000 −7.31529 −4.51908 2.48242 −4.13252 12.6730 9.00000 3.73942
1.18 −0.640078 −3.00000 −7.59030 12.4549 1.92023 12.5972 9.97901 9.00000 −7.97208
1.19 −0.336555 −3.00000 −7.88673 −22.1276 1.00966 −9.08795 5.34675 9.00000 7.44715
1.20 0.356814 −3.00000 −7.87268 −15.2120 −1.07044 −12.7777 −5.66359 9.00000 −5.42784
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
\(3\) \( +1 \)
\(337\) \( -1 \)

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 1011.4.a.b ✓ 38
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1011.4.a.b ✓ 38 1.a even 1 1 trivial