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Properties

Label 1511.2.a.b
Level $1511$
Weight $2$
Character orbit 1511.a
Self dual yes
Analytic conductor $12.065$
Analytic rank $0$
Dimension $87$
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] = [1511,2,Mod(1,1511)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1511, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1511.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1511 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1511.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: \(12.0653957454\)
Analytic rank: \(0\)
Dimension: \(87\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 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 −2.80582 3.17353 5.87262 −1.01693 −8.90436 1.50749 −10.8659 7.07132 2.85331
1.2 −2.77157 −1.56972 5.68161 1.40635 4.35060 3.36356 −10.2038 −0.535965 −3.89780
1.3 −2.74171 −1.83370 5.51700 −1.34905 5.02748 −1.43081 −9.64261 0.362459 3.69872
1.4 −2.70275 1.32462 5.30486 −3.53134 −3.58011 −4.82558 −8.93221 −1.24539 9.54434
1.5 −2.64690 0.0983848 5.00607 −2.89326 −0.260415 2.77598 −7.95678 −2.99032 7.65817
1.6 −2.61914 −3.14876 4.85992 4.24967 8.24705 −1.66067 −7.49053 6.91467 −11.1305
1.7 −2.51398 2.10592 4.32011 3.94519 −5.29424 4.57859 −5.83272 1.43489 −9.91814
1.8 −2.48500 −2.64034 4.17524 −4.22842 6.56126 2.88857 −5.40548 3.97140 10.5076
1.9 −2.44922 1.65862 3.99868 0.786699 −4.06233 1.92493 −4.89521 −0.248977 −1.92680
1.10 −2.43048 −3.20082 3.90723 −1.39193 7.77953 −2.04367 −4.63549 7.24524 3.38307
1.11 −2.25498 −1.25409 3.08494 1.71484 2.82794 4.94579 −2.44651 −1.42727 −3.86693
1.12 −2.23972 2.49888 3.01634 2.88388 −5.59680 −4.32598 −2.27632 3.24442 −6.45907
1.13 −2.18669 −0.0607376 2.78161 0.257121 0.132814 −3.58391 −1.70914 −2.99631 −0.562243
1.14 −2.17973 −1.52480 2.75122 2.09975 3.32365 −4.07128 −1.63745 −0.674992 −4.57690
1.15 −2.14655 2.30353 2.60767 −0.799621 −4.94463 −4.27058 −1.30440 2.30623 1.71642
1.16 −2.03442 0.699756 2.13886 −3.36773 −1.42360 1.70817 −0.282508 −2.51034 6.85138
1.17 −2.03013 2.75873 2.12143 −4.03669 −5.60059 4.76873 −0.246528 4.61059 8.19501
1.18 −1.87889 −0.471074 1.53023 −2.77573 0.885096 −0.337329 0.882648 −2.77809 5.21530
1.19 −1.82562 −0.163160 1.33288 3.84467 0.297868 1.48114 1.21791 −2.97338 −7.01889
1.20 −1.75162 2.89553 1.06816 2.42041 −5.07185 1.68282 1.63223 5.38408 −4.23963
See all 87 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.87
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(1511\) \(-1\)

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 1511.2.a.b ✓ 87
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1511.2.a.b ✓ 87 1.a even 1 1 trivial