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Properties

Label 1511.2.a.a
Level $1511$
Weight $2$
Character orbit 1511.a
Self dual yes
Analytic conductor $12.065$
Analytic rank $1$
Dimension $39$
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: \(1\)
Dimension: \(39\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 39 q - 5 q^{2} - 4 q^{3} + 19 q^{4} - 8 q^{5} - 8 q^{6} - 15 q^{7} - 12 q^{8} - q^{9} - 13 q^{10} - 13 q^{11} - 8 q^{12} - 24 q^{13} - 12 q^{14} - 16 q^{15} - 13 q^{16} - 26 q^{17} - 17 q^{18} - 40 q^{19} - 15 q^{20} - 26 q^{21} - 26 q^{22} - 8 q^{23} - 16 q^{24} - 35 q^{25} - 3 q^{26} - 10 q^{27} - 31 q^{28} - 30 q^{29} - 16 q^{30} - 21 q^{31} - 9 q^{32} - 25 q^{33} - 27 q^{34} - 2 q^{35} - 23 q^{36} - 27 q^{37} + q^{38} - 29 q^{39} - 36 q^{40} - 35 q^{41} - 6 q^{42} - 48 q^{43} - 17 q^{44} - 22 q^{45} - 31 q^{46} - 3 q^{47} + q^{48} - 64 q^{49} + 12 q^{50} - 27 q^{51} - 28 q^{52} - 14 q^{53} + q^{54} - 31 q^{55} - 12 q^{56} - 36 q^{57} - 19 q^{58} - 9 q^{59} - 6 q^{60} - 87 q^{61} + 32 q^{62} - 9 q^{63} - 52 q^{64} - 35 q^{65} + 5 q^{66} - 24 q^{67} - 13 q^{68} - 35 q^{69} - 8 q^{70} - 21 q^{71} - 11 q^{72} - 69 q^{73} - 23 q^{74} - 4 q^{75} - 58 q^{76} - 3 q^{77} + q^{78} - 72 q^{79} + 13 q^{80} - 73 q^{81} + 18 q^{82} - 11 q^{83} - 32 q^{84} - 70 q^{85} + 20 q^{86} - 9 q^{87} - 24 q^{88} - 25 q^{89} + 33 q^{90} - 32 q^{91} + 17 q^{92} - 19 q^{93} - 29 q^{94} - 9 q^{95} + 5 q^{96} - 56 q^{97} + 37 q^{98} - 19 q^{99}+O(q^{100}) \) 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 −2.62761 0.509058 4.90431 2.89864 −1.33760 −2.02208 −7.63140 −2.74086 −7.61649
1.2 −2.55669 1.42981 4.53667 −0.703290 −3.65557 0.249389 −6.48549 −0.955654 1.79810
1.3 −2.34046 −2.59155 3.47777 0.00564177 6.06542 1.46395 −3.45867 3.71611 −0.0132044
1.4 −2.34045 −1.21261 3.47772 −2.24058 2.83806 −2.07268 −3.45853 −1.52957 5.24397
1.5 −2.23663 2.94834 3.00251 −1.14900 −6.59433 −0.894921 −2.24225 5.69268 2.56989
1.6 −2.08094 −1.97639 2.33030 2.54973 4.11275 2.17959 −0.687343 0.906117 −5.30584
1.7 −1.90264 0.464594 1.62005 1.03358 −0.883957 0.00752269 0.722914 −2.78415 −1.96653
1.8 −1.86189 1.53366 1.46665 0.202467 −2.85551 1.37523 0.993038 −0.647887 −0.376973
1.9 −1.62353 −1.31927 0.635854 −3.18617 2.14187 −3.82139 2.21473 −1.25954 5.17284
1.10 −1.61899 −0.892608 0.621134 −2.10492 1.44512 3.46425 2.23237 −2.20325 3.40785
1.11 −1.47138 −2.69711 0.164957 0.298356 3.96848 −0.564843 2.70004 4.27442 −0.438994
1.12 −1.43158 1.75431 0.0494244 −1.70313 −2.51144 −2.85735 2.79241 0.0775993 2.43817
1.13 −1.20058 1.91165 −0.558606 3.14427 −2.29509 −3.56318 3.07181 0.654410 −3.77495
1.14 −1.06434 0.739457 −0.867188 1.62479 −0.787031 4.39505 3.05165 −2.45320 −1.72933
1.15 −0.962526 2.40637 −1.07354 −2.56158 −2.31620 −0.340450 2.95837 2.79063 2.46559
1.16 −0.831791 −0.319219 −1.30812 1.51204 0.265524 −2.78858 2.75167 −2.89810 −1.25770
1.17 −0.561486 −2.05702 −1.68473 2.98075 1.15499 −1.40917 2.06893 1.23133 −1.67365
1.18 −0.257169 −2.24860 −1.93386 −2.95445 0.578271 −1.92811 1.01167 2.05622 0.759791
1.19 −0.156512 1.68213 −1.97550 −2.50919 −0.263273 2.62593 0.622213 −0.170440 0.392718
1.20 −0.117793 −0.858124 −1.98612 −2.96573 0.101081 2.06875 0.469537 −2.26362 0.349342
See all 39 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.39
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.a ✓ 39
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1511.2.a.a ✓ 39 1.a even 1 1 trivial