↑

Properties

Label 547.2.a.c
Level $547$
Weight $2$
Character orbit 547.a
Self dual yes
Analytic conductor $4.368$
Analytic rank $0$
Dimension $25$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [547,2,Mod(1,547)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(547, 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("547.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 547.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: \(4.36781699056\)
Analytic rank: \(0\)
Dimension: \(25\)
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.

\(\operatorname{Tr}(f)(q) = \) \( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9}+O(q^{10}) \) Copy content Toggle raw display
\(\operatorname{Tr}(f)(q) = \) \( 25 q + 4 q^{2} + 8 q^{3} + 26 q^{4} + 29 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 29 q^{9} - q^{10} + 10 q^{11} + 14 q^{12} + 19 q^{13} + 9 q^{14} + 5 q^{15} + 16 q^{16} + 40 q^{17} - 8 q^{18} + 33 q^{20} - 8 q^{21} - 10 q^{22} + 26 q^{23} - 16 q^{24} + 36 q^{25} - 8 q^{26} + 11 q^{27} - 8 q^{28} + 30 q^{29} - 20 q^{30} - 5 q^{31} + 6 q^{32} + 10 q^{33} - 7 q^{34} + 11 q^{35} + 13 q^{36} + 26 q^{37} + 25 q^{38} - 17 q^{39} - 25 q^{40} + 9 q^{41} - 16 q^{42} - 10 q^{43} + 64 q^{45} - 34 q^{46} + 28 q^{47} + 23 q^{48} + 20 q^{49} - 9 q^{50} - 9 q^{51} - 2 q^{52} + 80 q^{53} - 13 q^{54} - q^{55} + 7 q^{56} - 8 q^{57} - 24 q^{58} - 2 q^{59} - 14 q^{60} + 22 q^{61} + 36 q^{62} - 9 q^{63} - 28 q^{64} + 30 q^{65} - 42 q^{66} - 16 q^{67} + 59 q^{68} + 22 q^{69} - 61 q^{70} - q^{71} - 44 q^{72} + 2 q^{73} - 8 q^{74} - 31 q^{75} - 46 q^{76} + 67 q^{77} - q^{78} - 34 q^{79} + 30 q^{80} - 11 q^{81} - 4 q^{82} + 15 q^{83} - 87 q^{84} + 15 q^{85} - 44 q^{86} - 29 q^{87} - 55 q^{88} + 38 q^{89} - 90 q^{90} - 41 q^{91} + 40 q^{92} - 4 q^{93} - 46 q^{94} - 46 q^{95} - 87 q^{96} - 2 q^{97} - 14 q^{98} - 41 q^{99}+O(q^{100}) \) 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 −2.77274 2.24632 5.68811 3.59228 −6.22846 −1.86730 −10.2262 2.04594 −9.96049
1.2 −2.25986 −1.07595 3.10698 −0.586151 2.43150 0.547575 −2.50163 −1.84234 1.32462
1.3 −2.13103 0.778073 2.54127 −1.92511 −1.65809 −4.90203 −1.15346 −2.39460 4.10246
1.4 −2.06676 −2.69874 2.27150 4.37160 5.57765 3.31581 −0.561116 4.28320 −9.03504
1.5 −1.98290 2.22215 1.93190 0.712381 −4.40631 4.39659 0.135039 1.93796 −1.41258
1.6 −1.71387 −2.58580 0.937360 0.849164 4.43173 −2.18891 1.82123 3.68636 −1.45536
1.7 −1.69494 3.21746 0.872829 1.65792 −5.45340 −0.657486 1.91049 7.35203 −2.81008
1.8 −1.12450 1.64314 −0.735491 3.20489 −1.84772 −0.477395 3.07607 −0.300096 −3.60392
1.9 −0.920985 −0.533377 −1.15179 1.81354 0.491232 3.82860 2.90275 −2.71551 −1.67024
1.10 −0.240893 −1.63498 −1.94197 −2.81730 0.393856 −2.32432 0.949592 −0.326830 0.678667
1.11 −0.106981 0.649055 −1.98856 −2.10046 −0.0694367 0.493203 0.426701 −2.57873 0.224710
1.12 0.0847555 −1.52830 −1.99282 2.94110 −0.129532 −4.64869 −0.338413 −0.664306 0.249274
1.13 0.215054 2.12625 −1.95375 4.42221 0.457259 1.19553 −0.850270 1.52095 0.951013
1.14 0.253557 3.24523 −1.93571 −0.595274 0.822849 1.62460 −0.997925 7.53151 −0.150936
1.15 0.760071 −2.84895 −1.42229 3.94928 −2.16541 1.21889 −2.60119 5.11653 3.00173
1.16 0.814364 1.40134 −1.33681 1.41612 1.14120 3.63098 −2.71738 −1.03623 1.15324
1.17 1.36387 −2.44170 −0.139855 −1.90373 −3.33016 2.23580 −2.91849 2.96188 −2.59645
1.18 1.73479 0.987380 1.00948 2.62354 1.71289 −1.48197 −1.71833 −2.02508 4.55128
1.19 1.75045 3.07069 1.06407 3.05017 5.37508 −4.64964 −1.63830 6.42911 5.33917
1.20 1.98267 2.42262 1.93099 −0.826438 4.80327 0.383471 −0.136826 2.86911 −1.63856
See all 25 embeddings
\(n\): e.g. 2-40 or 990-1000
Embeddings: e.g. 1-3 or 1.25
Significant digits:
Format:

Atkin-Lehner signs

\( p \) Sign
\(547\) \(-1\)

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 547.2.a.c ✓ 25
3.b odd 2 1 4923.2.a.n 25
4.b odd 2 1 8752.2.a.v 25
    
        By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
547.2.a.c ✓ 25 1.a even 1 1 trivial
4923.2.a.n 25 3.b odd 2 1
8752.2.a.v 25 4.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2}^{25} - 4 T_{2}^{24} - 30 T_{2}^{23} + 134 T_{2}^{22} + 365 T_{2}^{21} - 1926 T_{2}^{20} - 2226 T_{2}^{19} + \cdots + 8 \) acting on \(S_{2}^{\mathrm{new}}(\Gamma_0(547))\). Copy content Toggle raw display