# 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

## Newspace parameters

 Level: $$N$$ $$=$$ $$547$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 547.a (trivial)

## Newform invariants

 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.

 $$\operatorname{Tr}(f)(q) =$$ $$25q + 4q^{2} + 8q^{3} + 26q^{4} + 29q^{5} + q^{6} + 5q^{7} + 6q^{8} + 29q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$25q + 4q^{2} + 8q^{3} + 26q^{4} + 29q^{5} + q^{6} + 5q^{7} + 6q^{8} + 29q^{9} - q^{10} + 10q^{11} + 14q^{12} + 19q^{13} + 9q^{14} + 5q^{15} + 16q^{16} + 40q^{17} - 8q^{18} + 33q^{20} - 8q^{21} - 10q^{22} + 26q^{23} - 16q^{24} + 36q^{25} - 8q^{26} + 11q^{27} - 8q^{28} + 30q^{29} - 20q^{30} - 5q^{31} + 6q^{32} + 10q^{33} - 7q^{34} + 11q^{35} + 13q^{36} + 26q^{37} + 25q^{38} - 17q^{39} - 25q^{40} + 9q^{41} - 16q^{42} - 10q^{43} + 64q^{45} - 34q^{46} + 28q^{47} + 23q^{48} + 20q^{49} - 9q^{50} - 9q^{51} - 2q^{52} + 80q^{53} - 13q^{54} - q^{55} + 7q^{56} - 8q^{57} - 24q^{58} - 2q^{59} - 14q^{60} + 22q^{61} + 36q^{62} - 9q^{63} - 28q^{64} + 30q^{65} - 42q^{66} - 16q^{67} + 59q^{68} + 22q^{69} - 61q^{70} - q^{71} - 44q^{72} + 2q^{73} - 8q^{74} - 31q^{75} - 46q^{76} + 67q^{77} - q^{78} - 34q^{79} + 30q^{80} - 11q^{81} - 4q^{82} + 15q^{83} - 87q^{84} + 15q^{85} - 44q^{86} - 29q^{87} - 55q^{88} + 38q^{89} - 90q^{90} - 41q^{91} + 40q^{92} - 4q^{93} - 46q^{94} - 46q^{95} - 87q^{96} - 2q^{97} - 14q^{98} - 41q^{99} + O(q^{100})$$

## 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.

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: Complex embeddings Normalized embeddings Satake parameters Satake angles

## 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

## Atkin-Lehner signs

$$p$$ Sign
$$547$$ $$-1$$

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2}^{25} - \cdots$$ acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(547))$$.

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database