# Properties

 Label 6027.2.a.bo Level 6027 Weight 2 Character orbit 6027.a Self dual yes Analytic conductor 48.126 Analytic rank 0 Dimension 24 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ = $$6027 = 3 \cdot 7^{2} \cdot 41$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 6027.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$48.1258372982$$ Analytic rank: $$0$$ Dimension: $$24$$ Coefficient ring index: multiple of None 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.

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

## 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 −2.69245 1.00000 5.24930 3.40876 −2.69245 0 −8.74860 1.00000 −9.17792
1.2 −2.37986 1.00000 3.66372 3.68734 −2.37986 0 −3.95941 1.00000 −8.77534
1.3 −2.22021 1.00000 2.92934 0.165927 −2.22021 0 −2.06334 1.00000 −0.368393
1.4 −1.96907 1.00000 1.87725 −4.10878 −1.96907 0 0.241710 1.00000 8.09048
1.5 −1.80081 1.00000 1.24292 −2.17778 −1.80081 0 1.36336 1.00000 3.92176
1.6 −1.32413 1.00000 −0.246682 4.03355 −1.32413 0 2.97490 1.00000 −5.34094
1.7 −1.25316 1.00000 −0.429590 −1.76265 −1.25316 0 3.04466 1.00000 2.20889
1.8 −0.844195 1.00000 −1.28734 −1.91229 −0.844195 0 2.77515 1.00000 1.61434
1.9 −0.423828 1.00000 −1.82037 3.41632 −0.423828 0 1.61918 1.00000 −1.44793
1.10 −0.308797 1.00000 −1.90464 −0.898648 −0.308797 0 1.20574 1.00000 0.277499
1.11 −0.0650408 1.00000 −1.99577 −2.65358 −0.0650408 0 0.259888 1.00000 0.172591
1.12 0.154130 1.00000 −1.97624 1.29015 0.154130 0 −0.612860 1.00000 0.198852
1.13 0.368135 1.00000 −1.86448 −0.572097 0.368135 0 −1.42265 1.00000 −0.210609
1.14 1.11646 1.00000 −0.753512 −0.900581 1.11646 0 −3.07419 1.00000 −1.00546
1.15 1.33013 1.00000 −0.230742 −3.44355 1.33013 0 −2.96719 1.00000 −4.58038
1.16 1.50751 1.00000 0.272577 1.10903 1.50751 0 −2.60410 1.00000 1.67187
1.17 1.64420 1.00000 0.703405 3.28206 1.64420 0 −2.13187 1.00000 5.39638
1.18 1.95065 1.00000 1.80504 2.46699 1.95065 0 −0.380308 1.00000 4.81223
1.19 2.26259 1.00000 3.11931 3.51535 2.26259 0 2.53253 1.00000 7.95379
1.20 2.37367 1.00000 3.63432 −3.47491 2.37367 0 3.87933 1.00000 −8.24830
See all 24 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.24 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 6027.2.a.bo yes 24
7.b odd 2 1 6027.2.a.bn 24

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
6027.2.a.bn 24 7.b odd 2 1
6027.2.a.bo yes 24 1.a even 1 1 trivial

## Atkin-Lehner signs

$$p$$ Sign
$$3$$ $$-1$$
$$7$$ $$1$$
$$41$$ $$1$$

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(6027))$$:

 $$T_{2}^{24} - \cdots$$ $$T_{5}^{24} - \cdots$$ $$T_{13}^{24} - \cdots$$

## Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database