# Properties

 Label 8020.2.a.c Level 8020 Weight 2 Character orbit 8020.a Self dual yes Analytic conductor 64.040 Analytic rank 1 Dimension 28 CM no Inner twists 1

# Related objects

## Newspace parameters

 Level: $$N$$ = $$8020 = 2^{2} \cdot 5 \cdot 401$$ Weight: $$k$$ = $$2$$ Character orbit: $$[\chi]$$ = 8020.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$64.0400224211$$ Analytic rank: $$1$$ Dimension: $$28$$ 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.

 $$\operatorname{Tr}(f)(q) =$$ $$28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + O(q^{10})$$ $$\operatorname{Tr}(f)(q) =$$ $$28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + 2q^{11} + 3q^{13} - 3q^{15} - 10q^{17} - 2q^{19} - 12q^{21} - 23q^{23} + 28q^{25} + 9q^{27} - 37q^{29} - 11q^{31} + 2q^{33} + 4q^{35} - 3q^{37} - 19q^{39} - 30q^{41} + 13q^{43} - 17q^{45} - 15q^{47} + 12q^{49} - 8q^{51} - 35q^{53} - 2q^{55} - 22q^{57} - q^{59} - 33q^{61} - 20q^{63} - 3q^{65} + 19q^{67} - 8q^{69} - 31q^{71} + 31q^{73} + 3q^{75} - 42q^{77} - 29q^{79} - 36q^{81} + 14q^{83} + 10q^{85} - 32q^{87} - 32q^{89} - 7q^{91} - 11q^{93} + 2q^{95} + 2q^{97} - 39q^{99} + O(q^{100})$$

## 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 0 −3.10189 0 −1.00000 0 1.97262 0 6.62170 0
1.2 0 −2.61261 0 −1.00000 0 −1.36796 0 3.82575 0
1.3 0 −2.59496 0 −1.00000 0 1.42420 0 3.73381 0
1.4 0 −2.32143 0 −1.00000 0 0.515797 0 2.38904 0
1.5 0 −2.26002 0 −1.00000 0 −3.39221 0 2.10771 0
1.6 0 −1.62538 0 −1.00000 0 4.42157 0 −0.358130 0
1.7 0 −1.58112 0 −1.00000 0 3.33363 0 −0.500055 0
1.8 0 −1.53415 0 −1.00000 0 0.759833 0 −0.646394 0
1.9 0 −1.48695 0 −1.00000 0 −3.53428 0 −0.788974 0
1.10 0 −1.42561 0 −1.00000 0 −3.82644 0 −0.967639 0
1.11 0 −0.750059 0 −1.00000 0 −4.31732 0 −2.43741 0
1.12 0 −0.324068 0 −1.00000 0 −1.35293 0 −2.89498 0
1.13 0 −0.172341 0 −1.00000 0 3.94901 0 −2.97030 0
1.14 0 0.0547853 0 −1.00000 0 3.87235 0 −2.99700 0
1.15 0 0.167528 0 −1.00000 0 −3.89143 0 −2.97193 0
1.16 0 0.356039 0 −1.00000 0 −0.400497 0 −2.87324 0
1.17 0 0.910150 0 −1.00000 0 1.40834 0 −2.17163 0
1.18 0 1.05681 0 −1.00000 0 3.74444 0 −1.88316 0
1.19 0 1.28191 0 −1.00000 0 −0.791593 0 −1.35670 0
1.20 0 1.67955 0 −1.00000 0 −2.58133 0 −0.179108 0
See all 28 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.28 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 8020.2.a.c 28

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8020.2.a.c 28 1.a even 1 1 trivial

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$-1$$
$$5$$ $$1$$
$$401$$ $$-1$$

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3}^{28} - \cdots$$ acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(8020))$$.