# Properties

 Label 8018.2.a.i Level $8018$ Weight $2$ Character orbit 8018.a Self dual yes Analytic conductor $64.024$ Analytic rank $0$ Dimension $43$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$8018 = 2 \cdot 19 \cdot 211$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 8018.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$64.0240523407$$ Analytic rank: $$0$$ Dimension: $$43$$ 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.

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

## 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 −1.00000 −3.34431 1.00000 −3.91124 3.34431 0.821669 −1.00000 8.18441 3.91124
1.2 −1.00000 −3.24783 1.00000 2.20422 3.24783 3.82287 −1.00000 7.54837 −2.20422
1.3 −1.00000 −2.91293 1.00000 2.71400 2.91293 1.04550 −1.00000 5.48515 −2.71400
1.4 −1.00000 −2.88859 1.00000 −0.162345 2.88859 −3.68356 −1.00000 5.34393 0.162345
1.5 −1.00000 −2.71486 1.00000 −0.740916 2.71486 4.34624 −1.00000 4.37046 0.740916
1.6 −1.00000 −2.54429 1.00000 −4.40933 2.54429 −2.39004 −1.00000 3.47339 4.40933
1.7 −1.00000 −2.53282 1.00000 2.86896 2.53282 3.12244 −1.00000 3.41520 −2.86896
1.8 −1.00000 −2.22097 1.00000 0.529365 2.22097 −2.58907 −1.00000 1.93269 −0.529365
1.9 −1.00000 −2.12309 1.00000 0.333090 2.12309 −1.76432 −1.00000 1.50753 −0.333090
1.10 −1.00000 −2.06580 1.00000 4.42069 2.06580 −2.80943 −1.00000 1.26754 −4.42069
1.11 −1.00000 −1.98111 1.00000 −2.70035 1.98111 2.97081 −1.00000 0.924794 2.70035
1.12 −1.00000 −1.78337 1.00000 −3.15111 1.78337 −2.13059 −1.00000 0.180410 3.15111
1.13 −1.00000 −1.49345 1.00000 1.29948 1.49345 −1.68221 −1.00000 −0.769617 −1.29948
1.14 −1.00000 −1.36513 1.00000 0.286730 1.36513 −1.35155 −1.00000 −1.13641 −0.286730
1.15 −1.00000 −1.12203 1.00000 −3.99522 1.12203 0.851275 −1.00000 −1.74104 3.99522
1.16 −1.00000 −1.11378 1.00000 4.02830 1.11378 1.02145 −1.00000 −1.75949 −4.02830
1.17 −1.00000 −1.00471 1.00000 −1.06211 1.00471 0.645369 −1.00000 −1.99055 1.06211
1.18 −1.00000 −0.978925 1.00000 −2.13476 0.978925 5.08930 −1.00000 −2.04171 2.13476
1.19 −1.00000 −0.765202 1.00000 −1.80247 0.765202 4.51708 −1.00000 −2.41447 1.80247
1.20 −1.00000 −0.649534 1.00000 3.59840 0.649534 4.54706 −1.00000 −2.57811 −3.59840
See all 43 embeddings
 $$n$$: e.g. 2-40 or 990-1000 Embeddings: e.g. 1-3 or 1.43 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$1$$
$$19$$ $$-1$$
$$211$$ $$1$$

## 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 8018.2.a.i 43

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
8018.2.a.i 43 1.a even 1 1 trivial

## Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3}^{43} - \cdots$$ acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(8018))$$.

## Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database