Properties

 Label 1849.2.a.b Level $1849$ Weight $2$ Character orbit 1849.a Self dual yes Analytic conductor $14.764$ Analytic rank $1$ Dimension $1$ CM discriminant -43 Inner twists $2$

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Newspace parameters

 Level: $$N$$ $$=$$ $$1849 = 43^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1849.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$14.7643393337$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$1$$ Sato-Tate group: $N(\mathrm{U}(1))$

$q$-expansion

 $$f(q)$$ $$=$$ $$q - 2q^{4} - 3q^{9} + O(q^{10})$$ $$q - 2q^{4} - 3q^{9} - q^{11} + 3q^{13} + 4q^{16} + 5q^{17} + 7q^{23} - 5q^{25} - 9q^{31} + 6q^{36} - 11q^{41} + 2q^{44} - 4q^{47} - 7q^{49} - 6q^{52} - 13q^{53} + 8q^{59} - 8q^{64} - 15q^{67} - 10q^{68} + 12q^{79} + 9q^{81} - 17q^{83} - 14q^{92} - q^{97} + 3q^{99} + O(q^{100})$$

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 $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$
1.1
 0
0 0 −2.00000 0 0 0 0 −3.00000 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

$$p$$ Sign
$$43$$ $$1$$

Inner twists

Char Parity Ord Mult Type
1.a even 1 1 trivial
43.b odd 2 1 CM by $$\Q(\sqrt{-43})$$

Twists

By twisting character orbit
Char Parity Ord Mult Type Twist Min Dim
1.a even 1 1 trivial 1849.2.a.b 1
43.b odd 2 1 CM 1849.2.a.b 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1849.2.a.b 1 1.a even 1 1 trivial
1849.2.a.b 1 43.b odd 2 1 CM

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{2}$$ acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(1849))$$.

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 2 T^{2}$$
$3$ $$1 + 3 T^{2}$$
$5$ $$1 + 5 T^{2}$$
$7$ $$1 + 7 T^{2}$$
$11$ $$1 + T + 11 T^{2}$$
$13$ $$1 - 3 T + 13 T^{2}$$
$17$ $$1 - 5 T + 17 T^{2}$$
$19$ $$1 + 19 T^{2}$$
$23$ $$1 - 7 T + 23 T^{2}$$
$29$ $$1 + 29 T^{2}$$
$31$ $$1 + 9 T + 31 T^{2}$$
$37$ $$1 + 37 T^{2}$$
$41$ $$1 + 11 T + 41 T^{2}$$
$43$ 1
$47$ $$1 + 4 T + 47 T^{2}$$
$53$ $$1 + 13 T + 53 T^{2}$$
$59$ $$1 - 8 T + 59 T^{2}$$
$61$ $$1 + 61 T^{2}$$
$67$ $$1 + 15 T + 67 T^{2}$$
$71$ $$1 + 71 T^{2}$$
$73$ $$1 + 73 T^{2}$$
$79$ $$1 - 12 T + 79 T^{2}$$
$83$ $$1 + 17 T + 83 T^{2}$$
$89$ $$1 + 89 T^{2}$$
$97$ $$1 + T + 97 T^{2}$$
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