Properties

 Label 1849.4.a.a Level 1849 Weight 4 Character orbit 1849.a Self dual yes Analytic conductor 109.095 Analytic rank 0 Dimension 1 CM discriminant -43 Inner twists 2

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1849 = 43^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1849.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$109.094531601$$ Analytic rank: $$0$$ 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

 $$f(q)$$ $$=$$ $$q - 8q^{4} - 27q^{9} + O(q^{10})$$ $$q - 8q^{4} - 27q^{9} + 32q^{11} - 90q^{13} + 64q^{16} - 130q^{17} - 140q^{23} - 125q^{25} + 108q^{31} + 216q^{36} + 22q^{41} - 256q^{44} + 500q^{47} - 343q^{49} + 720q^{52} - 130q^{53} - 904q^{59} - 512q^{64} - 360q^{67} + 1040q^{68} - 1116q^{79} + 729q^{81} - 680q^{83} + 1120q^{92} + 290q^{97} - 864q^{99} + O(q^{100})$$

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 −8.00000 0 0 0 0 −27.0000 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 1849.4.a.a 1
43.b odd 2 1 CM 1849.4.a.a 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1849.4.a.a 1 1.a even 1 1 trivial
1849.4.a.a 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 $$S_{4}^{\mathrm{new}}(\Gamma_0(1849))$$.

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + 8 T^{2}$$
$3$ $$1 + 27 T^{2}$$
$5$ $$1 + 125 T^{2}$$
$7$ $$1 + 343 T^{2}$$
$11$ $$1 - 32 T + 1331 T^{2}$$
$13$ $$1 + 90 T + 2197 T^{2}$$
$17$ $$1 + 130 T + 4913 T^{2}$$
$19$ $$1 + 6859 T^{2}$$
$23$ $$1 + 140 T + 12167 T^{2}$$
$29$ $$1 + 24389 T^{2}$$
$31$ $$1 - 108 T + 29791 T^{2}$$
$37$ $$1 + 50653 T^{2}$$
$41$ $$1 - 22 T + 68921 T^{2}$$
$43$ 1
$47$ $$1 - 500 T + 103823 T^{2}$$
$53$ $$1 + 130 T + 148877 T^{2}$$
$59$ $$1 + 904 T + 205379 T^{2}$$
$61$ $$1 + 226981 T^{2}$$
$67$ $$1 + 360 T + 300763 T^{2}$$
$71$ $$1 + 357911 T^{2}$$
$73$ $$1 + 389017 T^{2}$$
$79$ $$1 + 1116 T + 493039 T^{2}$$
$83$ $$1 + 680 T + 571787 T^{2}$$
$89$ $$1 + 704969 T^{2}$$
$97$ $$1 - 290 T + 912673 T^{2}$$