# Properties

 Label 1848.2.a.k Level $1848$ Weight $2$ Character orbit 1848.a Self dual yes Analytic conductor $14.756$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1848 = 2^{3} \cdot 3 \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1848.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$14.7563542935$$ 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: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{3} + q^{5} - q^{7} + q^{9} + O(q^{10})$$ $$q + q^{3} + q^{5} - q^{7} + q^{9} - q^{11} + 3 q^{13} + q^{15} + 7 q^{19} - q^{21} + 6 q^{23} - 4 q^{25} + q^{27} - 9 q^{29} - q^{33} - q^{35} - 3 q^{37} + 3 q^{39} + 8 q^{41} + 10 q^{43} + q^{45} + 3 q^{47} + q^{49} + 6 q^{53} - q^{55} + 7 q^{57} + 7 q^{59} + 10 q^{61} - q^{63} + 3 q^{65} - 3 q^{67} + 6 q^{69} - 8 q^{71} - 7 q^{73} - 4 q^{75} + q^{77} + 8 q^{79} + q^{81} - 9 q^{87} - 6 q^{89} - 3 q^{91} + 7 q^{95} - 10 q^{97} - q^{99} + O(q^{100})$$

## 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 1.00000 0 1.00000 0 −1.00000 0 1.00000 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
$$2$$ $$1$$
$$3$$ $$-1$$
$$7$$ $$1$$
$$11$$ $$1$$

## 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 1848.2.a.k 1
3.b odd 2 1 5544.2.a.h 1
4.b odd 2 1 3696.2.a.l 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1848.2.a.k 1 1.a even 1 1 trivial
3696.2.a.l 1 4.b odd 2 1
5544.2.a.h 1 3.b odd 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(1848))$$:

 $$T_{5} - 1$$ $$T_{13} - 3$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$-1 + T$$
$5$ $$-1 + T$$
$7$ $$1 + T$$
$11$ $$1 + T$$
$13$ $$-3 + T$$
$17$ $$T$$
$19$ $$-7 + T$$
$23$ $$-6 + T$$
$29$ $$9 + T$$
$31$ $$T$$
$37$ $$3 + T$$
$41$ $$-8 + T$$
$43$ $$-10 + T$$
$47$ $$-3 + T$$
$53$ $$-6 + T$$
$59$ $$-7 + T$$
$61$ $$-10 + T$$
$67$ $$3 + T$$
$71$ $$8 + T$$
$73$ $$7 + T$$
$79$ $$-8 + T$$
$83$ $$T$$
$89$ $$6 + T$$
$97$ $$10 + T$$