# Properties

 Label 1792.2.a.g Level $1792$ Weight $2$ Character orbit 1792.a Self dual yes Analytic conductor $14.309$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1792 = 2^{8} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1792.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$14.3091920422$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 896) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + 2q^{3} + 2q^{5} + q^{7} + q^{9} + O(q^{10})$$ $$q + 2q^{3} + 2q^{5} + q^{7} + q^{9} - 2q^{13} + 4q^{15} + 6q^{17} + 6q^{19} + 2q^{21} - 4q^{23} - q^{25} - 4q^{27} + 8q^{31} + 2q^{35} - 8q^{37} - 4q^{39} + 6q^{41} + 8q^{43} + 2q^{45} + q^{49} + 12q^{51} + 4q^{53} + 12q^{57} + 6q^{59} + 2q^{61} + q^{63} - 4q^{65} + 4q^{67} - 8q^{69} - 16q^{71} - 6q^{73} - 2q^{75} - 16q^{79} - 11q^{81} + 14q^{83} + 12q^{85} - 14q^{89} - 2q^{91} + 16q^{93} + 12q^{95} - 2q^{97} + O(q^{100})$$

## 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 2.00000 0 2.00000 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
$$2$$ $$1$$
$$7$$ $$-1$$

## 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 1792.2.a.g 1
4.b odd 2 1 1792.2.a.c 1
8.b even 2 1 1792.2.a.b 1
8.d odd 2 1 1792.2.a.f 1
16.e even 4 2 896.2.b.a 2
16.f odd 4 2 896.2.b.c yes 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
896.2.b.a 2 16.e even 4 2
896.2.b.c yes 2 16.f odd 4 2
1792.2.a.b 1 8.b even 2 1
1792.2.a.c 1 4.b odd 2 1
1792.2.a.f 1 8.d odd 2 1
1792.2.a.g 1 1.a even 1 1 trivial

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(1792))$$:

 $$T_{3} - 2$$ $$T_{5} - 2$$ $$T_{23} + 4$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$-2 + T$$
$5$ $$-2 + T$$
$7$ $$-1 + T$$
$11$ $$T$$
$13$ $$2 + T$$
$17$ $$-6 + T$$
$19$ $$-6 + T$$
$23$ $$4 + T$$
$29$ $$T$$
$31$ $$-8 + T$$
$37$ $$8 + T$$
$41$ $$-6 + T$$
$43$ $$-8 + T$$
$47$ $$T$$
$53$ $$-4 + T$$
$59$ $$-6 + T$$
$61$ $$-2 + T$$
$67$ $$-4 + T$$
$71$ $$16 + T$$
$73$ $$6 + T$$
$79$ $$16 + T$$
$83$ $$-14 + T$$
$89$ $$14 + T$$
$97$ $$2 + T$$