# Properties

 Label 2142.2.a.g Level $2142$ Weight $2$ Character orbit 2142.a Self dual yes Analytic conductor $17.104$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2142 = 2 \cdot 3^{2} \cdot 7 \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2142.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$17.1039561130$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 714) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} + q^{4} + 2q^{5} - q^{7} - q^{8} + O(q^{10})$$ $$q - q^{2} + q^{4} + 2q^{5} - q^{7} - q^{8} - 2q^{10} - 6q^{13} + q^{14} + q^{16} - q^{17} + 2q^{20} + 8q^{23} - q^{25} + 6q^{26} - q^{28} + 6q^{29} - 8q^{31} - q^{32} + q^{34} - 2q^{35} + 10q^{37} - 2q^{40} + 6q^{41} + 12q^{43} - 8q^{46} + q^{49} + q^{50} - 6q^{52} + 10q^{53} + q^{56} - 6q^{58} + 8q^{59} + 6q^{61} + 8q^{62} + q^{64} - 12q^{65} + 12q^{67} - q^{68} + 2q^{70} - 6q^{73} - 10q^{74} - 8q^{79} + 2q^{80} - 6q^{82} - 16q^{83} - 2q^{85} - 12q^{86} - 2q^{89} + 6q^{91} + 8q^{92} + 2q^{97} - q^{98} + O(q^{100})$$

## 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
−1.00000 0 1.00000 2.00000 0 −1.00000 −1.00000 0 −2.00000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$1$$
$$3$$ $$-1$$
$$7$$ $$1$$
$$17$$ $$1$$

## 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 2142.2.a.g 1
3.b odd 2 1 714.2.a.e 1
12.b even 2 1 5712.2.a.q 1
21.c even 2 1 4998.2.a.bp 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
714.2.a.e 1 3.b odd 2 1
2142.2.a.g 1 1.a even 1 1 trivial
4998.2.a.bp 1 21.c even 2 1
5712.2.a.q 1 12.b even 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(2142))$$:

 $$T_{5} - 2$$ $$T_{11}$$ $$T_{13} + 6$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T$$
$3$ $$T$$
$5$ $$-2 + T$$
$7$ $$1 + T$$
$11$ $$T$$
$13$ $$6 + T$$
$17$ $$1 + T$$
$19$ $$T$$
$23$ $$-8 + T$$
$29$ $$-6 + T$$
$31$ $$8 + T$$
$37$ $$-10 + T$$
$41$ $$-6 + T$$
$43$ $$-12 + T$$
$47$ $$T$$
$53$ $$-10 + T$$
$59$ $$-8 + T$$
$61$ $$-6 + T$$
$67$ $$-12 + T$$
$71$ $$T$$
$73$ $$6 + T$$
$79$ $$8 + T$$
$83$ $$16 + T$$
$89$ $$2 + T$$
$97$ $$-2 + T$$