# Properties

 Label 2646.2.a.g Level $2646$ Weight $2$ Character orbit 2646.a Self dual yes Analytic conductor $21.128$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$2646 = 2 \cdot 3^{3} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2646.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$21.1284163748$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 378) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} + q^{4} - q^{8} + O(q^{10})$$ $$q - q^{2} + q^{4} - q^{8} + 6q^{11} - 5q^{13} + q^{16} - 6q^{17} + 4q^{19} - 6q^{22} + 6q^{23} - 5q^{25} + 5q^{26} + 6q^{29} + q^{31} - q^{32} + 6q^{34} - q^{37} - 4q^{38} + 6q^{41} - q^{43} + 6q^{44} - 6q^{46} + 6q^{47} + 5q^{50} - 5q^{52} - 6q^{53} - 6q^{58} + 6q^{59} + q^{61} - q^{62} + q^{64} - q^{67} - 6q^{68} + 12q^{71} - 2q^{73} + q^{74} + 4q^{76} - q^{79} - 6q^{82} - 6q^{83} + q^{86} - 6q^{88} + 6q^{92} - 6q^{94} - 17q^{97} + O(q^{100})$$

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

## 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 2646.2.a.g 1
3.b odd 2 1 2646.2.a.w 1
7.b odd 2 1 2646.2.a.h 1
7.d odd 6 2 378.2.g.e yes 2
21.c even 2 1 2646.2.a.x 1
21.g even 6 2 378.2.g.b 2
63.i even 6 2 1134.2.e.m 2
63.k odd 6 2 1134.2.h.n 2
63.s even 6 2 1134.2.h.d 2
63.t odd 6 2 1134.2.e.c 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
378.2.g.b 2 21.g even 6 2
378.2.g.e yes 2 7.d odd 6 2
1134.2.e.c 2 63.t odd 6 2
1134.2.e.m 2 63.i even 6 2
1134.2.h.d 2 63.s even 6 2
1134.2.h.n 2 63.k odd 6 2
2646.2.a.g 1 1.a even 1 1 trivial
2646.2.a.h 1 7.b odd 2 1
2646.2.a.w 1 3.b odd 2 1
2646.2.a.x 1 21.c even 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(2646))$$:

 $$T_{5}$$ $$T_{11} - 6$$ $$T_{13} + 5$$ $$T_{17} + 6$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T$$
$3$ $$T$$
$5$ $$T$$
$7$ $$T$$
$11$ $$-6 + T$$
$13$ $$5 + T$$
$17$ $$6 + T$$
$19$ $$-4 + T$$
$23$ $$-6 + T$$
$29$ $$-6 + T$$
$31$ $$-1 + T$$
$37$ $$1 + T$$
$41$ $$-6 + T$$
$43$ $$1 + T$$
$47$ $$-6 + T$$
$53$ $$6 + T$$
$59$ $$-6 + T$$
$61$ $$-1 + T$$
$67$ $$1 + T$$
$71$ $$-12 + T$$
$73$ $$2 + T$$
$79$ $$1 + T$$
$83$ $$6 + T$$
$89$ $$T$$
$97$ $$17 + T$$