Properties

 Label 2646.2.a.k 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

 $$f(q)$$ $$=$$ $$q - q^{2} + q^{4} + 2q^{5} - q^{8} + O(q^{10})$$ $$q - q^{2} + q^{4} + 2q^{5} - q^{8} - 2q^{10} - 5q^{11} + 6q^{13} + q^{16} + 4q^{17} - 4q^{19} + 2q^{20} + 5q^{22} + 4q^{23} - q^{25} - 6q^{26} - 7q^{29} + 3q^{31} - q^{32} - 4q^{34} + 8q^{37} + 4q^{38} - 2q^{40} + 6q^{41} + 8q^{43} - 5q^{44} - 4q^{46} - 6q^{47} + q^{50} + 6q^{52} + 6q^{53} - 10q^{55} + 7q^{58} - 7q^{59} - 3q^{62} + q^{64} + 12q^{65} + 10q^{67} + 4q^{68} + 4q^{71} + 13q^{73} - 8q^{74} - 4q^{76} - 3q^{79} + 2q^{80} - 6q^{82} + 7q^{83} + 8q^{85} - 8q^{86} + 5q^{88} - 6q^{89} + 4q^{92} + 6q^{94} - 8q^{95} - 5q^{97} + O(q^{100})$$

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 2.00000 0 0 −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
$$2$$ $$1$$
$$3$$ $$-1$$
$$7$$ $$1$$

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.k 1
3.b odd 2 1 2646.2.a.t 1
7.b odd 2 1 2646.2.a.c 1
7.c even 3 2 378.2.g.d yes 2
21.c even 2 1 2646.2.a.bb 1
21.h odd 6 2 378.2.g.c 2
63.g even 3 2 1134.2.h.o 2
63.h even 3 2 1134.2.e.b 2
63.j odd 6 2 1134.2.e.o 2
63.n odd 6 2 1134.2.h.b 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
378.2.g.c 2 21.h odd 6 2
378.2.g.d yes 2 7.c even 3 2
1134.2.e.b 2 63.h even 3 2
1134.2.e.o 2 63.j odd 6 2
1134.2.h.b 2 63.n odd 6 2
1134.2.h.o 2 63.g even 3 2
2646.2.a.c 1 7.b odd 2 1
2646.2.a.k 1 1.a even 1 1 trivial
2646.2.a.t 1 3.b odd 2 1
2646.2.a.bb 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 $$S_{2}^{\mathrm{new}}(\Gamma_0(2646))$$:

 $$T_{5} - 2$$ $$T_{11} + 5$$ $$T_{13} - 6$$ $$T_{17} - 4$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T$$
$3$ $$T$$
$5$ $$-2 + T$$
$7$ $$T$$
$11$ $$5 + T$$
$13$ $$-6 + T$$
$17$ $$-4 + T$$
$19$ $$4 + T$$
$23$ $$-4 + T$$
$29$ $$7 + T$$
$31$ $$-3 + T$$
$37$ $$-8 + T$$
$41$ $$-6 + T$$
$43$ $$-8 + T$$
$47$ $$6 + T$$
$53$ $$-6 + T$$
$59$ $$7 + T$$
$61$ $$T$$
$67$ $$-10 + T$$
$71$ $$-4 + T$$
$73$ $$-13 + T$$
$79$ $$3 + T$$
$83$ $$-7 + T$$
$89$ $$6 + T$$
$97$ $$5 + T$$