# Properties

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

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## 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: $$1$$ 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

 $$f(q)$$ $$=$$ $$q - q^{2} + q^{4} + q^{5} - q^{8} + O(q^{10})$$ $$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 5q^{11} + q^{16} + 2q^{17} + q^{19} + q^{20} + 5q^{22} + q^{23} - 4q^{25} - 4q^{29} + 9q^{31} - q^{32} - 2q^{34} + 5q^{37} - q^{38} - q^{40} - 9q^{41} - 10q^{43} - 5q^{44} - q^{46} + 6q^{47} + 4q^{50} - 12q^{53} - 5q^{55} + 4q^{58} - 14q^{59} - 9q^{62} + q^{64} - 8q^{67} + 2q^{68} + 13q^{71} + 2q^{73} - 5q^{74} + q^{76} + 6q^{79} + q^{80} + 9q^{82} - 4q^{83} + 2q^{85} + 10q^{86} + 5q^{88} - 9q^{89} + q^{92} - 6q^{94} + q^{95} - 16q^{97} + O(q^{100})$$

## 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 1.00000 0 0 −1.00000 0 −1.00000
 $$n$$: 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.i 1
3.b odd 2 1 2646.2.a.v 1
7.b odd 2 1 378.2.a.c 1
21.c even 2 1 378.2.a.f yes 1
28.d even 2 1 3024.2.a.m 1
35.c odd 2 1 9450.2.a.dc 1
63.l odd 6 2 1134.2.f.n 2
63.o even 6 2 1134.2.f.c 2
84.h odd 2 1 3024.2.a.t 1
105.g even 2 1 9450.2.a.bx 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
378.2.a.c 1 7.b odd 2 1
378.2.a.f yes 1 21.c even 2 1
1134.2.f.c 2 63.o even 6 2
1134.2.f.n 2 63.l odd 6 2
2646.2.a.i 1 1.a even 1 1 trivial
2646.2.a.v 1 3.b odd 2 1
3024.2.a.m 1 28.d even 2 1
3024.2.a.t 1 84.h odd 2 1
9450.2.a.bx 1 105.g even 2 1
9450.2.a.dc 1 35.c odd 2 1

## Hecke kernels

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

 $$T_{5} - 1$$ $$T_{11} + 5$$ $$T_{13}$$ $$T_{17} - 2$$

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T$$
$3$ $$T$$
$5$ $$-1 + T$$
$7$ $$T$$
$11$ $$5 + T$$
$13$ $$T$$
$17$ $$-2 + T$$
$19$ $$-1 + T$$
$23$ $$-1 + T$$
$29$ $$4 + T$$
$31$ $$-9 + T$$
$37$ $$-5 + T$$
$41$ $$9 + T$$
$43$ $$10 + T$$
$47$ $$-6 + T$$
$53$ $$12 + T$$
$59$ $$14 + T$$
$61$ $$T$$
$67$ $$8 + T$$
$71$ $$-13 + T$$
$73$ $$-2 + T$$
$79$ $$-6 + T$$
$83$ $$4 + T$$
$89$ $$9 + T$$
$97$ $$16 + T$$
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