# Properties

 Label 5635.2.a.j Level $5635$ Weight $2$ Character orbit 5635.a Self dual yes Analytic conductor $44.996$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5635 = 5 \cdot 7^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5635.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$44.9957015390$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 115) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + 2 q^{2} + 2 q^{4} + q^{5} - 3 q^{9} + O(q^{10})$$ $$q + 2 q^{2} + 2 q^{4} + q^{5} - 3 q^{9} + 2 q^{10} + 2 q^{11} + 2 q^{13} - 4 q^{16} - 3 q^{17} - 6 q^{18} + 2 q^{19} + 2 q^{20} + 4 q^{22} + q^{23} + q^{25} + 4 q^{26} + 7 q^{29} + 5 q^{31} - 8 q^{32} - 6 q^{34} - 6 q^{36} + 11 q^{37} + 4 q^{38} - q^{41} + 4 q^{44} - 3 q^{45} + 2 q^{46} + 2 q^{50} + 4 q^{52} + 11 q^{53} + 2 q^{55} + 14 q^{58} + 13 q^{59} + 8 q^{61} + 10 q^{62} - 8 q^{64} + 2 q^{65} + 5 q^{67} - 6 q^{68} + 5 q^{71} - 6 q^{73} + 22 q^{74} + 4 q^{76} - 12 q^{79} - 4 q^{80} + 9 q^{81} - 2 q^{82} - 9 q^{83} - 3 q^{85} - 4 q^{89} - 6 q^{90} + 2 q^{92} + 2 q^{95} + 14 q^{97} - 6 q^{99} + O(q^{100})$$

## 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
2.00000 0 2.00000 1.00000 0 0 0 −3.00000 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
$$5$$ $$-1$$
$$7$$ $$-1$$
$$23$$ $$-1$$

## 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 5635.2.a.j 1
7.b odd 2 1 115.2.a.a 1
21.c even 2 1 1035.2.a.b 1
28.d even 2 1 1840.2.a.d 1
35.c odd 2 1 575.2.a.b 1
35.f even 4 2 575.2.b.a 2
56.e even 2 1 7360.2.a.n 1
56.h odd 2 1 7360.2.a.q 1
105.g even 2 1 5175.2.a.y 1
140.c even 2 1 9200.2.a.t 1
161.c even 2 1 2645.2.a.c 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
115.2.a.a 1 7.b odd 2 1
575.2.a.b 1 35.c odd 2 1
575.2.b.a 2 35.f even 4 2
1035.2.a.b 1 21.c even 2 1
1840.2.a.d 1 28.d even 2 1
2645.2.a.c 1 161.c even 2 1
5175.2.a.y 1 105.g even 2 1
5635.2.a.j 1 1.a even 1 1 trivial
7360.2.a.n 1 56.e even 2 1
7360.2.a.q 1 56.h odd 2 1
9200.2.a.t 1 140.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 $$S_{2}^{\mathrm{new}}(\Gamma_0(5635))$$:

 $$T_{2} - 2$$ $$T_{3}$$ $$T_{11} - 2$$ $$T_{17} + 3$$

## Hecke characteristic polynomials

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