# Properties

 Label 5445.2.a.e Level $5445$ Weight $2$ Character orbit 5445.a Self dual yes Analytic conductor $43.479$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$5445 = 3^{2} \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5445.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$43.4785439006$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 1815) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{2} - q^{4} + q^{5} + 2 q^{7} + 3 q^{8}+O(q^{10})$$ q - q^2 - q^4 + q^5 + 2 * q^7 + 3 * q^8 $$q - q^{2} - q^{4} + q^{5} + 2 q^{7} + 3 q^{8} - q^{10} - 4 q^{13} - 2 q^{14} - q^{16} - 6 q^{17} + 6 q^{19} - q^{20} - 4 q^{23} + q^{25} + 4 q^{26} - 2 q^{28} + 6 q^{29} + 8 q^{31} - 5 q^{32} + 6 q^{34} + 2 q^{35} - 6 q^{37} - 6 q^{38} + 3 q^{40} - 6 q^{41} + 6 q^{43} + 4 q^{46} - 8 q^{47} - 3 q^{49} - q^{50} + 4 q^{52} - 6 q^{53} + 6 q^{56} - 6 q^{58} - 4 q^{61} - 8 q^{62} + 7 q^{64} - 4 q^{65} + 12 q^{67} + 6 q^{68} - 2 q^{70} - 8 q^{71} - 16 q^{73} + 6 q^{74} - 6 q^{76} - 2 q^{79} - q^{80} + 6 q^{82} - 6 q^{85} - 6 q^{86} - 10 q^{89} - 8 q^{91} + 4 q^{92} + 8 q^{94} + 6 q^{95} - 6 q^{97} + 3 q^{98}+O(q^{100})$$ q - q^2 - q^4 + q^5 + 2 * q^7 + 3 * q^8 - q^10 - 4 * q^13 - 2 * q^14 - q^16 - 6 * q^17 + 6 * q^19 - q^20 - 4 * q^23 + q^25 + 4 * q^26 - 2 * q^28 + 6 * q^29 + 8 * q^31 - 5 * q^32 + 6 * q^34 + 2 * q^35 - 6 * q^37 - 6 * q^38 + 3 * q^40 - 6 * q^41 + 6 * q^43 + 4 * q^46 - 8 * q^47 - 3 * q^49 - q^50 + 4 * q^52 - 6 * q^53 + 6 * q^56 - 6 * q^58 - 4 * q^61 - 8 * q^62 + 7 * q^64 - 4 * q^65 + 12 * q^67 + 6 * q^68 - 2 * q^70 - 8 * q^71 - 16 * q^73 + 6 * q^74 - 6 * q^76 - 2 * q^79 - q^80 + 6 * q^82 - 6 * q^85 - 6 * q^86 - 10 * q^89 - 8 * q^91 + 4 * q^92 + 8 * q^94 + 6 * q^95 - 6 * q^97 + 3 * q^98

## 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 2.00000 3.00000 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
$$3$$ $$-1$$
$$5$$ $$-1$$
$$11$$ $$1$$

## 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 5445.2.a.e 1
3.b odd 2 1 1815.2.a.e yes 1
11.b odd 2 1 5445.2.a.j 1
15.d odd 2 1 9075.2.a.d 1
33.d even 2 1 1815.2.a.a 1
165.d even 2 1 9075.2.a.n 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1815.2.a.a 1 33.d even 2 1
1815.2.a.e yes 1 3.b odd 2 1
5445.2.a.e 1 1.a even 1 1 trivial
5445.2.a.j 1 11.b odd 2 1
9075.2.a.d 1 15.d odd 2 1
9075.2.a.n 1 165.d even 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5445))$$:

 $$T_{2} + 1$$ T2 + 1 $$T_{7} - 2$$ T7 - 2 $$T_{23} + 4$$ T23 + 4 $$T_{53} + 6$$ T53 + 6

## Hecke characteristic polynomials

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