Properties

 Label 4410.2.a.ba Level $4410$ Weight $2$ Character orbit 4410.a Self dual yes Analytic conductor $35.214$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4410.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$35.2140272914$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 210) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

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

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
$$2$$ $$-1$$
$$3$$ $$-1$$
$$5$$ $$1$$
$$7$$ $$-1$$

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 4410.2.a.ba 1
3.b odd 2 1 1470.2.a.h 1
7.b odd 2 1 4410.2.a.bj 1
7.d odd 6 2 630.2.k.c 2
15.d odd 2 1 7350.2.a.bu 1
21.c even 2 1 1470.2.a.a 1
21.g even 6 2 210.2.i.d 2
21.h odd 6 2 1470.2.i.m 2
84.j odd 6 2 1680.2.bg.g 2
105.g even 2 1 7350.2.a.cp 1
105.p even 6 2 1050.2.i.b 2
105.w odd 12 4 1050.2.o.i 4

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
210.2.i.d 2 21.g even 6 2
630.2.k.c 2 7.d odd 6 2
1050.2.i.b 2 105.p even 6 2
1050.2.o.i 4 105.w odd 12 4
1470.2.a.a 1 21.c even 2 1
1470.2.a.h 1 3.b odd 2 1
1470.2.i.m 2 21.h odd 6 2
1680.2.bg.g 2 84.j odd 6 2
4410.2.a.ba 1 1.a even 1 1 trivial
4410.2.a.bj 1 7.b odd 2 1
7350.2.a.bu 1 15.d odd 2 1
7350.2.a.cp 1 105.g even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(4410))$$:

 $$T_{11} - 1$$ $$T_{13} + 1$$ $$T_{17}$$ $$T_{19} - 3$$ $$T_{29} - 8$$ $$T_{31} - 2$$

Hecke characteristic polynomials

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