Properties

 Label 4410.2.a.bl 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 630) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{4} + q^{5} + q^{8} + O(q^{10})$$ $$q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} + 4q^{11} - 6q^{13} + q^{16} + 4q^{17} - 6q^{19} + q^{20} + 4q^{22} + q^{25} - 6q^{26} + 6q^{29} + 4q^{31} + q^{32} + 4q^{34} + 8q^{37} - 6q^{38} + q^{40} + 10q^{41} - 2q^{43} + 4q^{44} + 10q^{47} + q^{50} - 6q^{52} - 14q^{53} + 4q^{55} + 6q^{58} - 4q^{59} + 8q^{61} + 4q^{62} + q^{64} - 6q^{65} + 6q^{67} + 4q^{68} + 2q^{71} + 10q^{73} + 8q^{74} - 6q^{76} + 16q^{79} + q^{80} + 10q^{82} - 8q^{83} + 4q^{85} - 2q^{86} + 4q^{88} + 2q^{89} + 10q^{94} - 6q^{95} - 2q^{97} + O(q^{100})$$

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.bl 1
3.b odd 2 1 4410.2.a.a 1
7.b odd 2 1 630.2.a.g yes 1
21.c even 2 1 630.2.a.e 1
28.d even 2 1 5040.2.a.n 1
35.c odd 2 1 3150.2.a.s 1
35.f even 4 2 3150.2.g.s 2
84.h odd 2 1 5040.2.a.bp 1
105.g even 2 1 3150.2.a.bh 1
105.k odd 4 2 3150.2.g.b 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
630.2.a.e 1 21.c even 2 1
630.2.a.g yes 1 7.b odd 2 1
3150.2.a.s 1 35.c odd 2 1
3150.2.a.bh 1 105.g even 2 1
3150.2.g.b 2 105.k odd 4 2
3150.2.g.s 2 35.f even 4 2
4410.2.a.a 1 3.b odd 2 1
4410.2.a.bl 1 1.a even 1 1 trivial
5040.2.a.n 1 28.d even 2 1
5040.2.a.bp 1 84.h odd 2 1

Hecke kernels

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

 $$T_{11} - 4$$ $$T_{13} + 6$$ $$T_{17} - 4$$ $$T_{19} + 6$$ $$T_{29} - 6$$ $$T_{31} - 4$$

Hecke characteristic polynomials

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