Properties

 Label 2240.2.a.v Level $2240$ Weight $2$ Character orbit 2240.a Self dual yes Analytic conductor $17.886$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$2240 = 2^{6} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 2240.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$17.8864900528$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 280) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{3} + q^{5} - q^{7} - 2q^{9} + O(q^{10})$$ $$q + q^{3} + q^{5} - q^{7} - 2q^{9} + 5q^{11} - q^{13} + q^{15} + 3q^{17} + 6q^{19} - q^{21} - 6q^{23} + q^{25} - 5q^{27} + 9q^{29} + 5q^{33} - q^{35} - 6q^{37} - q^{39} + 8q^{41} - 6q^{43} - 2q^{45} + 3q^{47} + q^{49} + 3q^{51} + 12q^{53} + 5q^{55} + 6q^{57} - 8q^{59} + 4q^{61} + 2q^{63} - q^{65} + 4q^{67} - 6q^{69} + 8q^{71} + 10q^{73} + q^{75} - 5q^{77} - 3q^{79} + q^{81} + 12q^{83} + 3q^{85} + 9q^{87} - 16q^{89} + q^{91} + 6q^{95} + 7q^{97} - 10q^{99} + O(q^{100})$$

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
0 1.00000 0 1.00000 0 −1.00000 0 −2.00000 0
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$1$$
$$5$$ $$-1$$
$$7$$ $$1$$

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 2240.2.a.v 1
4.b odd 2 1 2240.2.a.j 1
8.b even 2 1 280.2.a.b 1
8.d odd 2 1 560.2.a.e 1
24.f even 2 1 5040.2.a.be 1
24.h odd 2 1 2520.2.a.p 1
40.e odd 2 1 2800.2.a.i 1
40.f even 2 1 1400.2.a.k 1
40.i odd 4 2 1400.2.g.e 2
40.k even 4 2 2800.2.g.m 2
56.e even 2 1 3920.2.a.r 1
56.h odd 2 1 1960.2.a.k 1
56.j odd 6 2 1960.2.q.e 2
56.p even 6 2 1960.2.q.m 2
280.c odd 2 1 9800.2.a.n 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
280.2.a.b 1 8.b even 2 1
560.2.a.e 1 8.d odd 2 1
1400.2.a.k 1 40.f even 2 1
1400.2.g.e 2 40.i odd 4 2
1960.2.a.k 1 56.h odd 2 1
1960.2.q.e 2 56.j odd 6 2
1960.2.q.m 2 56.p even 6 2
2240.2.a.j 1 4.b odd 2 1
2240.2.a.v 1 1.a even 1 1 trivial
2520.2.a.p 1 24.h odd 2 1
2800.2.a.i 1 40.e odd 2 1
2800.2.g.m 2 40.k even 4 2
3920.2.a.r 1 56.e even 2 1
5040.2.a.be 1 24.f even 2 1
9800.2.a.n 1 280.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 $$S_{2}^{\mathrm{new}}(\Gamma_0(2240))$$:

 $$T_{3} - 1$$ $$T_{11} - 5$$ $$T_{13} + 1$$ $$T_{19} - 6$$

Hecke characteristic polynomials

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