Properties

 Label 2240.2.a.n 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 70) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{5} - q^{7} - 3q^{9} + O(q^{10})$$ $$q + q^{5} - q^{7} - 3q^{9} - 4q^{11} + 6q^{13} + 2q^{17} + q^{25} - 6q^{29} + 8q^{31} - q^{35} + 10q^{37} + 2q^{41} - 4q^{43} - 3q^{45} + 8q^{47} + q^{49} + 2q^{53} - 4q^{55} + 8q^{59} + 14q^{61} + 3q^{63} + 6q^{65} + 12q^{67} - 16q^{71} + 2q^{73} + 4q^{77} - 8q^{79} + 9q^{81} - 8q^{83} + 2q^{85} + 10q^{89} - 6q^{91} + 2q^{97} + 12q^{99} + O(q^{100})$$

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 0 0 1.00000 0 −1.00000 0 −3.00000 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.n 1
4.b odd 2 1 2240.2.a.q 1
8.b even 2 1 70.2.a.a 1
8.d odd 2 1 560.2.a.d 1
24.f even 2 1 5040.2.a.bm 1
24.h odd 2 1 630.2.a.d 1
40.e odd 2 1 2800.2.a.m 1
40.f even 2 1 350.2.a.b 1
40.i odd 4 2 350.2.c.b 2
40.k even 4 2 2800.2.g.n 2
56.e even 2 1 3920.2.a.t 1
56.h odd 2 1 490.2.a.h 1
56.j odd 6 2 490.2.e.c 2
56.p even 6 2 490.2.e.d 2
88.b odd 2 1 8470.2.a.j 1
120.i odd 2 1 3150.2.a.bj 1
120.w even 4 2 3150.2.g.c 2
168.i even 2 1 4410.2.a.b 1
280.c odd 2 1 2450.2.a.l 1
280.s even 4 2 2450.2.c.k 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
70.2.a.a 1 8.b even 2 1
350.2.a.b 1 40.f even 2 1
350.2.c.b 2 40.i odd 4 2
490.2.a.h 1 56.h odd 2 1
490.2.e.c 2 56.j odd 6 2
490.2.e.d 2 56.p even 6 2
560.2.a.d 1 8.d odd 2 1
630.2.a.d 1 24.h odd 2 1
2240.2.a.n 1 1.a even 1 1 trivial
2240.2.a.q 1 4.b odd 2 1
2450.2.a.l 1 280.c odd 2 1
2450.2.c.k 2 280.s even 4 2
2800.2.a.m 1 40.e odd 2 1
2800.2.g.n 2 40.k even 4 2
3150.2.a.bj 1 120.i odd 2 1
3150.2.g.c 2 120.w even 4 2
3920.2.a.t 1 56.e even 2 1
4410.2.a.b 1 168.i even 2 1
5040.2.a.bm 1 24.f even 2 1
8470.2.a.j 1 88.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(2240))$$:

 $$T_{3}$$ $$T_{11} + 4$$ $$T_{13} - 6$$ $$T_{19}$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T$$
$5$ $$-1 + T$$
$7$ $$1 + T$$
$11$ $$4 + T$$
$13$ $$-6 + T$$
$17$ $$-2 + T$$
$19$ $$T$$
$23$ $$T$$
$29$ $$6 + T$$
$31$ $$-8 + T$$
$37$ $$-10 + T$$
$41$ $$-2 + T$$
$43$ $$4 + T$$
$47$ $$-8 + T$$
$53$ $$-2 + T$$
$59$ $$-8 + T$$
$61$ $$-14 + T$$
$67$ $$-12 + T$$
$71$ $$16 + T$$
$73$ $$-2 + T$$
$79$ $$8 + T$$
$83$ $$8 + T$$
$89$ $$-10 + T$$
$97$ $$-2 + T$$