Properties

 Label 5040.2.a.v Level $5040$ Weight $2$ Character orbit 5040.a Self dual yes Analytic conductor $40.245$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$5040 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 5040.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$40.2446026187$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 35) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{5} - q^{7} + O(q^{10})$$ $$q + q^{5} - q^{7} - 3q^{11} + 5q^{13} - 3q^{17} - 2q^{19} - 6q^{23} + q^{25} - 3q^{29} + 4q^{31} - q^{35} + 2q^{37} + 12q^{41} + 10q^{43} + 9q^{47} + q^{49} - 12q^{53} - 3q^{55} + 8q^{61} + 5q^{65} + 4q^{67} + 2q^{73} + 3q^{77} + q^{79} + 12q^{83} - 3q^{85} + 12q^{89} - 5q^{91} - 2q^{95} - q^{97} + O(q^{100})$$

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
0 0 0 1.00000 0 −1.00000 0 0 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
$$2$$ $$-1$$
$$3$$ $$-1$$
$$5$$ $$-1$$
$$7$$ $$1$$

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 5040.2.a.v 1
3.b odd 2 1 560.2.a.b 1
4.b odd 2 1 315.2.a.b 1
12.b even 2 1 35.2.a.a 1
15.d odd 2 1 2800.2.a.z 1
15.e even 4 2 2800.2.g.l 2
20.d odd 2 1 1575.2.a.f 1
20.e even 4 2 1575.2.d.c 2
21.c even 2 1 3920.2.a.ba 1
24.f even 2 1 2240.2.a.k 1
24.h odd 2 1 2240.2.a.u 1
28.d even 2 1 2205.2.a.e 1
60.h even 2 1 175.2.a.b 1
60.l odd 4 2 175.2.b.a 2
84.h odd 2 1 245.2.a.c 1
84.j odd 6 2 245.2.e.b 2
84.n even 6 2 245.2.e.a 2
132.d odd 2 1 4235.2.a.c 1
156.h even 2 1 5915.2.a.f 1
420.o odd 2 1 1225.2.a.e 1
420.w even 4 2 1225.2.b.d 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
35.2.a.a 1 12.b even 2 1
175.2.a.b 1 60.h even 2 1
175.2.b.a 2 60.l odd 4 2
245.2.a.c 1 84.h odd 2 1
245.2.e.a 2 84.n even 6 2
245.2.e.b 2 84.j odd 6 2
315.2.a.b 1 4.b odd 2 1
560.2.a.b 1 3.b odd 2 1
1225.2.a.e 1 420.o odd 2 1
1225.2.b.d 2 420.w even 4 2
1575.2.a.f 1 20.d odd 2 1
1575.2.d.c 2 20.e even 4 2
2205.2.a.e 1 28.d even 2 1
2240.2.a.k 1 24.f even 2 1
2240.2.a.u 1 24.h odd 2 1
2800.2.a.z 1 15.d odd 2 1
2800.2.g.l 2 15.e even 4 2
3920.2.a.ba 1 21.c even 2 1
4235.2.a.c 1 132.d odd 2 1
5040.2.a.v 1 1.a even 1 1 trivial
5915.2.a.f 1 156.h even 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(5040))$$:

 $$T_{11} + 3$$ $$T_{13} - 5$$ $$T_{17} + 3$$ $$T_{19} + 2$$ $$T_{29} + 3$$

Hecke characteristic polynomials

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