Properties

 Label 7920.2.a.z Level $7920$ Weight $2$ Character orbit 7920.a Self dual yes Analytic conductor $63.242$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$7920 = 2^{4} \cdot 3^{2} \cdot 5 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 7920.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$63.2415184009$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 990) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{5} + O(q^{10})$$ $$q + q^{5} - q^{11} + 2q^{17} - 2q^{19} - 6q^{23} + q^{25} + 2q^{29} - 6q^{37} + 2q^{41} + 2q^{43} + 2q^{47} - 7q^{49} + 2q^{53} - q^{55} - 8q^{59} + 4q^{61} + 4q^{67} + 2q^{71} - 10q^{73} - 4q^{79} - 12q^{83} + 2q^{85} - 2q^{95} - 18q^{97} + O(q^{100})$$

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 0 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
$$2$$ $$-1$$
$$3$$ $$1$$
$$5$$ $$-1$$
$$11$$ $$1$$

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 7920.2.a.z 1
3.b odd 2 1 7920.2.a.k 1
4.b odd 2 1 990.2.a.k yes 1
12.b even 2 1 990.2.a.a 1
20.d odd 2 1 4950.2.a.m 1
20.e even 4 2 4950.2.c.u 2
60.h even 2 1 4950.2.a.bi 1
60.l odd 4 2 4950.2.c.h 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
990.2.a.a 1 12.b even 2 1
990.2.a.k yes 1 4.b odd 2 1
4950.2.a.m 1 20.d odd 2 1
4950.2.a.bi 1 60.h even 2 1
4950.2.c.h 2 60.l odd 4 2
4950.2.c.u 2 20.e even 4 2
7920.2.a.k 1 3.b odd 2 1
7920.2.a.z 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(7920))$$:

 $$T_{7}$$ $$T_{13}$$ $$T_{17} - 2$$ $$T_{19} + 2$$ $$T_{23} + 6$$ $$T_{29} - 2$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T$$
$5$ $$-1 + T$$
$7$ $$T$$
$11$ $$1 + T$$
$13$ $$T$$
$17$ $$-2 + T$$
$19$ $$2 + T$$
$23$ $$6 + T$$
$29$ $$-2 + T$$
$31$ $$T$$
$37$ $$6 + T$$
$41$ $$-2 + T$$
$43$ $$-2 + T$$
$47$ $$-2 + T$$
$53$ $$-2 + T$$
$59$ $$8 + T$$
$61$ $$-4 + T$$
$67$ $$-4 + T$$
$71$ $$-2 + T$$
$73$ $$10 + T$$
$79$ $$4 + T$$
$83$ $$12 + T$$
$89$ $$T$$
$97$ $$18 + T$$