Properties

 Label 1260.2.a.g Level $1260$ Weight $2$ Character orbit 1260.a Self dual yes Analytic conductor $10.061$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1260.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$10.0611506547$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 420) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{5} - q^{7} + O(q^{10})$$ $$q + q^{5} - q^{7} - 2q^{11} + 4q^{13} - 6q^{17} + 6q^{19} + 8q^{23} + q^{25} + 2q^{29} + 10q^{31} - q^{35} + 2q^{37} - 10q^{41} - 4q^{43} + 8q^{47} + q^{49} - 4q^{53} - 2q^{55} + 8q^{59} + 6q^{61} + 4q^{65} + 12q^{67} + 6q^{71} - 12q^{73} + 2q^{77} - 8q^{79} + 4q^{83} - 6q^{85} + 10q^{89} - 4q^{91} + 6q^{95} + 8q^{97} + O(q^{100})$$

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 1260.2.a.g 1
3.b odd 2 1 420.2.a.a 1
4.b odd 2 1 5040.2.a.bl 1
5.b even 2 1 6300.2.a.v 1
5.c odd 4 2 6300.2.k.e 2
7.b odd 2 1 8820.2.a.f 1
12.b even 2 1 1680.2.a.n 1
15.d odd 2 1 2100.2.a.q 1
15.e even 4 2 2100.2.k.g 2
21.c even 2 1 2940.2.a.l 1
21.g even 6 2 2940.2.q.a 2
21.h odd 6 2 2940.2.q.m 2
24.f even 2 1 6720.2.a.bd 1
24.h odd 2 1 6720.2.a.cb 1
60.h even 2 1 8400.2.a.c 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
420.2.a.a 1 3.b odd 2 1
1260.2.a.g 1 1.a even 1 1 trivial
1680.2.a.n 1 12.b even 2 1
2100.2.a.q 1 15.d odd 2 1
2100.2.k.g 2 15.e even 4 2
2940.2.a.l 1 21.c even 2 1
2940.2.q.a 2 21.g even 6 2
2940.2.q.m 2 21.h odd 6 2
5040.2.a.bl 1 4.b odd 2 1
6300.2.a.v 1 5.b even 2 1
6300.2.k.e 2 5.c odd 4 2
6720.2.a.bd 1 24.f even 2 1
6720.2.a.cb 1 24.h odd 2 1
8400.2.a.c 1 60.h even 2 1
8820.2.a.f 1 7.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 $$S_{2}^{\mathrm{new}}(\Gamma_0(1260))$$:

 $$T_{11} + 2$$ $$T_{17} + 6$$

Hecke characteristic polynomials

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