Properties

 Label 460.2.a.d Level $460$ Weight $2$ Character orbit 460.a Self dual yes Analytic conductor $3.673$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$460 = 2^{2} \cdot 5 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 460.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$3.67311849298$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: yes Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + 3 q^{3} - q^{5} + 2 q^{7} + 6 q^{9}+O(q^{10})$$ q + 3 * q^3 - q^5 + 2 * q^7 + 6 * q^9 $$q + 3 q^{3} - q^{5} + 2 q^{7} + 6 q^{9} - 3 q^{13} - 3 q^{15} + 4 q^{17} - 4 q^{19} + 6 q^{21} - q^{23} + q^{25} + 9 q^{27} + q^{29} + q^{31} - 2 q^{35} - 8 q^{37} - 9 q^{39} + 11 q^{41} - 10 q^{43} - 6 q^{45} - q^{47} - 3 q^{49} + 12 q^{51} - 6 q^{53} - 12 q^{57} - 8 q^{59} - 8 q^{61} + 12 q^{63} + 3 q^{65} + 12 q^{67} - 3 q^{69} + 13 q^{71} + 7 q^{73} + 3 q^{75} - 12 q^{79} + 9 q^{81} + 16 q^{83} - 4 q^{85} + 3 q^{87} - 6 q^{89} - 6 q^{91} + 3 q^{93} + 4 q^{95} + 2 q^{97}+O(q^{100})$$ q + 3 * q^3 - q^5 + 2 * q^7 + 6 * q^9 - 3 * q^13 - 3 * q^15 + 4 * q^17 - 4 * q^19 + 6 * q^21 - q^23 + q^25 + 9 * q^27 + q^29 + q^31 - 2 * q^35 - 8 * q^37 - 9 * q^39 + 11 * q^41 - 10 * q^43 - 6 * q^45 - q^47 - 3 * q^49 + 12 * q^51 - 6 * q^53 - 12 * q^57 - 8 * q^59 - 8 * q^61 + 12 * q^63 + 3 * q^65 + 12 * q^67 - 3 * q^69 + 13 * q^71 + 7 * q^73 + 3 * q^75 - 12 * q^79 + 9 * q^81 + 16 * q^83 - 4 * q^85 + 3 * q^87 - 6 * q^89 - 6 * q^91 + 3 * q^93 + 4 * q^95 + 2 * q^97

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 3.00000 0 −1.00000 0 2.00000 0 6.00000 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
$$2$$ $$-1$$
$$5$$ $$1$$
$$23$$ $$1$$

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 460.2.a.d 1
3.b odd 2 1 4140.2.a.k 1
4.b odd 2 1 1840.2.a.a 1
5.b even 2 1 2300.2.a.a 1
5.c odd 4 2 2300.2.c.a 2
8.b even 2 1 7360.2.a.b 1
8.d odd 2 1 7360.2.a.bb 1
20.d odd 2 1 9200.2.a.bk 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
460.2.a.d 1 1.a even 1 1 trivial
1840.2.a.a 1 4.b odd 2 1
2300.2.a.a 1 5.b even 2 1
2300.2.c.a 2 5.c odd 4 2
4140.2.a.k 1 3.b odd 2 1
7360.2.a.b 1 8.b even 2 1
7360.2.a.bb 1 8.d odd 2 1
9200.2.a.bk 1 20.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3} - 3$$ acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(460))$$.

Hecke characteristic polynomials

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