Properties

 Label 490.2.a.c Level $490$ Weight $2$ Character orbit 490.a Self dual yes Analytic conductor $3.913$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$490 = 2 \cdot 5 \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 490.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$3.91266969904$$ Analytic rank: $$1$$ 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

 $$f(q)$$ $$=$$ $$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} - 2q^{9} + O(q^{10})$$ $$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} - 2q^{9} + q^{10} - 6q^{11} + q^{12} - 4q^{13} - q^{15} + q^{16} + 2q^{18} + 2q^{19} - q^{20} + 6q^{22} - 3q^{23} - q^{24} + q^{25} + 4q^{26} - 5q^{27} - 3q^{29} + q^{30} + 8q^{31} - q^{32} - 6q^{33} - 2q^{36} - 4q^{37} - 2q^{38} - 4q^{39} + q^{40} + 9q^{41} - 7q^{43} - 6q^{44} + 2q^{45} + 3q^{46} + q^{48} - q^{50} - 4q^{52} - 6q^{53} + 5q^{54} + 6q^{55} + 2q^{57} + 3q^{58} - 6q^{59} - q^{60} + 5q^{61} - 8q^{62} + q^{64} + 4q^{65} + 6q^{66} + 5q^{67} - 3q^{69} - 6q^{71} + 2q^{72} - 16q^{73} + 4q^{74} + q^{75} + 2q^{76} + 4q^{78} + 2q^{79} - q^{80} + q^{81} - 9q^{82} + 3q^{83} + 7q^{86} - 3q^{87} + 6q^{88} - 15q^{89} - 2q^{90} - 3q^{92} + 8q^{93} - 2q^{95} - q^{96} + 14q^{97} + 12q^{99} + O(q^{100})$$

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
−1.00000 1.00000 1.00000 −1.00000 −1.00000 0 −1.00000 −2.00000 1.00000
 $$n$$: 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 490.2.a.c 1
3.b odd 2 1 4410.2.a.bm 1
4.b odd 2 1 3920.2.a.p 1
5.b even 2 1 2450.2.a.w 1
5.c odd 4 2 2450.2.c.g 2
7.b odd 2 1 490.2.a.b 1
7.c even 3 2 70.2.e.c 2
7.d odd 6 2 490.2.e.h 2
21.c even 2 1 4410.2.a.bd 1
21.h odd 6 2 630.2.k.b 2
28.d even 2 1 3920.2.a.bc 1
28.g odd 6 2 560.2.q.g 2
35.c odd 2 1 2450.2.a.bc 1
35.f even 4 2 2450.2.c.l 2
35.j even 6 2 350.2.e.e 2
35.l odd 12 4 350.2.j.b 4

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
70.2.e.c 2 7.c even 3 2
350.2.e.e 2 35.j even 6 2
350.2.j.b 4 35.l odd 12 4
490.2.a.b 1 7.b odd 2 1
490.2.a.c 1 1.a even 1 1 trivial
490.2.e.h 2 7.d odd 6 2
560.2.q.g 2 28.g odd 6 2
630.2.k.b 2 21.h odd 6 2
2450.2.a.w 1 5.b even 2 1
2450.2.a.bc 1 35.c odd 2 1
2450.2.c.g 2 5.c odd 4 2
2450.2.c.l 2 35.f even 4 2
3920.2.a.p 1 4.b odd 2 1
3920.2.a.bc 1 28.d even 2 1
4410.2.a.bd 1 21.c even 2 1
4410.2.a.bm 1 3.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 $$S_{2}^{\mathrm{new}}(\Gamma_0(490))$$:

 $$T_{3} - 1$$ $$T_{11} + 6$$ $$T_{13} + 4$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$1 + T$$
$3$ $$-1 + T$$
$5$ $$1 + T$$
$7$ $$T$$
$11$ $$6 + T$$
$13$ $$4 + T$$
$17$ $$T$$
$19$ $$-2 + T$$
$23$ $$3 + T$$
$29$ $$3 + T$$
$31$ $$-8 + T$$
$37$ $$4 + T$$
$41$ $$-9 + T$$
$43$ $$7 + T$$
$47$ $$T$$
$53$ $$6 + T$$
$59$ $$6 + T$$
$61$ $$-5 + T$$
$67$ $$-5 + T$$
$71$ $$6 + T$$
$73$ $$16 + T$$
$79$ $$-2 + T$$
$83$ $$-3 + T$$
$89$ $$15 + T$$
$97$ $$-14 + T$$