Properties

 Label 190.2.a.c Level $190$ Weight $2$ Character orbit 190.a Self dual yes Analytic conductor $1.517$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$190 = 2 \cdot 5 \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 190.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$1.51715763840$$ 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

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} - 2q^{9} + O(q^{10})$$ $$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - q^{7} + q^{8} - 2q^{9} + q^{10} + q^{12} - q^{13} - q^{14} + q^{15} + q^{16} - 3q^{17} - 2q^{18} + q^{19} + q^{20} - q^{21} + 3q^{23} + q^{24} + q^{25} - q^{26} - 5q^{27} - q^{28} - 3q^{29} + q^{30} + 2q^{31} + q^{32} - 3q^{34} - q^{35} - 2q^{36} - 10q^{37} + q^{38} - q^{39} + q^{40} + 6q^{41} - q^{42} + 2q^{43} - 2q^{45} + 3q^{46} + q^{48} - 6q^{49} + q^{50} - 3q^{51} - q^{52} + 3q^{53} - 5q^{54} - q^{56} + q^{57} - 3q^{58} + 3q^{59} + q^{60} + 8q^{61} + 2q^{62} + 2q^{63} + q^{64} - q^{65} - 7q^{67} - 3q^{68} + 3q^{69} - q^{70} + 12q^{71} - 2q^{72} - 13q^{73} - 10q^{74} + q^{75} + q^{76} - q^{78} + 14q^{79} + q^{80} + q^{81} + 6q^{82} + 6q^{83} - q^{84} - 3q^{85} + 2q^{86} - 3q^{87} + 6q^{89} - 2q^{90} + q^{91} + 3q^{92} + 2q^{93} + q^{95} + q^{96} - 10q^{97} - 6q^{98} + O(q^{100})$$

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 −1.00000 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
$$2$$ $$-1$$
$$5$$ $$-1$$
$$19$$ $$-1$$

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 190.2.a.c 1
3.b odd 2 1 1710.2.a.d 1
4.b odd 2 1 1520.2.a.d 1
5.b even 2 1 950.2.a.a 1
5.c odd 4 2 950.2.b.e 2
7.b odd 2 1 9310.2.a.o 1
8.b even 2 1 6080.2.a.h 1
8.d odd 2 1 6080.2.a.p 1
15.d odd 2 1 8550.2.a.bd 1
19.b odd 2 1 3610.2.a.b 1
20.d odd 2 1 7600.2.a.m 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.2.a.c 1 1.a even 1 1 trivial
950.2.a.a 1 5.b even 2 1
950.2.b.e 2 5.c odd 4 2
1520.2.a.d 1 4.b odd 2 1
1710.2.a.d 1 3.b odd 2 1
3610.2.a.b 1 19.b odd 2 1
6080.2.a.h 1 8.b even 2 1
6080.2.a.p 1 8.d odd 2 1
7600.2.a.m 1 20.d odd 2 1
8550.2.a.bd 1 15.d odd 2 1
9310.2.a.o 1 7.b odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3} - 1$$ acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(190))$$.

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$-1 + T$$
$3$ $$-1 + T$$
$5$ $$-1 + T$$
$7$ $$1 + T$$
$11$ $$T$$
$13$ $$1 + T$$
$17$ $$3 + T$$
$19$ $$-1 + T$$
$23$ $$-3 + T$$
$29$ $$3 + T$$
$31$ $$-2 + T$$
$37$ $$10 + T$$
$41$ $$-6 + T$$
$43$ $$-2 + T$$
$47$ $$T$$
$53$ $$-3 + T$$
$59$ $$-3 + T$$
$61$ $$-8 + T$$
$67$ $$7 + T$$
$71$ $$-12 + T$$
$73$ $$13 + T$$
$79$ $$-14 + T$$
$83$ $$-6 + T$$
$89$ $$-6 + T$$
$97$ $$10 + T$$