# Properties

 Label 950.2.a.a Level $950$ Weight $2$ Character orbit 950.a Self dual yes Analytic conductor $7.586$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$950 = 2 \cdot 5^{2} \cdot 19$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 950.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$7.58578819202$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 190) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

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

## 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 0 1.00000 1.00000 −1.00000 −2.00000 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
$$2$$ $$1$$
$$5$$ $$1$$
$$19$$ $$-1$$

## 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 950.2.a.a 1
3.b odd 2 1 8550.2.a.bd 1
4.b odd 2 1 7600.2.a.m 1
5.b even 2 1 190.2.a.c 1
5.c odd 4 2 950.2.b.e 2
15.d odd 2 1 1710.2.a.d 1
20.d odd 2 1 1520.2.a.d 1
35.c odd 2 1 9310.2.a.o 1
40.e odd 2 1 6080.2.a.p 1
40.f even 2 1 6080.2.a.h 1
95.d odd 2 1 3610.2.a.b 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
190.2.a.c 1 5.b even 2 1
950.2.a.a 1 1.a even 1 1 trivial
950.2.b.e 2 5.c odd 4 2
1520.2.a.d 1 20.d odd 2 1
1710.2.a.d 1 15.d odd 2 1
3610.2.a.b 1 95.d odd 2 1
6080.2.a.h 1 40.f even 2 1
6080.2.a.p 1 40.e odd 2 1
7600.2.a.m 1 4.b odd 2 1
8550.2.a.bd 1 3.b odd 2 1
9310.2.a.o 1 35.c odd 2 1

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(950))$$:

 $$T_{3} + 1$$ $$T_{7} - 1$$ $$T_{11}$$

## Hecke characteristic polynomials

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