Properties

 Label 1932.2.a.b Level $1932$ Weight $2$ Character orbit 1932.a Self dual yes Analytic conductor $15.427$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1932.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$15.4270976705$$ 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

 $$f(q)$$ $$=$$ $$q + q^{3} + q^{7} + q^{9}+O(q^{10})$$ q + q^3 + q^7 + q^9 $$q + q^{3} + q^{7} + q^{9} + 3 q^{11} + 2 q^{13} + 5 q^{19} + q^{21} - q^{23} - 5 q^{25} + q^{27} + 6 q^{29} - 10 q^{31} + 3 q^{33} + 2 q^{37} + 2 q^{39} + 3 q^{41} - 4 q^{43} + 3 q^{47} + q^{49} + 3 q^{53} + 5 q^{57} + 9 q^{59} - q^{61} + q^{63} + 8 q^{67} - q^{69} - 12 q^{71} + 8 q^{73} - 5 q^{75} + 3 q^{77} + 14 q^{79} + q^{81} + 6 q^{83} + 6 q^{87} - 6 q^{89} + 2 q^{91} - 10 q^{93} - 10 q^{97} + 3 q^{99}+O(q^{100})$$ q + q^3 + q^7 + q^9 + 3 * q^11 + 2 * q^13 + 5 * q^19 + q^21 - q^23 - 5 * q^25 + q^27 + 6 * q^29 - 10 * q^31 + 3 * q^33 + 2 * q^37 + 2 * q^39 + 3 * q^41 - 4 * q^43 + 3 * q^47 + q^49 + 3 * q^53 + 5 * q^57 + 9 * q^59 - q^61 + q^63 + 8 * q^67 - q^69 - 12 * q^71 + 8 * q^73 - 5 * q^75 + 3 * q^77 + 14 * q^79 + q^81 + 6 * q^83 + 6 * q^87 - 6 * q^89 + 2 * q^91 - 10 * q^93 - 10 * q^97 + 3 * q^99

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 1.00000 0 0 0 1.00000 0 1.00000 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
$$2$$ $$-1$$
$$3$$ $$-1$$
$$7$$ $$-1$$
$$23$$ $$1$$

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 1932.2.a.b 1
3.b odd 2 1 5796.2.a.d 1
4.b odd 2 1 7728.2.a.d 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
1932.2.a.b 1 1.a even 1 1 trivial
5796.2.a.d 1 3.b odd 2 1
7728.2.a.d 1 4.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 $$S_{2}^{\mathrm{new}}(\Gamma_0(1932))$$:

 $$T_{5}$$ T5 $$T_{11} - 3$$ T11 - 3

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T - 1$$
$5$ $$T$$
$7$ $$T - 1$$
$11$ $$T - 3$$
$13$ $$T - 2$$
$17$ $$T$$
$19$ $$T - 5$$
$23$ $$T + 1$$
$29$ $$T - 6$$
$31$ $$T + 10$$
$37$ $$T - 2$$
$41$ $$T - 3$$
$43$ $$T + 4$$
$47$ $$T - 3$$
$53$ $$T - 3$$
$59$ $$T - 9$$
$61$ $$T + 1$$
$67$ $$T - 8$$
$71$ $$T + 12$$
$73$ $$T - 8$$
$79$ $$T - 14$$
$83$ $$T - 6$$
$89$ $$T + 6$$
$97$ $$T + 10$$