Properties

 Label 92.2.a.b Level $92$ Weight $2$ Character orbit 92.a Self dual yes Analytic conductor $0.735$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$92 = 2^{2} \cdot 23$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 92.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$0.734623698596$$ 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

 $$f(q)$$ $$=$$ $$q + q^{3} + 2q^{7} - 2q^{9} + O(q^{10})$$ $$q + q^{3} + 2q^{7} - 2q^{9} - q^{13} - 6q^{17} + 2q^{19} + 2q^{21} - q^{23} - 5q^{25} - 5q^{27} - 3q^{29} + 5q^{31} + 8q^{37} - q^{39} + 3q^{41} + 8q^{43} + 9q^{47} - 3q^{49} - 6q^{51} + 6q^{53} + 2q^{57} - 12q^{59} + 14q^{61} - 4q^{63} + 8q^{67} - q^{69} - 15q^{71} - 7q^{73} - 5q^{75} - 10q^{79} + q^{81} + 6q^{83} - 3q^{87} - 2q^{91} + 5q^{93} - 10q^{97} + O(q^{100})$$

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
0 1.00000 0 0 0 2.00000 0 −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
$$2$$ $$-1$$
$$23$$ $$1$$

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 92.2.a.b 1
3.b odd 2 1 828.2.a.b 1
4.b odd 2 1 368.2.a.b 1
5.b even 2 1 2300.2.a.c 1
5.c odd 4 2 2300.2.c.f 2
7.b odd 2 1 4508.2.a.a 1
8.b even 2 1 1472.2.a.c 1
8.d odd 2 1 1472.2.a.j 1
12.b even 2 1 3312.2.a.g 1
20.d odd 2 1 9200.2.a.ba 1
23.b odd 2 1 2116.2.a.d 1
92.b even 2 1 8464.2.a.f 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
92.2.a.b 1 1.a even 1 1 trivial
368.2.a.b 1 4.b odd 2 1
828.2.a.b 1 3.b odd 2 1
1472.2.a.c 1 8.b even 2 1
1472.2.a.j 1 8.d odd 2 1
2116.2.a.d 1 23.b odd 2 1
2300.2.a.c 1 5.b even 2 1
2300.2.c.f 2 5.c odd 4 2
3312.2.a.g 1 12.b even 2 1
4508.2.a.a 1 7.b odd 2 1
8464.2.a.f 1 92.b even 2 1
9200.2.a.ba 1 20.d odd 2 1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $$T_{3} - 1$$ acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(92))$$.

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$-1 + T$$
$5$ $$T$$
$7$ $$-2 + T$$
$11$ $$T$$
$13$ $$1 + T$$
$17$ $$6 + T$$
$19$ $$-2 + T$$
$23$ $$1 + T$$
$29$ $$3 + T$$
$31$ $$-5 + T$$
$37$ $$-8 + T$$
$41$ $$-3 + T$$
$43$ $$-8 + T$$
$47$ $$-9 + T$$
$53$ $$-6 + T$$
$59$ $$12 + T$$
$61$ $$-14 + T$$
$67$ $$-8 + T$$
$71$ $$15 + T$$
$73$ $$7 + T$$
$79$ $$10 + T$$
$83$ $$-6 + T$$
$89$ $$T$$
$97$ $$10 + T$$