Properties

 Label 4928.2.a.bf Level $4928$ Weight $2$ Character orbit 4928.a Self dual yes Analytic conductor $39.350$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$4928 = 2^{6} \cdot 7 \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 4928.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$39.3502781161$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 154) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + 2 q^{3} - 2 q^{5} + q^{7} + q^{9} + O(q^{10})$$ $$q + 2 q^{3} - 2 q^{5} + q^{7} + q^{9} + q^{11} + 4 q^{13} - 4 q^{15} + 4 q^{19} + 2 q^{21} - 4 q^{23} - q^{25} - 4 q^{27} - 2 q^{29} + 10 q^{31} + 2 q^{33} - 2 q^{35} + 6 q^{37} + 8 q^{39} - 4 q^{43} - 2 q^{45} - 10 q^{47} + q^{49} + 14 q^{53} - 2 q^{55} + 8 q^{57} + 10 q^{59} + 8 q^{61} + q^{63} - 8 q^{65} + 8 q^{67} - 8 q^{69} + 4 q^{71} + 4 q^{73} - 2 q^{75} + q^{77} - 16 q^{79} - 11 q^{81} + 4 q^{83} - 4 q^{87} + 10 q^{89} + 4 q^{91} + 20 q^{93} - 8 q^{95} + 6 q^{97} + q^{99} + O(q^{100})$$

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
0 2.00000 0 −2.00000 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
$$2$$ $$-1$$
$$7$$ $$-1$$
$$11$$ $$-1$$

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 4928.2.a.bf 1
4.b odd 2 1 4928.2.a.d 1
8.b even 2 1 1232.2.a.c 1
8.d odd 2 1 154.2.a.b 1
24.f even 2 1 1386.2.a.f 1
40.e odd 2 1 3850.2.a.o 1
40.k even 4 2 3850.2.c.d 2
56.e even 2 1 1078.2.a.b 1
56.h odd 2 1 8624.2.a.z 1
56.k odd 6 2 1078.2.e.h 2
56.m even 6 2 1078.2.e.l 2
88.g even 2 1 1694.2.a.i 1
168.e odd 2 1 9702.2.a.bz 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
154.2.a.b 1 8.d odd 2 1
1078.2.a.b 1 56.e even 2 1
1078.2.e.h 2 56.k odd 6 2
1078.2.e.l 2 56.m even 6 2
1232.2.a.c 1 8.b even 2 1
1386.2.a.f 1 24.f even 2 1
1694.2.a.i 1 88.g even 2 1
3850.2.a.o 1 40.e odd 2 1
3850.2.c.d 2 40.k even 4 2
4928.2.a.d 1 4.b odd 2 1
4928.2.a.bf 1 1.a even 1 1 trivial
8624.2.a.z 1 56.h odd 2 1
9702.2.a.bz 1 168.e odd 2 1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(4928))$$:

 $$T_{3} - 2$$ $$T_{5} + 2$$ $$T_{13} - 4$$ $$T_{17}$$ $$T_{19} - 4$$ $$T_{23} + 4$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$-2 + T$$
$5$ $$2 + T$$
$7$ $$-1 + T$$
$11$ $$-1 + T$$
$13$ $$-4 + T$$
$17$ $$T$$
$19$ $$-4 + T$$
$23$ $$4 + T$$
$29$ $$2 + T$$
$31$ $$-10 + T$$
$37$ $$-6 + T$$
$41$ $$T$$
$43$ $$4 + T$$
$47$ $$10 + T$$
$53$ $$-14 + T$$
$59$ $$-10 + T$$
$61$ $$-8 + T$$
$67$ $$-8 + T$$
$71$ $$-4 + T$$
$73$ $$-4 + T$$
$79$ $$16 + T$$
$83$ $$-4 + T$$
$89$ $$-10 + T$$
$97$ $$-6 + T$$