Properties

 Label 1856.4.a.f Level $1856$ Weight $4$ Character orbit 1856.a Self dual yes Analytic conductor $109.508$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1856 = 2^{6} \cdot 29$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 1856.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$109.507544971$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 58) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q + 7 q^{3} + 15 q^{5} - 18 q^{7} + 22 q^{9} + O(q^{10})$$ $$q + 7 q^{3} + 15 q^{5} - 18 q^{7} + 22 q^{9} - 27 q^{11} + 57 q^{13} + 105 q^{15} - 44 q^{17} - 152 q^{19} - 126 q^{21} - 152 q^{23} + 100 q^{25} - 35 q^{27} + 29 q^{29} - 173 q^{31} - 189 q^{33} - 270 q^{35} + 120 q^{37} + 399 q^{39} - 314 q^{41} - 339 q^{43} + 330 q^{45} - 357 q^{47} - 19 q^{49} - 308 q^{51} + 59 q^{53} - 405 q^{55} - 1064 q^{57} + 572 q^{59} + 420 q^{61} - 396 q^{63} + 855 q^{65} - 660 q^{67} - 1064 q^{69} + 726 q^{71} + 1004 q^{73} + 700 q^{75} + 486 q^{77} + 361 q^{79} - 839 q^{81} + 168 q^{83} - 660 q^{85} + 203 q^{87} + 58 q^{89} - 1026 q^{91} - 1211 q^{93} - 2280 q^{95} - 1206 q^{97} - 594 q^{99} + O(q^{100})$$

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 7.00000 0 15.0000 0 −18.0000 0 22.0000 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
$$2$$ $$1$$
$$29$$ $$-1$$

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 1856.4.a.f 1
4.b odd 2 1 1856.4.a.c 1
8.b even 2 1 58.4.a.b 1
8.d odd 2 1 464.4.a.b 1
24.h odd 2 1 522.4.a.b 1
40.f even 2 1 1450.4.a.d 1
232.g even 2 1 1682.4.a.a 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
58.4.a.b 1 8.b even 2 1
464.4.a.b 1 8.d odd 2 1
522.4.a.b 1 24.h odd 2 1
1450.4.a.d 1 40.f even 2 1
1682.4.a.a 1 232.g even 2 1
1856.4.a.c 1 4.b odd 2 1
1856.4.a.f 1 1.a even 1 1 trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{4}^{\mathrm{new}}(\Gamma_0(1856))$$:

 $$T_{3} - 7$$ $$T_{5} - 15$$ $$T_{7} + 18$$

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$-7 + T$$
$5$ $$-15 + T$$
$7$ $$18 + T$$
$11$ $$27 + T$$
$13$ $$-57 + T$$
$17$ $$44 + T$$
$19$ $$152 + T$$
$23$ $$152 + T$$
$29$ $$-29 + T$$
$31$ $$173 + T$$
$37$ $$-120 + T$$
$41$ $$314 + T$$
$43$ $$339 + T$$
$47$ $$357 + T$$
$53$ $$-59 + T$$
$59$ $$-572 + T$$
$61$ $$-420 + T$$
$67$ $$660 + T$$
$71$ $$-726 + T$$
$73$ $$-1004 + T$$
$79$ $$-361 + T$$
$83$ $$-168 + T$$
$89$ $$-58 + T$$
$97$ $$1206 + T$$