Properties

 Label 1088.2.a.c Level $1088$ Weight $2$ Character orbit 1088.a Self dual yes Analytic conductor $8.688$ Analytic rank $1$ Dimension $1$ CM no Inner twists $1$

Related objects

Newspace parameters

 Level: $$N$$ $$=$$ $$1088 = 2^{6} \cdot 17$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1088.a (trivial)

Newform invariants

 Self dual: yes Analytic conductor: $$8.68772373992$$ Analytic rank: $$1$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 136) Fricke sign: $$1$$ Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

 $$f(q)$$ $$=$$ $$q - 2 q^{3} + q^{9}+O(q^{10})$$ q - 2 * q^3 + q^9 $$q - 2 q^{3} + q^{9} - 2 q^{11} + 6 q^{13} - q^{17} - 4 q^{19} + 4 q^{23} - 5 q^{25} + 4 q^{27} - 8 q^{31} + 4 q^{33} + 4 q^{37} - 12 q^{39} + 6 q^{41} - 8 q^{43} - 8 q^{47} - 7 q^{49} + 2 q^{51} - 10 q^{53} + 8 q^{57} - 12 q^{61} - 8 q^{67} - 8 q^{69} + 12 q^{71} + 2 q^{73} + 10 q^{75} - 4 q^{79} - 11 q^{81} - 16 q^{83} + 10 q^{89} + 16 q^{93} - 18 q^{97} - 2 q^{99}+O(q^{100})$$ q - 2 * q^3 + q^9 - 2 * q^11 + 6 * q^13 - q^17 - 4 * q^19 + 4 * q^23 - 5 * q^25 + 4 * q^27 - 8 * q^31 + 4 * q^33 + 4 * q^37 - 12 * q^39 + 6 * q^41 - 8 * q^43 - 8 * q^47 - 7 * q^49 + 2 * q^51 - 10 * q^53 + 8 * q^57 - 12 * q^61 - 8 * q^67 - 8 * q^69 + 12 * q^71 + 2 * q^73 + 10 * q^75 - 4 * q^79 - 11 * q^81 - 16 * q^83 + 10 * q^89 + 16 * q^93 - 18 * q^97 - 2 * 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 −2.00000 0 0 0 0 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
$$2$$ $$1$$
$$17$$ $$1$$

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 1088.2.a.c 1
3.b odd 2 1 9792.2.a.be 1
4.b odd 2 1 1088.2.a.m 1
8.b even 2 1 136.2.a.b 1
8.d odd 2 1 272.2.a.a 1
12.b even 2 1 9792.2.a.bd 1
24.f even 2 1 2448.2.a.j 1
24.h odd 2 1 1224.2.a.d 1
40.e odd 2 1 6800.2.a.w 1
40.f even 2 1 3400.2.a.b 1
40.i odd 4 2 3400.2.e.c 2
56.h odd 2 1 6664.2.a.b 1
136.e odd 2 1 4624.2.a.f 1
136.h even 2 1 2312.2.a.a 1
136.i even 4 2 2312.2.b.b 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
136.2.a.b 1 8.b even 2 1
272.2.a.a 1 8.d odd 2 1
1088.2.a.c 1 1.a even 1 1 trivial
1088.2.a.m 1 4.b odd 2 1
1224.2.a.d 1 24.h odd 2 1
2312.2.a.a 1 136.h even 2 1
2312.2.b.b 2 136.i even 4 2
2448.2.a.j 1 24.f even 2 1
3400.2.a.b 1 40.f even 2 1
3400.2.e.c 2 40.i odd 4 2
4624.2.a.f 1 136.e odd 2 1
6664.2.a.b 1 56.h odd 2 1
6800.2.a.w 1 40.e odd 2 1
9792.2.a.bd 1 12.b even 2 1
9792.2.a.be 1 3.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 $$S_{2}^{\mathrm{new}}(\Gamma_0(1088))$$:

 $$T_{3} + 2$$ T3 + 2 $$T_{5}$$ T5 $$T_{7}$$ T7

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T + 2$$
$5$ $$T$$
$7$ $$T$$
$11$ $$T + 2$$
$13$ $$T - 6$$
$17$ $$T + 1$$
$19$ $$T + 4$$
$23$ $$T - 4$$
$29$ $$T$$
$31$ $$T + 8$$
$37$ $$T - 4$$
$41$ $$T - 6$$
$43$ $$T + 8$$
$47$ $$T + 8$$
$53$ $$T + 10$$
$59$ $$T$$
$61$ $$T + 12$$
$67$ $$T + 8$$
$71$ $$T - 12$$
$73$ $$T - 2$$
$79$ $$T + 4$$
$83$ $$T + 16$$
$89$ $$T - 10$$
$97$ $$T + 18$$