# Properties

 Label 1134.2.a.h Level $1134$ Weight $2$ Character orbit 1134.a Self dual yes Analytic conductor $9.055$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1134 = 2 \cdot 3^{4} \cdot 7$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1134.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$9.05503558921$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 126) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q + q^{2} + q^{4} + 3q^{5} + q^{7} + q^{8} + O(q^{10})$$ $$q + q^{2} + q^{4} + 3q^{5} + q^{7} + q^{8} + 3q^{10} + 6q^{11} + 2q^{13} + q^{14} + q^{16} - 6q^{17} - 7q^{19} + 3q^{20} + 6q^{22} - 3q^{23} + 4q^{25} + 2q^{26} + q^{28} - 6q^{29} + 2q^{31} + q^{32} - 6q^{34} + 3q^{35} + 2q^{37} - 7q^{38} + 3q^{40} + 2q^{43} + 6q^{44} - 3q^{46} + q^{49} + 4q^{50} + 2q^{52} - 6q^{53} + 18q^{55} + q^{56} - 6q^{58} + 5q^{61} + 2q^{62} + q^{64} + 6q^{65} + 8q^{67} - 6q^{68} + 3q^{70} - 3q^{71} + 2q^{73} + 2q^{74} - 7q^{76} + 6q^{77} + 5q^{79} + 3q^{80} - 12q^{83} - 18q^{85} + 2q^{86} + 6q^{88} + 2q^{91} - 3q^{92} - 21q^{95} + 2q^{97} + q^{98} + O(q^{100})$$

## 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
1.00000 0 1.00000 3.00000 0 1.00000 1.00000 0 3.00000
 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles

## Atkin-Lehner signs

$$p$$ Sign
$$2$$ $$-1$$
$$3$$ $$-1$$
$$7$$ $$-1$$

## 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 1134.2.a.h 1
3.b odd 2 1 1134.2.a.a 1
4.b odd 2 1 9072.2.a.w 1
7.b odd 2 1 7938.2.a.u 1
9.c even 3 2 378.2.f.a 2
9.d odd 6 2 126.2.f.a 2
12.b even 2 1 9072.2.a.c 1
21.c even 2 1 7938.2.a.l 1
36.f odd 6 2 3024.2.r.a 2
36.h even 6 2 1008.2.r.d 2
63.g even 3 2 2646.2.h.e 2
63.h even 3 2 2646.2.e.f 2
63.i even 6 2 882.2.e.d 2
63.j odd 6 2 882.2.e.b 2
63.k odd 6 2 2646.2.h.a 2
63.l odd 6 2 2646.2.f.c 2
63.n odd 6 2 882.2.h.j 2
63.o even 6 2 882.2.f.h 2
63.s even 6 2 882.2.h.f 2
63.t odd 6 2 2646.2.e.j 2

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
126.2.f.a 2 9.d odd 6 2
378.2.f.a 2 9.c even 3 2
882.2.e.b 2 63.j odd 6 2
882.2.e.d 2 63.i even 6 2
882.2.f.h 2 63.o even 6 2
882.2.h.f 2 63.s even 6 2
882.2.h.j 2 63.n odd 6 2
1008.2.r.d 2 36.h even 6 2
1134.2.a.a 1 3.b odd 2 1
1134.2.a.h 1 1.a even 1 1 trivial
2646.2.e.f 2 63.h even 3 2
2646.2.e.j 2 63.t odd 6 2
2646.2.f.c 2 63.l odd 6 2
2646.2.h.a 2 63.k odd 6 2
2646.2.h.e 2 63.g even 3 2
3024.2.r.a 2 36.f odd 6 2
7938.2.a.l 1 21.c even 2 1
7938.2.a.u 1 7.b odd 2 1
9072.2.a.c 1 12.b even 2 1
9072.2.a.w 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 $$S_{2}^{\mathrm{new}}(\Gamma_0(1134))$$:

 $$T_{5} - 3$$ $$T_{11} - 6$$ $$T_{13} - 2$$

## Hecke characteristic polynomials

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