# Properties

 Label 1100.2.a.b Level $1100$ Weight $2$ Character orbit 1100.a Self dual yes Analytic conductor $8.784$ Analytic rank $0$ Dimension $1$ CM no Inner twists $1$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$1100 = 2^{2} \cdot 5^{2} \cdot 11$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 1100.a (trivial)

## Newform invariants

 Self dual: yes Analytic conductor: $$8.78354422234$$ Analytic rank: $$0$$ Dimension: $$1$$ Coefficient field: $$\mathbb{Q}$$ Coefficient ring: $$\mathbb{Z}$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 44) Fricke sign: $$-1$$ Sato-Tate group: $\mathrm{SU}(2)$

## $q$-expansion

 $$f(q)$$ $$=$$ $$q - q^{3} - 2 q^{7} - 2 q^{9}+O(q^{10})$$ q - q^3 - 2 * q^7 - 2 * q^9 $$q - q^{3} - 2 q^{7} - 2 q^{9} - q^{11} + 4 q^{13} - 6 q^{17} + 8 q^{19} + 2 q^{21} + 3 q^{23} + 5 q^{27} + 5 q^{31} + q^{33} + q^{37} - 4 q^{39} + 10 q^{43} - 3 q^{49} + 6 q^{51} + 6 q^{53} - 8 q^{57} + 3 q^{59} - 4 q^{61} + 4 q^{63} + q^{67} - 3 q^{69} + 15 q^{71} + 4 q^{73} + 2 q^{77} + 2 q^{79} + q^{81} - 6 q^{83} - 9 q^{89} - 8 q^{91} - 5 q^{93} + 7 q^{97} + 2 q^{99}+O(q^{100})$$ q - q^3 - 2 * q^7 - 2 * q^9 - q^11 + 4 * q^13 - 6 * q^17 + 8 * q^19 + 2 * q^21 + 3 * q^23 + 5 * q^27 + 5 * q^31 + q^33 + q^37 - 4 * q^39 + 10 * q^43 - 3 * q^49 + 6 * q^51 + 6 * q^53 - 8 * q^57 + 3 * q^59 - 4 * q^61 + 4 * q^63 + q^67 - 3 * q^69 + 15 * q^71 + 4 * q^73 + 2 * q^77 + 2 * q^79 + q^81 - 6 * q^83 - 9 * q^89 - 8 * q^91 - 5 * q^93 + 7 * 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 −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
$$2$$ $$-1$$
$$5$$ $$1$$
$$11$$ $$1$$

## 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 1100.2.a.b 1
3.b odd 2 1 9900.2.a.h 1
4.b odd 2 1 4400.2.a.v 1
5.b even 2 1 44.2.a.a 1
5.c odd 4 2 1100.2.b.c 2
15.d odd 2 1 396.2.a.c 1
15.e even 4 2 9900.2.c.g 2
20.d odd 2 1 176.2.a.a 1
20.e even 4 2 4400.2.b.k 2
35.c odd 2 1 2156.2.a.a 1
35.i odd 6 2 2156.2.i.c 2
35.j even 6 2 2156.2.i.b 2
40.e odd 2 1 704.2.a.i 1
40.f even 2 1 704.2.a.f 1
45.h odd 6 2 3564.2.i.a 2
45.j even 6 2 3564.2.i.j 2
55.d odd 2 1 484.2.a.a 1
55.h odd 10 4 484.2.e.b 4
55.j even 10 4 484.2.e.a 4
60.h even 2 1 1584.2.a.p 1
65.d even 2 1 7436.2.a.d 1
80.k odd 4 2 2816.2.c.k 2
80.q even 4 2 2816.2.c.e 2
120.i odd 2 1 6336.2.a.j 1
120.m even 2 1 6336.2.a.i 1
140.c even 2 1 8624.2.a.w 1
165.d even 2 1 4356.2.a.j 1
220.g even 2 1 1936.2.a.c 1
440.c even 2 1 7744.2.a.bc 1
440.o odd 2 1 7744.2.a.m 1

By twisted newform orbit
Twist Min Dim Char Parity Ord Mult Type
44.2.a.a 1 5.b even 2 1
176.2.a.a 1 20.d odd 2 1
396.2.a.c 1 15.d odd 2 1
484.2.a.a 1 55.d odd 2 1
484.2.e.a 4 55.j even 10 4
484.2.e.b 4 55.h odd 10 4
704.2.a.f 1 40.f even 2 1
704.2.a.i 1 40.e odd 2 1
1100.2.a.b 1 1.a even 1 1 trivial
1100.2.b.c 2 5.c odd 4 2
1584.2.a.p 1 60.h even 2 1
1936.2.a.c 1 220.g even 2 1
2156.2.a.a 1 35.c odd 2 1
2156.2.i.b 2 35.j even 6 2
2156.2.i.c 2 35.i odd 6 2
2816.2.c.e 2 80.q even 4 2
2816.2.c.k 2 80.k odd 4 2
3564.2.i.a 2 45.h odd 6 2
3564.2.i.j 2 45.j even 6 2
4356.2.a.j 1 165.d even 2 1
4400.2.a.v 1 4.b odd 2 1
4400.2.b.k 2 20.e even 4 2
6336.2.a.i 1 120.m even 2 1
6336.2.a.j 1 120.i odd 2 1
7436.2.a.d 1 65.d even 2 1
7744.2.a.m 1 440.o odd 2 1
7744.2.a.bc 1 440.c even 2 1
8624.2.a.w 1 140.c even 2 1
9900.2.a.h 1 3.b odd 2 1
9900.2.c.g 2 15.e even 4 2

## Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(\Gamma_0(1100))$$:

 $$T_{3} + 1$$ T3 + 1 $$T_{7} + 2$$ T7 + 2

## Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ $$T$$
$3$ $$T + 1$$
$5$ $$T$$
$7$ $$T + 2$$
$11$ $$T + 1$$
$13$ $$T - 4$$
$17$ $$T + 6$$
$19$ $$T - 8$$
$23$ $$T - 3$$
$29$ $$T$$
$31$ $$T - 5$$
$37$ $$T - 1$$
$41$ $$T$$
$43$ $$T - 10$$
$47$ $$T$$
$53$ $$T - 6$$
$59$ $$T - 3$$
$61$ $$T + 4$$
$67$ $$T - 1$$
$71$ $$T - 15$$
$73$ $$T - 4$$
$79$ $$T - 2$$
$83$ $$T + 6$$
$89$ $$T + 9$$
$97$ $$T - 7$$