Newform orbit 855.2.c.a

• Label: 855.2.c.a
• Level: $855$
• Weight: $2$
• Character orbit: 855.c
• Analytic conductor: $6.827$
• Analytic rank: $0$
• Dimension: $2$
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$855 = 3^{2} \cdot 5 \cdot 19$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	855.c (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{-1})$
Defining polynomial:	$x^{2} + 1$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $i = \sqrt{-1}$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q + i * q^2 + q^4 + (-i - 2) * q^5 + 2*i * q^7 + 3*i * q^8 + (-2*i + 1) * q^10 - 2 * q^11 + 2*i * q^13 - 2 * q^14 - q^16 + 2*i * q^17 - q^19 + (-i - 2) * q^20 - 2*i * q^22 + (4*i + 3) * q^25 - 2 * q^26 + 2*i * q^28 - 6 * q^29 - 4 * q^31 + 5*i * q^32 - 2 * q^34 + (-4*i + 2) * q^35 + 2*i * q^37 - i * q^38 + (-6*i + 3) * q^40 - 2 * q^41 + 10*i * q^43 - 2 * q^44 + 3 * q^49 + (3*i - 4) * q^50 + 2*i * q^52 + 10*i * q^53 + (2*i + 4) * q^55 - 6 * q^56 - 6*i * q^58 - 10 * q^61 - 4*i * q^62 - 7 * q^64 + (-4*i + 2) * q^65 - 4*i * q^67 + 2*i * q^68 + (2*i + 4) * q^70 + 8 * q^71 - 4*i * q^73 - 2 * q^74 - q^76 - 4*i * q^77 + 8 * q^79 + (i + 2) * q^80 - 2*i * q^82 + 12*i * q^83 + (-4*i + 2) * q^85 - 10 * q^86 - 6*i * q^88 + 10 * q^89 - 4 * q^91 + (i + 2) * q^95 - 18*i * q^97 + 3*i * q^98
$\operatorname{Tr}(f)(q)$	$=$	2 * q + 2 * q^4 - 4 * q^5 + 2 * q^10 - 4 * q^11 - 4 * q^14 - 2 * q^16 - 2 * q^19 - 4 * q^20 + 6 * q^25 - 4 * q^26 - 12 * q^29 - 8 * q^31 - 4 * q^34 + 4 * q^35 + 6 * q^40 - 4 * q^41 - 4 * q^44 + 6 * q^49 - 8 * q^50 + 8 * q^55 - 12 * q^56 - 20 * q^61 - 14 * q^64 + 4 * q^65 + 8 * q^70 + 16 * q^71 - 4 * q^74 - 2 * q^76 + 16 * q^79 + 4 * q^80 + 4 * q^85 - 20 * q^86 + 20 * q^89 - 8 * q^91 + 4 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

514.1

	−	1.00000i
		1.00000i

−

1.00000i

0

1.00000

−2.00000

+

1.00000i

0

−

2.00000i

−

3.00000i

0

1.00000

+

2.00000i

514.2

1.00000i

0

1.00000

−2.00000

−

1.00000i

0

2.00000i

3.00000i

0

1.00000

−

2.00000i

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
5.b	even	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	855.2.c.a	✓	2
3.b	odd	2	1		855.2.c.c	yes	2
5.b	even	2	1	inner	855.2.c.a	✓	2
5.c	odd	4	1		4275.2.a.d		1
5.c	odd	4	1		4275.2.a.n		1
15.d	odd	2	1		855.2.c.c	yes	2
15.e	even	4	1		4275.2.a.g		1
15.e	even	4	1		4275.2.a.k		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
855.2.c.a	✓	2	1.a	even	1	1	trivial
855.2.c.a	✓	2	5.b	even	2	1	inner
855.2.c.c	yes	2	3.b	odd	2	1
855.2.c.c	yes	2	15.d	odd	2	1
4275.2.a.d		1	5.c	odd	4	1
4275.2.a.g		1	15.e	even	4	1
4275.2.a.k		1	15.e	even	4	1
4275.2.a.n		1	5.c	odd	4	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{2}^{\mathrm{new}}(855, [\chi])$:

$T_{2}^{2} + 1$

$T_{11} + 2$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2} + 1$
$3$	$T^{2}$
$5$	$T^{2} + 4T + 5$
$7$	$T^{2} + 4$
$11$	$(T + 2)^{2}$