Newform orbit 855.3.g.a

• Label: 855.3.g.a
• Level: $855$
• Weight: $3$
• Character orbit: 855.g
• Analytic conductor: $23.297$
• Analytic rank: $0$
• Dimension: $2$
• CM discriminant: -19
• Inner twists: $4$

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	\(23.2970626028\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{-19}) \)
Defining polynomial:	\( x^{2} - x + 5 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{-19})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q - 4 * q^4 + (-b + 5) * q^5 + (-6*b + 3) * q^7 + 3 * q^11 + 16 * q^16 + (-14*b + 7) * q^17 - 19 * q^19 + (4*b - 20) * q^20 + (16*b - 8) * q^23 + (-9*b + 20) * q^25 + (24*b - 12) * q^28 + (-27*b - 15) * q^35 + (-6*b + 3) * q^43 - 12 * q^44 + (26*b - 13) * q^47 - 122 * q^49 + (-3*b + 15) * q^55 - 103 * q^61 - 64 * q^64 + (56*b - 28) * q^68 + (-66*b + 33) * q^73 + 76 * q^76 + (-18*b + 9) * q^77 + (-16*b + 80) * q^80 + (-64*b + 32) * q^83 + (-63*b - 35) * q^85 + (-64*b + 32) * q^92 + (19*b - 95) * q^95
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{4} + 9 q^{5} + 6 q^{11} + 32 q^{16} - 38 q^{19} - 36 q^{20} + 31 q^{25} - 57 q^{35} - 24 q^{44} - 244 q^{49} + 27 q^{55} - 206 q^{61} - 128 q^{64} + 152 q^{76} + 144 q^{80} - 133 q^{85} - 171 q^{95}+O(q^{100}) \)

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  

\(\iota_m(\nu)\)

\( a_{2} \)

\( a_{3} \)

\( a_{4} \)

\( a_{5} \)

\( a_{6} \)

\( a_{7} \)

\( a_{8} \)

\( a_{9} \)

\( a_{10} \)

379.1

0.500000	+	2.17945i
0.500000	−	2.17945i

0

0

−4.00000

4.50000

−

2.17945i

0

−

13.0767i

0

0

0

379.2

0

0

−4.00000

4.50000

+

2.17945i

0

13.0767i

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
19.b	odd	2	1	CM by \(\Q(\sqrt{-19}) \)
5.b	even	2	1	inner
95.d	odd	2	1	inner

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	855.3.g.a		2
3.b	odd	2	1		95.3.d.a	✓	2
5.b	even	2	1	inner	855.3.g.a		2
15.d	odd	2	1		95.3.d.a	✓	2
15.e	even	4	2		475.3.c.c		2
19.b	odd	2	1	CM	855.3.g.a		2
57.d	even	2	1		95.3.d.a	✓	2
95.d	odd	2	1	inner	855.3.g.a		2
285.b	even	2	1		95.3.d.a	✓	2
285.j	odd	4	2		475.3.c.c		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.3.d.a	✓	2	3.b	odd	2	1
95.3.d.a	✓	2	15.d	odd	2	1
95.3.d.a	✓	2	57.d	even	2	1
95.3.d.a	✓	2	285.b	even	2	1
475.3.c.c		2	15.e	even	4	2
475.3.c.c		2	285.j	odd	4	2
855.3.g.a		2	1.a	even	1	1	trivial
855.3.g.a		2	5.b	even	2	1	inner
855.3.g.a		2	19.b	odd	2	1	CM
855.3.g.a		2	95.d	odd	2	1	inner

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{3}^{\mathrm{new}}(855, [\chi])\):

\( T_{2} \)

\( T_{11} - 3 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} - 9T + 25 \)
$7$	\( T^{2} + 171 \)
$11$	\( (T - 3)^{2} \)