Newform orbit 185.2.a.b

• Label: 185.2.a.b
• Level: $185$
• Weight: $2$
• Character orbit: 185.a
• Self dual: yes
• Analytic conductor: $1.477$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$185 = 5 \cdot 37$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	185.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$1.47723243739$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - q^3 - 2 * q^4 + q^5 - 3 * q^7 - 2 * q^9 - 5 * q^11 + 2 * q^12 + 4 * q^13 - q^15 + 4 * q^16 - 4 * q^17 - 8 * q^19 - 2 * q^20 + 3 * q^21 + 4 * q^23 + q^25 + 5 * q^27 + 6 * q^28 + 4 * q^29 + 2 * q^31 + 5 * q^33 - 3 * q^35 + 4 * q^36 + q^37 - 4 * q^39 - 5 * q^41 - 6 * q^43 + 10 * q^44 - 2 * q^45 + 9 * q^47 - 4 * q^48 + 2 * q^49 + 4 * q^51 - 8 * q^52 + 3 * q^53 - 5 * q^55 + 8 * q^57 - 8 * q^59 + 2 * q^60 - 10 * q^61 + 6 * q^63 - 8 * q^64 + 4 * q^65 - 4 * q^67 + 8 * q^68 - 4 * q^69 + 5 * q^71 - 15 * q^73 - q^75 + 16 * q^76 + 15 * q^77 - 14 * q^79 + 4 * q^80 + q^81 + 11 * q^83 - 6 * q^84 - 4 * q^85 - 4 * q^87 - 2 * q^89 - 12 * q^91 - 8 * q^92 - 2 * q^93 - 8 * q^95 + 10 * q^97 + 10 * 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

−2.00000

1.00000

0

−3.00000

0

−2.00000

0

Atkin-Lehner signs

$p$	Sign
$5$	$-1$
$37$	$-1$

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	185.2.a.b	✓	1
3.b	odd	2	1		1665.2.a.c		1
4.b	odd	2	1		2960.2.a.i		1
5.b	even	2	1		925.2.a.c		1
5.c	odd	4	2		925.2.b.d		2
7.b	odd	2	1		9065.2.a.c		1
15.d	odd	2	1		8325.2.a.x		1
37.b	even	2	1		6845.2.a.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
185.2.a.b	✓	1	1.a	even	1	1	trivial
925.2.a.c		1	5.b	even	2	1
925.2.b.d		2	5.c	odd	4	2
1665.2.a.c		1	3.b	odd	2	1
2960.2.a.i		1	4.b	odd	2	1
6845.2.a.b		1	37.b	even	2	1
8325.2.a.x		1	15.d	odd	2	1
9065.2.a.c		1	7.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2}$ acting on $S_{2}^{\mathrm{new}}(\Gamma_0(185))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T + 1$
$5$	$T - 1$
$7$	$T + 3$
$11$	$T + 5$