Newform orbit 315.5.e.a

• Label: 315.5.e.a
• Level: $315$
• Weight: $5$
• Character orbit: 315.e
• Self dual: yes
• Analytic conductor: $32.562$
• Analytic rank: $0$
• Dimension: $1$
• CM discriminant: -35
• Inner twists: $2$

Newspace parameters

Level:	$N$	$=$	$315 = 3^{2} \cdot 5 \cdot 7$
Weight:	$k$	$=$	$5$
Character orbit:	$[\chi]$	$=$	315.e (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	yes
Analytic conductor:	$32.5615383714$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

$q$-expansion

$f(q)$

$=$

q + 16 * q^4 - 25 * q^5 + 49 * q^7 + 73 * q^11 + 23 * q^13 + 256 * q^16 - 263 * q^17 - 400 * q^20 + 625 * q^25 + 784 * q^28 + 1153 * q^29 - 1225 * q^35 + 1168 * q^44 + 3457 * q^47 + 2401 * q^49 + 368 * q^52 - 1825 * q^55 + 4096 * q^64 - 575 * q^65 - 4208 * q^68 + 10078 * q^71 - 9502 * q^73 + 3577 * q^77 + 12167 * q^79 - 6400 * q^80 + 6382 * q^83 + 6575 * q^85 + 1127 * q^91 + 3383 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$-1$	$1$

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  

$\iota_m(\nu)$

$a_{2}$

$a_{3}$

$a_{4}$

$a_{5}$

$a_{6}$

$a_{7}$

$a_{8}$

$a_{9}$

$a_{10}$

244.1

0

0

0

16.0000

−25.0000

0

49.0000

0

0

0

Inner twists

Char	Parity	Ord	Mult	Type
1.a	even	1	1	trivial
35.c	odd	2	1	CM by $\Q(\sqrt{-35})$

Twists

By twisting character orbit
Char	Parity	Ord	Mult	Type	Twist	Min	Dim
1.a	even	1	1	trivial	315.5.e.a		1
3.b	odd	2	1		35.5.c.a	✓	1
5.b	even	2	1		315.5.e.b		1
7.b	odd	2	1		315.5.e.b		1
12.b	even	2	1		560.5.p.b		1
15.d	odd	2	1		35.5.c.b	yes	1
15.e	even	4	2		175.5.d.c		2
21.c	even	2	1		35.5.c.b	yes	1
35.c	odd	2	1	CM	315.5.e.a		1
60.h	even	2	1		560.5.p.a		1
84.h	odd	2	1		560.5.p.a		1
105.g	even	2	1		35.5.c.a	✓	1
105.k	odd	4	2		175.5.d.c		2
420.o	odd	2	1		560.5.p.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.5.c.a	✓	1	3.b	odd	2	1
35.5.c.a	✓	1	105.g	even	2	1
35.5.c.b	yes	1	15.d	odd	2	1
35.5.c.b	yes	1	21.c	even	2	1
175.5.d.c		2	15.e	even	4	2
175.5.d.c		2	105.k	odd	4	2
315.5.e.a		1	1.a	even	1	1	trivial
315.5.e.a		1	35.c	odd	2	1	CM
315.5.e.b		1	5.b	even	2	1
315.5.e.b		1	7.b	odd	2	1
560.5.p.a		1	60.h	even	2	1
560.5.p.a		1	84.h	odd	2	1
560.5.p.b		1	12.b	even	2	1
560.5.p.b		1	420.o	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{5}^{\mathrm{new}}(315, [\chi])$:

$T_{2}$

$T_{13} - 23$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T$
$3$	$T$
$5$	$T + 25$
$7$	$T - 49$
$11$	$T - 73$