Newform orbit 2023.4.a.a

• Label: 2023.4.a.a
• Level: $2023$
• Weight: $4$
• Character orbit: 2023.a
• Self dual: yes
• Analytic conductor: $119.361$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$2023 = 7 \cdot 17^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	2023.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$119.360863942$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 7)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - q^2 + 2 * q^3 - 7 * q^4 - 16 * q^5 - 2 * q^6 + 7 * q^7 + 15 * q^8 - 23 * q^9 + 16 * q^10 + 8 * q^11 - 14 * q^12 + 28 * q^13 - 7 * q^14 - 32 * q^15 + 41 * q^16 + 23 * q^18 - 110 * q^19 + 112 * q^20 + 14 * q^21 - 8 * q^22 - 48 * q^23 + 30 * q^24 + 131 * q^25 - 28 * q^26 - 100 * q^27 - 49 * q^28 + 110 * q^29 + 32 * q^30 - 12 * q^31 - 161 * q^32 + 16 * q^33 - 112 * q^35 + 161 * q^36 + 246 * q^37 + 110 * q^38 + 56 * q^39 - 240 * q^40 - 182 * q^41 - 14 * q^42 + 128 * q^43 - 56 * q^44 + 368 * q^45 + 48 * q^46 + 324 * q^47 + 82 * q^48 + 49 * q^49 - 131 * q^50 - 196 * q^52 - 162 * q^53 + 100 * q^54 - 128 * q^55 + 105 * q^56 - 220 * q^57 - 110 * q^58 + 810 * q^59 + 224 * q^60 + 488 * q^61 + 12 * q^62 - 161 * q^63 - 167 * q^64 - 448 * q^65 - 16 * q^66 + 244 * q^67 - 96 * q^69 + 112 * q^70 + 768 * q^71 - 345 * q^72 + 702 * q^73 - 246 * q^74 + 262 * q^75 + 770 * q^76 + 56 * q^77 - 56 * q^78 - 440 * q^79 - 656 * q^80 + 421 * q^81 + 182 * q^82 - 1302 * q^83 - 98 * q^84 - 128 * q^86 + 220 * q^87 + 120 * q^88 + 730 * q^89 - 368 * q^90 + 196 * q^91 + 336 * q^92 - 24 * q^93 - 324 * q^94 + 1760 * q^95 - 322 * q^96 - 294 * q^97 - 49 * q^98 - 184 * 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

−1.00000

2.00000

−7.00000

−16.0000

−2.00000

7.00000

15.0000

−23.0000

16.0000

Atkin-Lehner signs

$p$	Sign
$7$	$-1$
$17$	$+1$

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	2023.4.a.a		1
17.b	even	2	1		7.4.a.a	✓	1
51.c	odd	2	1		63.4.a.b		1
68.d	odd	2	1		112.4.a.f		1
85.c	even	2	1		175.4.a.b		1
85.g	odd	4	2		175.4.b.b		2
119.d	odd	2	1		49.4.a.b		1
119.h	odd	6	2		49.4.c.b		2
119.j	even	6	2		49.4.c.c		2
136.e	odd	2	1		448.4.a.e		1
136.h	even	2	1		448.4.a.i		1
187.b	odd	2	1		847.4.a.b		1
204.h	even	2	1		1008.4.a.c		1
221.b	even	2	1		1183.4.a.b		1
255.h	odd	2	1		1575.4.a.e		1
357.c	even	2	1		441.4.a.i		1
357.q	odd	6	2		441.4.e.h		2
357.s	even	6	2		441.4.e.e		2
476.e	even	2	1		784.4.a.g		1
595.b	odd	2	1		1225.4.a.j		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
7.4.a.a	✓	1	17.b	even	2	1
49.4.a.b		1	119.d	odd	2	1
49.4.c.b		2	119.h	odd	6	2
49.4.c.c		2	119.j	even	6	2
63.4.a.b		1	51.c	odd	2	1
112.4.a.f		1	68.d	odd	2	1
175.4.a.b		1	85.c	even	2	1
175.4.b.b		2	85.g	odd	4	2
441.4.a.i		1	357.c	even	2	1
441.4.e.e		2	357.s	even	6	2
441.4.e.h		2	357.q	odd	6	2
448.4.a.e		1	136.e	odd	2	1
448.4.a.i		1	136.h	even	2	1
784.4.a.g		1	476.e	even	2	1
847.4.a.b		1	187.b	odd	2	1
1008.4.a.c		1	204.h	even	2	1
1183.4.a.b		1	221.b	even	2	1
1225.4.a.j		1	595.b	odd	2	1
1575.4.a.e		1	255.h	odd	2	1
2023.4.a.a		1	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(2023))$:

$T_{2} + 1$

$T_{3} - 2$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 1$
$3$	$T - 2$
$5$	$T + 16$
$7$	$T - 7$
$11$	$T - 8$