Newform orbit 363.4.a.d

• Label: 363.4.a.d
• Level: $363$
• Weight: $4$
• Character orbit: 363.a
• Self dual: yes
• Analytic conductor: $21.418$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$363 = 3 \cdot 11^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	363.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$21.4176933321$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + q^2 - 3 * q^3 - 7 * q^4 - 4 * q^5 - 3 * q^6 + 26 * q^7 - 15 * q^8 + 9 * q^9 - 4 * q^10 + 21 * q^12 + 32 * q^13 + 26 * q^14 + 12 * q^15 + 41 * q^16 - 74 * q^17 + 9 * q^18 + 60 * q^19 + 28 * q^20 - 78 * q^21 - 182 * q^23 + 45 * q^24 - 109 * q^25 + 32 * q^26 - 27 * q^27 - 182 * q^28 + 90 * q^29 + 12 * q^30 - 8 * q^31 + 161 * q^32 - 74 * q^34 - 104 * q^35 - 63 * q^36 - 66 * q^37 + 60 * q^38 - 96 * q^39 + 60 * q^40 - 422 * q^41 - 78 * q^42 - 408 * q^43 - 36 * q^45 - 182 * q^46 - 506 * q^47 - 123 * q^48 + 333 * q^49 - 109 * q^50 + 222 * q^51 - 224 * q^52 + 348 * q^53 - 27 * q^54 - 390 * q^56 - 180 * q^57 + 90 * q^58 - 200 * q^59 - 84 * q^60 - 132 * q^61 - 8 * q^62 + 234 * q^63 - 167 * q^64 - 128 * q^65 - 1036 * q^67 + 518 * q^68 + 546 * q^69 - 104 * q^70 + 762 * q^71 - 135 * q^72 + 542 * q^73 - 66 * q^74 + 327 * q^75 - 420 * q^76 - 96 * q^78 + 550 * q^79 - 164 * q^80 + 81 * q^81 - 422 * q^82 + 132 * q^83 + 546 * q^84 + 296 * q^85 - 408 * q^86 - 270 * q^87 + 570 * q^89 - 36 * q^90 + 832 * q^91 + 1274 * q^92 + 24 * q^93 - 506 * q^94 - 240 * q^95 - 483 * q^96 + 14 * q^97 + 333 * q^98

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

−3.00000

−7.00000

−4.00000

−3.00000

26.0000

−15.0000

9.00000

−4.00000

Atkin-Lehner signs

$p$	Sign
$3$	$+1$
$11$	$-1$

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	363.4.a.d		1
3.b	odd	2	1		1089.4.a.e		1
11.b	odd	2	1		33.4.a.b	✓	1
33.d	even	2	1		99.4.a.a		1
44.c	even	2	1		528.4.a.h		1
55.d	odd	2	1		825.4.a.f		1
55.e	even	4	2		825.4.c.f		2
77.b	even	2	1		1617.4.a.d		1
88.b	odd	2	1		2112.4.a.u		1
88.g	even	2	1		2112.4.a.h		1
132.d	odd	2	1		1584.4.a.l		1
165.d	even	2	1		2475.4.a.e		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
33.4.a.b	✓	1	11.b	odd	2	1
99.4.a.a		1	33.d	even	2	1
363.4.a.d		1	1.a	even	1	1	trivial
528.4.a.h		1	44.c	even	2	1
825.4.a.f		1	55.d	odd	2	1
825.4.c.f		2	55.e	even	4	2
1089.4.a.e		1	3.b	odd	2	1
1584.4.a.l		1	132.d	odd	2	1
1617.4.a.d		1	77.b	even	2	1
2112.4.a.h		1	88.g	even	2	1
2112.4.a.u		1	88.b	odd	2	1
2475.4.a.e		1	165.d	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(363))$:

$T_{2} - 1$

$T_{5} + 4$

$T_{7} - 26$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 1$
$3$	$T + 3$
$5$	$T + 4$
$7$	$T - 26$
$11$	$T$