Newform orbit 294.4.a.i

• Label: 294.4.a.i
• Level: $294$
• Weight: $4$
• Character orbit: 294.a
• Self dual: yes
• Analytic conductor: $17.347$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$294 = 2 \cdot 3 \cdot 7^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	294.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$17.3465615417$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 42)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q + 2 * q^2 + 3 * q^3 + 4 * q^4 - 18 * q^5 + 6 * q^6 + 8 * q^8 + 9 * q^9 - 36 * q^10 - 72 * q^11 + 12 * q^12 + 34 * q^13 - 54 * q^15 + 16 * q^16 - 6 * q^17 + 18 * q^18 - 92 * q^19 - 72 * q^20 - 144 * q^22 - 180 * q^23 + 24 * q^24 + 199 * q^25 + 68 * q^26 + 27 * q^27 - 114 * q^29 - 108 * q^30 - 56 * q^31 + 32 * q^32 - 216 * q^33 - 12 * q^34 + 36 * q^36 - 34 * q^37 - 184 * q^38 + 102 * q^39 - 144 * q^40 - 6 * q^41 + 164 * q^43 - 288 * q^44 - 162 * q^45 - 360 * q^46 - 168 * q^47 + 48 * q^48 + 398 * q^50 - 18 * q^51 + 136 * q^52 + 654 * q^53 + 54 * q^54 + 1296 * q^55 - 276 * q^57 - 228 * q^58 + 492 * q^59 - 216 * q^60 + 250 * q^61 - 112 * q^62 + 64 * q^64 - 612 * q^65 - 432 * q^66 - 124 * q^67 - 24 * q^68 - 540 * q^69 + 36 * q^71 + 72 * q^72 - 1010 * q^73 - 68 * q^74 + 597 * q^75 - 368 * q^76 + 204 * q^78 + 56 * q^79 - 288 * q^80 + 81 * q^81 - 12 * q^82 - 228 * q^83 + 108 * q^85 + 328 * q^86 - 342 * q^87 - 576 * q^88 - 390 * q^89 - 324 * q^90 - 720 * q^92 - 168 * q^93 - 336 * q^94 + 1656 * q^95 + 96 * q^96 + 70 * q^97 - 648 * 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

2.00000

3.00000

4.00000

−18.0000

6.00000

0

8.00000

9.00000

−36.0000

Atkin-Lehner signs

$p$	Sign
$2$	$-1$
$3$	$-1$
$7$	$-1$

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	294.4.a.i		1
3.b	odd	2	1		882.4.a.g		1
4.b	odd	2	1		2352.4.a.a		1
7.b	odd	2	1		42.4.a.a	✓	1
7.c	even	3	2		294.4.e.b		2
7.d	odd	6	2		294.4.e.c		2
21.c	even	2	1		126.4.a.a		1
21.g	even	6	2		882.4.g.w		2
21.h	odd	6	2		882.4.g.o		2
28.d	even	2	1		336.4.a.l		1
35.c	odd	2	1		1050.4.a.g		1
35.f	even	4	2		1050.4.g.a		2
56.e	even	2	1		1344.4.a.a		1
56.h	odd	2	1		1344.4.a.o		1
84.h	odd	2	1		1008.4.a.b		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
42.4.a.a	✓	1	7.b	odd	2	1
126.4.a.a		1	21.c	even	2	1
294.4.a.i		1	1.a	even	1	1	trivial
294.4.e.b		2	7.c	even	3	2
294.4.e.c		2	7.d	odd	6	2
336.4.a.l		1	28.d	even	2	1
882.4.a.g		1	3.b	odd	2	1
882.4.g.o		2	21.h	odd	6	2
882.4.g.w		2	21.g	even	6	2
1008.4.a.b		1	84.h	odd	2	1
1050.4.a.g		1	35.c	odd	2	1
1050.4.g.a		2	35.f	even	4	2
1344.4.a.a		1	56.e	even	2	1
1344.4.a.o		1	56.h	odd	2	1
2352.4.a.a		1	4.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(294))$:

$T_{5} + 18$

$T_{11} + 72$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T - 2$
$3$	$T - 3$
$5$	$T + 18$
$7$	$T$
$11$	$T + 72$