Newform orbit 1694.4.a.b

• Label: 1694.4.a.b
• Level: $1694$
• Weight: $4$
• Character orbit: 1694.a
• Self dual: yes
• Analytic conductor: $99.949$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$1694 = 2 \cdot 7 \cdot 11^{2}$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1694.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$99.9492355497$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

$f(q)$

$=$

q - 2 * q^2 - 2 * q^3 + 4 * q^4 - 12 * q^5 + 4 * q^6 - 7 * q^7 - 8 * q^8 - 23 * q^9 + 24 * q^10 - 8 * q^12 - 56 * q^13 + 14 * q^14 + 24 * q^15 + 16 * q^16 + 114 * q^17 + 46 * q^18 - 2 * q^19 - 48 * q^20 + 14 * q^21 - 120 * q^23 + 16 * q^24 + 19 * q^25 + 112 * q^26 + 100 * q^27 - 28 * q^28 + 54 * q^29 - 48 * q^30 + 236 * q^31 - 32 * q^32 - 228 * q^34 + 84 * q^35 - 92 * q^36 + 146 * q^37 + 4 * q^38 + 112 * q^39 + 96 * q^40 - 126 * q^41 - 28 * q^42 + 376 * q^43 + 276 * q^45 + 240 * q^46 - 12 * q^47 - 32 * q^48 + 49 * q^49 - 38 * q^50 - 228 * q^51 - 224 * q^52 + 174 * q^53 - 200 * q^54 + 56 * q^56 + 4 * q^57 - 108 * q^58 + 138 * q^59 + 96 * q^60 - 380 * q^61 - 472 * q^62 + 161 * q^63 + 64 * q^64 + 672 * q^65 - 484 * q^67 + 456 * q^68 + 240 * q^69 - 168 * q^70 + 576 * q^71 + 184 * q^72 + 1150 * q^73 - 292 * q^74 - 38 * q^75 - 8 * q^76 - 224 * q^78 - 776 * q^79 - 192 * q^80 + 421 * q^81 + 252 * q^82 - 378 * q^83 + 56 * q^84 - 1368 * q^85 - 752 * q^86 - 108 * q^87 - 390 * q^89 - 552 * q^90 + 392 * q^91 - 480 * q^92 - 472 * q^93 + 24 * q^94 + 24 * q^95 + 64 * q^96 - 1330 * q^97 - 98 * 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

−2.00000

−2.00000

4.00000

−12.0000

4.00000

−7.00000

−8.00000

−23.0000

24.0000

Atkin-Lehner signs

$p$	Sign
$2$	$+1$
$7$	$+1$
$11$	$-1$

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	1694.4.a.b		1
11.b	odd	2	1		14.4.a.b	✓	1
33.d	even	2	1		126.4.a.d		1
44.c	even	2	1		112.4.a.e		1
55.d	odd	2	1		350.4.a.f		1
55.e	even	4	2		350.4.c.g		2
77.b	even	2	1		98.4.a.e		1
77.h	odd	6	2		98.4.c.c		2
77.i	even	6	2		98.4.c.b		2
88.b	odd	2	1		448.4.a.k		1
88.g	even	2	1		448.4.a.g		1
132.d	odd	2	1		1008.4.a.r		1
143.d	odd	2	1		2366.4.a.c		1
231.h	odd	2	1		882.4.a.b		1
231.k	odd	6	2		882.4.g.v		2
231.l	even	6	2		882.4.g.p		2
308.g	odd	2	1		784.4.a.h		1
385.h	even	2	1		2450.4.a.i		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
14.4.a.b	✓	1	11.b	odd	2	1
98.4.a.e		1	77.b	even	2	1
98.4.c.b		2	77.i	even	6	2
98.4.c.c		2	77.h	odd	6	2
112.4.a.e		1	44.c	even	2	1
126.4.a.d		1	33.d	even	2	1
350.4.a.f		1	55.d	odd	2	1
350.4.c.g		2	55.e	even	4	2
448.4.a.g		1	88.g	even	2	1
448.4.a.k		1	88.b	odd	2	1
784.4.a.h		1	308.g	odd	2	1
882.4.a.b		1	231.h	odd	2	1
882.4.g.p		2	231.l	even	6	2
882.4.g.v		2	231.k	odd	6	2
1008.4.a.r		1	132.d	odd	2	1
1694.4.a.b		1	1.a	even	1	1	trivial
2366.4.a.c		1	143.d	odd	2	1
2450.4.a.i		1	385.h	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1694))$:

$T_{3} + 2$

$T_{5} + 12$

$T_{13} + 56$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T + 2$
$3$	$T + 2$
$5$	$T + 12$
$7$	$T + 7$
$11$	$T$