Newform orbit 1922.4.a.b

• Label: 1922.4.a.b
• Level: $1922$
• Weight: $4$
• Character orbit: 1922.a
• Self dual: yes
• Analytic conductor: $113.402$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1922 = 2 \cdot 31^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1922.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(113.401671031\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 62)
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

q + 2 * q^2 + 8 * q^3 + 4 * q^4 - 3 * q^5 + 16 * q^6 - 35 * q^7 + 8 * q^8 + 37 * q^9 - 6 * q^10 + 46 * q^11 + 32 * q^12 - 20 * q^13 - 70 * q^14 - 24 * q^15 + 16 * q^16 - 8 * q^17 + 74 * q^18 + 97 * q^19 - 12 * q^20 - 280 * q^21 + 92 * q^22 - 28 * q^23 + 64 * q^24 - 116 * q^25 - 40 * q^26 + 80 * q^27 - 140 * q^28 + 206 * q^29 - 48 * q^30 + 32 * q^32 + 368 * q^33 - 16 * q^34 + 105 * q^35 + 148 * q^36 + 282 * q^37 + 194 * q^38 - 160 * q^39 - 24 * q^40 + 367 * q^41 - 560 * q^42 + 562 * q^43 + 184 * q^44 - 111 * q^45 - 56 * q^46 - 148 * q^47 + 128 * q^48 + 882 * q^49 - 232 * q^50 - 64 * q^51 - 80 * q^52 + 84 * q^53 + 160 * q^54 - 138 * q^55 - 280 * q^56 + 776 * q^57 + 412 * q^58 - 301 * q^59 - 96 * q^60 + 236 * q^61 - 1295 * q^63 + 64 * q^64 + 60 * q^65 + 736 * q^66 + 60 * q^67 - 32 * q^68 - 224 * q^69 + 210 * q^70 + 699 * q^71 + 296 * q^72 + 814 * q^73 + 564 * q^74 - 928 * q^75 + 388 * q^76 - 1610 * q^77 - 320 * q^78 - 670 * q^79 - 48 * q^80 - 359 * q^81 + 734 * q^82 + 650 * q^83 - 1120 * q^84 + 24 * q^85 + 1124 * q^86 + 1648 * q^87 + 368 * q^88 - 1566 * q^89 - 222 * q^90 + 700 * q^91 - 112 * q^92 - 296 * q^94 - 291 * q^95 + 256 * q^96 - 615 * q^97 + 1764 * q^98 + 1702 * 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

8.00000

4.00000

−3.00000

16.0000

−35.0000

8.00000

37.0000

−6.00000

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(31\)	\( -1 \)

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	1922.4.a.b		1
31.b	odd	2	1		62.4.a.b	✓	1
93.c	even	2	1		558.4.a.b		1
124.d	even	2	1		496.4.a.b		1
155.c	odd	2	1		1550.4.a.c		1
248.b	even	2	1		1984.4.a.a		1
248.g	odd	2	1		1984.4.a.d		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
62.4.a.b	✓	1	31.b	odd	2	1
496.4.a.b		1	124.d	even	2	1
558.4.a.b		1	93.c	even	2	1
1550.4.a.c		1	155.c	odd	2	1
1922.4.a.b		1	1.a	even	1	1	trivial
1984.4.a.a		1	248.b	even	2	1
1984.4.a.d		1	248.g	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{3} - 8 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1922))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T - 2 \)
$3$	\( T - 8 \)
$5$	\( T + 3 \)
$7$	\( T + 35 \)
$11$	\( T - 46 \)