Newform orbit 1210.4.a.h

• Label: 1210.4.a.h
• Level: $1210$
• Weight: $4$
• Character orbit: 1210.a
• Self dual: yes
• Analytic conductor: $71.392$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1210.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(71.3923111069\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 110)
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

q - 2 * q^2 + 8 * q^3 + 4 * q^4 + 5 * q^5 - 16 * q^6 + 12 * q^7 - 8 * q^8 + 37 * q^9 - 10 * q^10 + 32 * q^12 + 34 * q^13 - 24 * q^14 + 40 * q^15 + 16 * q^16 + 86 * q^17 - 74 * q^18 + 4 * q^19 + 20 * q^20 + 96 * q^21 + 148 * q^23 - 64 * q^24 + 25 * q^25 - 68 * q^26 + 80 * q^27 + 48 * q^28 - 134 * q^29 - 80 * q^30 - 280 * q^31 - 32 * q^32 - 172 * q^34 + 60 * q^35 + 148 * q^36 + 430 * q^37 - 8 * q^38 + 272 * q^39 - 40 * q^40 + 6 * q^41 - 192 * q^42 + 136 * q^43 + 185 * q^45 - 296 * q^46 - 28 * q^47 + 128 * q^48 - 199 * q^49 - 50 * q^50 + 688 * q^51 + 136 * q^52 - 658 * q^53 - 160 * q^54 - 96 * q^56 + 32 * q^57 + 268 * q^58 + 4 * q^59 + 160 * q^60 + 90 * q^61 + 560 * q^62 + 444 * q^63 + 64 * q^64 + 170 * q^65 + 96 * q^67 + 344 * q^68 + 1184 * q^69 - 120 * q^70 + 816 * q^71 - 296 * q^72 + 430 * q^73 - 860 * q^74 + 200 * q^75 + 16 * q^76 - 544 * q^78 - 1296 * q^79 + 80 * q^80 - 359 * q^81 - 12 * q^82 + 608 * q^83 + 384 * q^84 + 430 * q^85 - 272 * q^86 - 1072 * q^87 + 810 * q^89 - 370 * q^90 + 408 * q^91 + 592 * q^92 - 2240 * q^93 + 56 * q^94 + 20 * q^95 - 256 * q^96 + 706 * q^97 + 398 * 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

8.00000

4.00000

5.00000

−16.0000

12.0000

−8.00000

37.0000

−10.0000

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( +1 \)
\(5\)	\( -1 \)
\(11\)	\( -1 \)

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	1210.4.a.h		1
11.b	odd	2	1		110.4.a.h	✓	1
33.d	even	2	1		990.4.a.b		1
44.c	even	2	1		880.4.a.b		1
55.d	odd	2	1		550.4.a.a		1
55.e	even	4	2		550.4.b.l		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
110.4.a.h	✓	1	11.b	odd	2	1
550.4.a.a		1	55.d	odd	2	1
550.4.b.l		2	55.e	even	4	2
880.4.a.b		1	44.c	even	2	1
990.4.a.b		1	33.d	even	2	1
1210.4.a.h		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 \(S_{4}^{\mathrm{new}}(\Gamma_0(1210))\):

\( T_{3} - 8 \)

\( T_{7} - 12 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T + 2 \)
$3$	\( T - 8 \)
$5$	\( T - 5 \)
$7$	\( T - 12 \)
$11$	\( T \)