Newform orbit 85.4.a.c

• Label: 85.4.a.c
• Level: $85$
• Weight: $4$
• Character orbit: 85.a
• Self dual: yes
• Analytic conductor: $5.015$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	85.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(5.01516235049\)
Analytic rank:	\(0\)
Dimension:	\(1\)
Coefficient field:	\(\mathbb{Q}\)
Coefficient ring:	\(\mathbb{Z}\)
Coefficient ring index:	\( 1 \)
Twist minimal:	yes
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

\(f(q)\)

\(=\)

q + 3 * q^2 + 10 * q^3 + q^4 + 5 * q^5 + 30 * q^6 - 22 * q^7 - 21 * q^8 + 73 * q^9 + 15 * q^10 - 30 * q^11 + 10 * q^12 - 46 * q^13 - 66 * q^14 + 50 * q^15 - 71 * q^16 + 17 * q^17 + 219 * q^18 + 104 * q^19 + 5 * q^20 - 220 * q^21 - 90 * q^22 + 42 * q^23 - 210 * q^24 + 25 * q^25 - 138 * q^26 + 460 * q^27 - 22 * q^28 - 66 * q^29 + 150 * q^30 + 194 * q^31 - 45 * q^32 - 300 * q^33 + 51 * q^34 - 110 * q^35 + 73 * q^36 + 206 * q^37 + 312 * q^38 - 460 * q^39 - 105 * q^40 - 126 * q^41 - 660 * q^42 - 388 * q^43 - 30 * q^44 + 365 * q^45 + 126 * q^46 - 540 * q^47 - 710 * q^48 + 141 * q^49 + 75 * q^50 + 170 * q^51 - 46 * q^52 + 78 * q^53 + 1380 * q^54 - 150 * q^55 + 462 * q^56 + 1040 * q^57 - 198 * q^58 + 432 * q^59 + 50 * q^60 - 610 * q^61 + 582 * q^62 - 1606 * q^63 + 433 * q^64 - 230 * q^65 - 900 * q^66 + 848 * q^67 + 17 * q^68 + 420 * q^69 - 330 * q^70 - 174 * q^71 - 1533 * q^72 + 362 * q^73 + 618 * q^74 + 250 * q^75 + 104 * q^76 + 660 * q^77 - 1380 * q^78 + 398 * q^79 - 355 * q^80 + 2629 * q^81 - 378 * q^82 + 828 * q^83 - 220 * q^84 + 85 * q^85 - 1164 * q^86 - 660 * q^87 + 630 * q^88 + 630 * q^89 + 1095 * q^90 + 1012 * q^91 + 42 * q^92 + 1940 * q^93 - 1620 * q^94 + 520 * q^95 - 450 * q^96 - 1486 * q^97 + 423 * q^98 - 2190 * 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

3.00000

10.0000

1.00000

5.00000

30.0000

−22.0000

−21.0000

73.0000

15.0000

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\( -1 \)
\(17\)	\( -1 \)

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	85.4.a.c	✓	1
3.b	odd	2	1		765.4.a.a		1
4.b	odd	2	1		1360.4.a.a		1
5.b	even	2	1		425.4.a.a		1
5.c	odd	4	2		425.4.b.d		2
17.b	even	2	1		1445.4.a.f		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
85.4.a.c	✓	1	1.a	even	1	1	trivial
425.4.a.a		1	5.b	even	2	1
425.4.b.d		2	5.c	odd	4	2
765.4.a.a		1	3.b	odd	2	1
1360.4.a.a		1	4.b	odd	2	1
1445.4.a.f		1	17.b	even	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(85))\):

\( T_{2} - 3 \)

\( T_{3} - 10 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T - 3 \)
$3$	\( T - 10 \)
$5$	\( T - 5 \)
$7$	\( T + 22 \)
$11$	\( T + 30 \)