Newform orbit 95.4.a.c

• Label: 95.4.a.c
• Level: $95$
• Weight: $4$
• Character orbit: 95.a
• Self dual: yes
• Analytic conductor: $5.605$
• Analytic rank: $0$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	95.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(5.60518145055\)
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 + 7 * q^3 + q^4 + 5 * q^5 + 21 * q^6 + 11 * q^7 - 21 * q^8 + 22 * q^9 + 15 * q^10 - 36 * q^11 + 7 * q^12 + 65 * q^13 + 33 * q^14 + 35 * q^15 - 71 * q^16 - 87 * q^17 + 66 * q^18 + 19 * q^19 + 5 * q^20 + 77 * q^21 - 108 * q^22 - 129 * q^23 - 147 * q^24 + 25 * q^25 + 195 * q^26 - 35 * q^27 + 11 * q^28 + 231 * q^29 + 105 * q^30 + 110 * q^31 - 45 * q^32 - 252 * q^33 - 261 * q^34 + 55 * q^35 + 22 * q^36 - 142 * q^37 + 57 * q^38 + 455 * q^39 - 105 * q^40 - 330 * q^41 + 231 * q^42 + 74 * q^43 - 36 * q^44 + 110 * q^45 - 387 * q^46 - 336 * q^47 - 497 * q^48 - 222 * q^49 + 75 * q^50 - 609 * q^51 + 65 * q^52 + 501 * q^53 - 105 * q^54 - 180 * q^55 - 231 * q^56 + 133 * q^57 + 693 * q^58 + 633 * q^59 + 35 * q^60 - 88 * q^61 + 330 * q^62 + 242 * q^63 + 433 * q^64 + 325 * q^65 - 756 * q^66 + 119 * q^67 - 87 * q^68 - 903 * q^69 + 165 * q^70 - 204 * q^71 - 462 * q^72 + 407 * q^73 - 426 * q^74 + 175 * q^75 + 19 * q^76 - 396 * q^77 + 1365 * q^78 + 1262 * q^79 - 355 * q^80 - 839 * q^81 - 990 * q^82 + 270 * q^83 + 77 * q^84 - 435 * q^85 + 222 * q^86 + 1617 * q^87 + 756 * q^88 - 30 * q^89 + 330 * q^90 + 715 * q^91 - 129 * q^92 + 770 * q^93 - 1008 * q^94 + 95 * q^95 - 315 * q^96 + 1406 * q^97 - 666 * q^98 - 792 * 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

7.00000

1.00000

5.00000

21.0000

11.0000

−21.0000

22.0000

15.0000

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\( -1 \)
\(19\)	\( -1 \)

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	95.4.a.c	✓	1
3.b	odd	2	1		855.4.a.c		1
4.b	odd	2	1		1520.4.a.a		1
5.b	even	2	1		475.4.a.b		1
5.c	odd	4	2		475.4.b.d		2
19.b	odd	2	1		1805.4.a.c		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
95.4.a.c	✓	1	1.a	even	1	1	trivial
475.4.a.b		1	5.b	even	2	1
475.4.b.d		2	5.c	odd	4	2
855.4.a.c		1	3.b	odd	2	1
1520.4.a.a		1	4.b	odd	2	1
1805.4.a.c		1	19.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 \(S_{4}^{\mathrm{new}}(\Gamma_0(95))\):

\( T_{2} - 3 \)

\( T_{3} - 7 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T - 3 \)
$3$	\( T - 7 \)
$5$	\( T - 5 \)
$7$	\( T - 11 \)
$11$	\( T + 36 \)