Newform orbit 35.6.a.a

• Label: 35.6.a.a
• Level: $35$
• Weight: $6$
• Character orbit: 35.a
• Self dual: yes
• Analytic conductor: $5.613$
• Analytic rank: $1$
• Dimension: $1$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(5.61343369345\)
Analytic rank:	\(1\)
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 - 8 * q^2 + q^3 + 32 * q^4 + 25 * q^5 - 8 * q^6 + 49 * q^7 - 242 * q^9 - 200 * q^10 - 453 * q^11 + 32 * q^12 - 969 * q^13 - 392 * q^14 + 25 * q^15 - 1024 * q^16 + 1637 * q^17 + 1936 * q^18 - 1550 * q^19 + 800 * q^20 + 49 * q^21 + 3624 * q^22 - 1654 * q^23 + 625 * q^25 + 7752 * q^26 - 485 * q^27 + 1568 * q^28 - 4985 * q^29 - 200 * q^30 + 1192 * q^31 + 8192 * q^32 - 453 * q^33 - 13096 * q^34 + 1225 * q^35 - 7744 * q^36 - 11018 * q^37 + 12400 * q^38 - 969 * q^39 - 1728 * q^41 - 392 * q^42 - 10814 * q^43 - 14496 * q^44 - 6050 * q^45 + 13232 * q^46 + 26237 * q^47 - 1024 * q^48 + 2401 * q^49 - 5000 * q^50 + 1637 * q^51 - 31008 * q^52 + 25936 * q^53 + 3880 * q^54 - 11325 * q^55 - 1550 * q^57 + 39880 * q^58 - 4580 * q^59 + 800 * q^60 - 12488 * q^61 - 9536 * q^62 - 11858 * q^63 - 32768 * q^64 - 24225 * q^65 + 3624 * q^66 - 15848 * q^67 + 52384 * q^68 - 1654 * q^69 - 9800 * q^70 + 51792 * q^71 + 4846 * q^73 + 88144 * q^74 + 625 * q^75 - 49600 * q^76 - 22197 * q^77 + 7752 * q^78 + 62765 * q^79 - 25600 * q^80 + 58321 * q^81 + 13824 * q^82 - 23644 * q^83 + 1568 * q^84 + 40925 * q^85 + 86512 * q^86 - 4985 * q^87 - 147300 * q^89 + 48400 * q^90 - 47481 * q^91 - 52928 * q^92 + 1192 * q^93 - 209896 * q^94 - 38750 * q^95 + 8192 * q^96 - 8343 * q^97 - 19208 * q^98 + 109626 * 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

−8.00000

1.00000

32.0000

25.0000

−8.00000

49.0000

0

−242.000

−200.000

Atkin-Lehner signs

\( p \)	Sign
\(5\)	\( -1 \)
\(7\)	\( -1 \)

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	35.6.a.a	✓	1
3.b	odd	2	1		315.6.a.a		1
4.b	odd	2	1		560.6.a.c		1
5.b	even	2	1		175.6.a.a		1
5.c	odd	4	2		175.6.b.b		2
7.b	odd	2	1		245.6.a.a		1

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.6.a.a	✓	1	1.a	even	1	1	trivial
175.6.a.a		1	5.b	even	2	1
175.6.b.b		2	5.c	odd	4	2
245.6.a.a		1	7.b	odd	2	1
315.6.a.a		1	3.b	odd	2	1
560.6.a.c		1	4.b	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{2} + 8 \) acting on \(S_{6}^{\mathrm{new}}(\Gamma_0(35))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T + 8 \)
$3$	\( T - 1 \)
$5$	\( T - 25 \)
$7$	\( T - 49 \)
$11$	\( T + 453 \)