Newform orbit 950.4.a.f

• Label: 950.4.a.f
• Level: $950$
• Weight: $4$
• Character orbit: 950.a
• Self dual: yes
• Analytic conductor: $56.052$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	950.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(56.0518145055\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{34}) \)
Defining polynomial:	\( x^{2} - 34 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 190)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{34}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q - 2 * q^2 + b * q^3 + 4 * q^4 - 2*b * q^6 + (2*b - 12) * q^7 - 8 * q^8 + 7 * q^9 + (2*b + 26) * q^11 + 4*b * q^12 + (-5*b - 22) * q^13 + (-4*b + 24) * q^14 + 16 * q^16 + (-2*b - 50) * q^17 - 14 * q^18 + 19 * q^19 + (-12*b + 68) * q^21 + (-4*b - 52) * q^22 + (-8*b - 8) * q^23 - 8*b * q^24 + (10*b + 44) * q^26 - 20*b * q^27 + (8*b - 48) * q^28 + (-18*b - 6) * q^29 + (20*b - 8) * q^31 - 32 * q^32 + (26*b + 68) * q^33 + (4*b + 100) * q^34 + 28 * q^36 + (-31*b - 18) * q^37 - 38 * q^38 + (-22*b - 170) * q^39 + (26*b + 74) * q^41 + (24*b - 136) * q^42 + (-26*b + 236) * q^43 + (8*b + 104) * q^44 + (16*b + 16) * q^46 + (-26*b - 188) * q^47 + 16*b * q^48 + (-48*b - 63) * q^49 + (-50*b - 68) * q^51 + (-20*b - 88) * q^52 + (47*b - 58) * q^53 + 40*b * q^54 + (-16*b + 96) * q^56 + 19*b * q^57 + (36*b + 12) * q^58 + (-82*b + 56) * q^59 + (-36*b - 340) * q^61 + (-40*b + 16) * q^62 + (14*b - 84) * q^63 + 64 * q^64 + (-52*b - 136) * q^66 + (-95*b + 104) * q^67 + (-8*b - 200) * q^68 + (-8*b - 272) * q^69 + (-20*b - 308) * q^71 - 56 * q^72 + (14*b + 666) * q^73 + (62*b + 36) * q^74 + 76 * q^76 + (28*b - 176) * q^77 + (44*b + 340) * q^78 + (94*b + 108) * q^79 - 869 * q^81 + (-52*b - 148) * q^82 + (-184*b + 20) * q^83 + (-48*b + 272) * q^84 + (52*b - 472) * q^86 + (-6*b - 612) * q^87 + (-16*b - 208) * q^88 + (26*b + 242) * q^89 + (16*b - 76) * q^91 + (-32*b - 32) * q^92 + (-8*b + 680) * q^93 + (52*b + 376) * q^94 - 32*b * q^96 + (39*b - 278) * q^97 + (96*b + 126) * q^98 + (14*b + 182) * q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q - 4 * q^2 + 8 * q^4 - 24 * q^7 - 16 * q^8 + 14 * q^9 + 52 * q^11 - 44 * q^13 + 48 * q^14 + 32 * q^16 - 100 * q^17 - 28 * q^18 + 38 * q^19 + 136 * q^21 - 104 * q^22 - 16 * q^23 + 88 * q^26 - 96 * q^28 - 12 * q^29 - 16 * q^31 - 64 * q^32 + 136 * q^33 + 200 * q^34 + 56 * q^36 - 36 * q^37 - 76 * q^38 - 340 * q^39 + 148 * q^41 - 272 * q^42 + 472 * q^43 + 208 * q^44 + 32 * q^46 - 376 * q^47 - 126 * q^49 - 136 * q^51 - 176 * q^52 - 116 * q^53 + 192 * q^56 + 24 * q^58 + 112 * q^59 - 680 * q^61 + 32 * q^62 - 168 * q^63 + 128 * q^64 - 272 * q^66 + 208 * q^67 - 400 * q^68 - 544 * q^69 - 616 * q^71 - 112 * q^72 + 1332 * q^73 + 72 * q^74 + 152 * q^76 - 352 * q^77 + 680 * q^78 + 216 * q^79 - 1738 * q^81 - 296 * q^82 + 40 * q^83 + 544 * q^84 - 944 * q^86 - 1224 * q^87 - 416 * q^88 + 484 * q^89 - 152 * q^91 - 64 * q^92 + 1360 * q^93 + 752 * q^94 - 556 * q^97 + 252 * q^98 + 364 * 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

−5.83095
5.83095

−2.00000

−5.83095

4.00000

0

11.6619

−23.6619

−8.00000

7.00000

0

1.2

−2.00000

5.83095

4.00000

0

−11.6619

−0.338096

−8.00000

7.00000

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( +1 \)
\(5\)	\( +1 \)
\(19\)	\( -1 \)

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	950.4.a.f		2
5.b	even	2	1		190.4.a.f	✓	2
5.c	odd	4	2		950.4.b.h		4
15.d	odd	2	1		1710.4.a.l		2
20.d	odd	2	1		1520.4.a.l		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
190.4.a.f	✓	2	5.b	even	2	1
950.4.a.f		2	1.a	even	1	1	trivial
950.4.b.h		4	5.c	odd	4	2
1520.4.a.l		2	20.d	odd	2	1
1710.4.a.l		2	15.d	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(950))\):

\( T_{3}^{2} - 34 \)

\( T_{7}^{2} + 24T_{7} + 8 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( (T + 2)^{2} \)
$3$	\( T^{2} - 34 \)
$5$	\( T^{2} \)
$7$	\( T^{2} + 24T + 8 \)
$11$	\( T^{2} - 52T + 540 \)