Newform orbit 936.4.a.j

• Label: 936.4.a.j
• Level: $936$
• Weight: $4$
• Character orbit: 936.a
• Self dual: yes
• Analytic conductor: $55.226$
• Analytic rank: $0$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	936.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(55.2257877654\)
Analytic rank:	\(0\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{17}) \)
Defining polynomial:	\( x^{2} - x - 4 \)
Coefficient ring:	\(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index:	\( 2 \)
Twist minimal:	no (minimal twist has level 312)
Fricke sign:	\(+1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{17}\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q + (-b + 9) * q^5 + (-5*b - 5) * q^7 + (-14*b - 2) * q^11 + 13 * q^13 + (12*b + 26) * q^17 + (-11*b - 71) * q^19 + (-12*b + 140) * q^23 + (-18*b - 27) * q^25 + (-6*b + 212) * q^29 + (-33*b - 89) * q^31 + (-40*b + 40) * q^35 + (54*b + 68) * q^37 + (19*b + 113) * q^41 + (88*b - 36) * q^43 + (120*b - 88) * q^47 + (50*b + 107) * q^49 + (8*b + 394) * q^53 + (-124*b + 220) * q^55 + (8*b - 364) * q^59 + (-38*b - 368) * q^61 + (-13*b + 117) * q^65 + (107*b + 527) * q^67 + (-78*b + 330) * q^71 + (-222*b + 12) * q^73 + (80*b + 1200) * q^77 + (276*b + 20) * q^79 + (-68*b - 672) * q^83 + (82*b + 30) * q^85 + (-219*b - 157) * q^89 + (-65*b - 65) * q^91 + (-28*b - 452) * q^95 + (10*b - 132) * q^97
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q + 18 * q^5 - 10 * q^7 - 4 * q^11 + 26 * q^13 + 52 * q^17 - 142 * q^19 + 280 * q^23 - 54 * q^25 + 424 * q^29 - 178 * q^31 + 80 * q^35 + 136 * q^37 + 226 * q^41 - 72 * q^43 - 176 * q^47 + 214 * q^49 + 788 * q^53 + 440 * q^55 - 728 * q^59 - 736 * q^61 + 234 * q^65 + 1054 * q^67 + 660 * q^71 + 24 * q^73 + 2400 * q^77 + 40 * q^79 - 1344 * q^83 + 60 * q^85 - 314 * q^89 - 130 * q^91 - 904 * q^95 - 264 * q^97

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

2.56155
−1.56155

0

0

0

4.87689

0

−25.6155

0

0

0

1.2

0

0

0

13.1231

0

15.6155

0

0

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( +1 \)
\(3\)	\( -1 \)
\(13\)	\( -1 \)

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	936.4.a.j		2
3.b	odd	2	1		312.4.a.d	✓	2
4.b	odd	2	1		1872.4.a.bi		2
12.b	even	2	1		624.4.a.j		2
24.f	even	2	1		2496.4.a.bj		2
24.h	odd	2	1		2496.4.a.ba		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
312.4.a.d	✓	2	3.b	odd	2	1
624.4.a.j		2	12.b	even	2	1
936.4.a.j		2	1.a	even	1	1	trivial
1872.4.a.bi		2	4.b	odd	2	1
2496.4.a.ba		2	24.h	odd	2	1
2496.4.a.bj		2	24.f	even	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator \( T_{5}^{2} - 18T_{5} + 64 \) acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(936))\).

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} \)
$5$	\( T^{2} - 18T + 64 \)
$7$	\( T^{2} + 10T - 400 \)
$11$	\( T^{2} + 4T - 3328 \)