Newform orbit 1840.4.a.h

• Label: 1840.4.a.h
• Level: $1840$
• Weight: $4$
• Character orbit: 1840.a
• Self dual: yes
• Analytic conductor: $108.564$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	\( N \)	\(=\)	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1840.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	\(108.563514411\)
Analytic rank:	\(1\)
Dimension:	\(2\)
Coefficient field:	\(\Q(\sqrt{109}) \)
Defining polynomial:	\( x^{2} - x - 27 \)
Coefficient ring:	\(\Z[a_1, a_2, a_3]\)
Coefficient ring index:	\( 1 \)
Twist minimal:	no (minimal twist has level 115)
Fricke sign:	\(-1\)
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{109})\). We also show the integral \(q\)-expansion of the trace form.

\(f(q)\)	\(=\)	q + (b + 1) * q^3 + 5 * q^5 + (-5*b + 2) * q^7 + (3*b + 1) * q^9 + (5*b + 11) * q^11 + (-3*b - 6) * q^13 + (5*b + 5) * q^15 + (7*b - 43) * q^17 + (-13*b + 42) * q^19 + (-8*b - 133) * q^21 + 23 * q^23 + 25 * q^25 + (-20*b + 55) * q^27 + (10*b - 220) * q^29 + (17*b + 144) * q^31 + (21*b + 146) * q^33 + (-25*b + 10) * q^35 + (-28*b - 20) * q^37 + (-12*b - 87) * q^39 + (-11*b - 291) * q^41 + (-8*b - 320) * q^43 + (15*b + 5) * q^45 + (74*b - 228) * q^47 + (5*b + 336) * q^49 + (-29*b + 146) * q^51 + (-44*b - 210) * q^53 + (25*b + 55) * q^55 + (16*b - 309) * q^57 + (54*b - 18) * q^59 + (-57*b + 25) * q^61 + (-14*b - 403) * q^63 + (-15*b - 30) * q^65 + (76*b - 68) * q^67 + (23*b + 23) * q^69 + (-97*b + 563) * q^71 + (62*b + 6) * q^73 + (25*b + 25) * q^75 + (-70*b - 653) * q^77 + (-172*b - 260) * q^79 + (-66*b - 512) * q^81 + (144*b + 658) * q^83 + (35*b - 215) * q^85 + (-200*b + 50) * q^87 + (180*b - 200) * q^89 + (39*b + 393) * q^91 + (178*b + 603) * q^93 + (-65*b + 210) * q^95 + (-203*b + 771) * q^97 + (53*b + 416) * q^99
\(\operatorname{Tr}(f)(q)\)	\(=\)	2 * q + 3 * q^3 + 10 * q^5 - q^7 + 5 * q^9 + 27 * q^11 - 15 * q^13 + 15 * q^15 - 79 * q^17 + 71 * q^19 - 274 * q^21 + 46 * q^23 + 50 * q^25 + 90 * q^27 - 430 * q^29 + 305 * q^31 + 313 * q^33 - 5 * q^35 - 68 * q^37 - 186 * q^39 - 593 * q^41 - 648 * q^43 + 25 * q^45 - 382 * q^47 + 677 * q^49 + 263 * q^51 - 464 * q^53 + 135 * q^55 - 602 * q^57 + 18 * q^59 - 7 * q^61 - 820 * q^63 - 75 * q^65 - 60 * q^67 + 69 * q^69 + 1029 * q^71 + 74 * q^73 + 75 * q^75 - 1376 * q^77 - 692 * q^79 - 1090 * q^81 + 1460 * q^83 - 395 * q^85 - 100 * q^87 - 220 * q^89 + 825 * q^91 + 1384 * q^93 + 355 * q^95 + 1339 * q^97 + 885 * 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

−4.72015
5.72015

0

−3.72015

0

5.00000

0

25.6008

0

−13.1605

0

1.2

0

6.72015

0

5.00000

0

−26.6008

0

18.1605

0

Atkin-Lehner signs

\( p \)	Sign
\(2\)	\( -1 \)
\(5\)	\( -1 \)
\(23\)	\( -1 \)

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	1840.4.a.h		2
4.b	odd	2	1		115.4.a.c	✓	2
12.b	even	2	1		1035.4.a.g		2
20.d	odd	2	1		575.4.a.h		2
20.e	even	4	2		575.4.b.f		4

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
115.4.a.c	✓	2	4.b	odd	2	1
575.4.a.h		2	20.d	odd	2	1
575.4.b.f		4	20.e	even	4	2
1035.4.a.g		2	12.b	even	2	1
1840.4.a.h		2	1.a	even	1	1	trivial

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on \(S_{4}^{\mathrm{new}}(\Gamma_0(1840))\):

\( T_{3}^{2} - 3T_{3} - 25 \)

\( T_{7}^{2} + T_{7} - 681 \)

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	\( T^{2} \)
$3$	\( T^{2} - 3T - 25 \)
$5$	\( (T - 5)^{2} \)
$7$	\( T^{2} + T - 681 \)
$11$	\( T^{2} - 27T - 499 \)