Newform orbit 1911.4.a.h

• Label: 1911.4.a.h
• Level: $1911$
• Weight: $4$
• Character orbit: 1911.a
• Self dual: yes
• Analytic conductor: $112.753$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$1911 = 3 \cdot 7^{2} \cdot 13$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	1911.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$112.752650021$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{14})$
Defining polynomial:	$x^{2} - 14$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 39)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \sqrt{14}$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q + (b + 1) * q^2 + 3 * q^3 + (2*b + 7) * q^4 + (2*b - 12) * q^5 + (3*b + 3) * q^6 + (b + 27) * q^8 + 9 * q^9 + (-10*b + 16) * q^10 + (-12*b - 22) * q^11 + (6*b + 21) * q^12 + 13 * q^13 + (6*b - 36) * q^15 + (12*b - 15) * q^16 + (-4*b - 82) * q^17 + (9*b + 9) * q^18 + (-2*b - 24) * q^19 + (-10*b - 28) * q^20 + (-34*b - 190) * q^22 + (48*b + 4) * q^23 + (3*b + 81) * q^24 + (-48*b + 75) * q^25 + (13*b + 13) * q^26 + 27 * q^27 + (-24*b + 202) * q^29 + (-30*b + 48) * q^30 + (26*b - 20) * q^31 + (-11*b - 63) * q^32 + (-36*b - 66) * q^33 + (-86*b - 138) * q^34 + (18*b + 63) * q^36 + (28*b - 50) * q^37 + (-26*b - 52) * q^38 + 39 * q^39 + (42*b - 296) * q^40 + (-94*b - 100) * q^41 + (52*b - 308) * q^43 + (-128*b - 490) * q^44 + (18*b - 108) * q^45 + (52*b + 676) * q^46 + (-32*b + 162) * q^47 + (36*b - 45) * q^48 + (27*b - 597) * q^50 + (-12*b - 246) * q^51 + (26*b + 91) * q^52 + (-120*b - 82) * q^53 + (27*b + 27) * q^54 + (100*b - 72) * q^55 + (-6*b - 72) * q^57 + (178*b - 134) * q^58 + (-40*b - 70) * q^59 + (-30*b - 84) * q^60 + (-136*b - 314) * q^61 + (6*b + 344) * q^62 + (-170*b - 97) * q^64 + (26*b - 156) * q^65 + (-102*b - 570) * q^66 + (-170*b - 236) * q^67 + (-192*b - 686) * q^68 + (144*b + 12) * q^69 + (-84*b + 214) * q^71 + (9*b + 243) * q^72 + (-76*b + 450) * q^73 + (-22*b + 342) * q^74 + (-144*b + 225) * q^75 + (-62*b - 224) * q^76 + (39*b + 39) * q^78 + (-88*b - 216) * q^79 + (-174*b + 516) * q^80 + 81 * q^81 + (-194*b - 1416) * q^82 + (-64*b + 694) * q^83 + (-116*b + 872) * q^85 + (-256*b + 420) * q^86 + (-72*b + 606) * q^87 + (-346*b - 762) * q^88 + (190*b - 480) * q^89 + (-90*b + 144) * q^90 + (344*b + 1372) * q^92 + (78*b - 60) * q^93 + (130*b - 286) * q^94 + (-24*b + 232) * q^95 + (-33*b - 189) * q^96 + (220*b + 266) * q^97 + (-108*b - 198) * q^99
$\operatorname{Tr}(f)(q)$	$=$	2 * q + 2 * q^2 + 6 * q^3 + 14 * q^4 - 24 * q^5 + 6 * q^6 + 54 * q^8 + 18 * q^9 + 32 * q^10 - 44 * q^11 + 42 * q^12 + 26 * q^13 - 72 * q^15 - 30 * q^16 - 164 * q^17 + 18 * q^18 - 48 * q^19 - 56 * q^20 - 380 * q^22 + 8 * q^23 + 162 * q^24 + 150 * q^25 + 26 * q^26 + 54 * q^27 + 404 * q^29 + 96 * q^30 - 40 * q^31 - 126 * q^32 - 132 * q^33 - 276 * q^34 + 126 * q^36 - 100 * q^37 - 104 * q^38 + 78 * q^39 - 592 * q^40 - 200 * q^41 - 616 * q^43 - 980 * q^44 - 216 * q^45 + 1352 * q^46 + 324 * q^47 - 90 * q^48 - 1194 * q^50 - 492 * q^51 + 182 * q^52 - 164 * q^53 + 54 * q^54 - 144 * q^55 - 144 * q^57 - 268 * q^58 - 140 * q^59 - 168 * q^60 - 628 * q^61 + 688 * q^62 - 194 * q^64 - 312 * q^65 - 1140 * q^66 - 472 * q^67 - 1372 * q^68 + 24 * q^69 + 428 * q^71 + 486 * q^72 + 900 * q^73 + 684 * q^74 + 450 * q^75 - 448 * q^76 + 78 * q^78 - 432 * q^79 + 1032 * q^80 + 162 * q^81 - 2832 * q^82 + 1388 * q^83 + 1744 * q^85 + 840 * q^86 + 1212 * q^87 - 1524 * q^88 - 960 * q^89 + 288 * q^90 + 2744 * q^92 - 120 * q^93 - 572 * q^94 + 464 * q^95 - 378 * q^96 + 532 * q^97 - 396 * 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

−3.74166
3.74166

−2.74166

3.00000

−0.483315

−19.4833

−8.22497

0

23.2583

9.00000

53.4166

1.2

4.74166

3.00000

14.4833

−4.51669

14.2250

0

30.7417

9.00000

−21.4166

Atkin-Lehner signs

$p$	Sign
$3$	$-1$
$7$	$-1$
$13$	$-1$

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	1911.4.a.h		2
7.b	odd	2	1		39.4.a.b	✓	2
21.c	even	2	1		117.4.a.c		2
28.d	even	2	1		624.4.a.r		2
35.c	odd	2	1		975.4.a.j		2
56.e	even	2	1		2496.4.a.s		2
56.h	odd	2	1		2496.4.a.bc		2
84.h	odd	2	1		1872.4.a.t		2
91.b	odd	2	1		507.4.a.f		2
91.i	even	4	2		507.4.b.f		4
273.g	even	2	1		1521.4.a.s		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
39.4.a.b	✓	2	7.b	odd	2	1
117.4.a.c		2	21.c	even	2	1
507.4.a.f		2	91.b	odd	2	1
507.4.b.f		4	91.i	even	4	2
624.4.a.r		2	28.d	even	2	1
975.4.a.j		2	35.c	odd	2	1
1521.4.a.s		2	273.g	even	2	1
1872.4.a.t		2	84.h	odd	2	1
1911.4.a.h		2	1.a	even	1	1	trivial
2496.4.a.s		2	56.e	even	2	1
2496.4.a.bc		2	56.h	odd	2	1

Hecke kernels

This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $S_{4}^{\mathrm{new}}(\Gamma_0(1911))$:

$T_{2}^{2} - 2T_{2} - 13$

$T_{5}^{2} + 24T_{5} + 88$

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2} - 2T - 13$
$3$	$(T - 3)^{2}$
$5$	$T^{2} + 24T + 88$
$7$	$T^{2}$
$11$	$T^{2} + 44T - 1532$