Newform orbit 175.4.a.c

• Label: 175.4.a.c
• Level: $175$
• Weight: $4$
• Character orbit: 175.a
• Self dual: yes
• Analytic conductor: $10.325$
• Analytic rank: $1$
• Dimension: $2$
• CM: no
• Inner twists: $1$

Newspace parameters

Level:	$N$	$=$	$175 = 5^{2} \cdot 7$
Weight:	$k$	$=$	$4$
Character orbit:	$[\chi]$	$=$	175.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$10.3253342510$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2})$
Defining polynomial:	$x^{2} - 2$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

$q$-expansion

Coefficients of the $q$-expansion are expressed in terms of $\beta = \sqrt{2}$. We also show the integral $q$-expansion of the trace form.

$f(q)$	$=$	q + (b - 4) * q^2 + (-4*b - 1) * q^3 + (-8*b + 10) * q^4 + (15*b - 4) * q^6 + 7 * q^7 + (34*b - 24) * q^8 + (8*b + 6) * q^9 + (32*b - 7) * q^11 + (-32*b + 54) * q^12 + (4*b - 25) * q^13 + (7*b - 28) * q^14 + (-96*b + 84) * q^16 + (44*b + 25) * q^17 + (-26*b - 8) * q^18 + (-44*b + 18) * q^19 + (-28*b - 7) * q^21 + (-135*b + 92) * q^22 + (-68*b - 122) * q^23 + (62*b - 248) * q^24 + (-41*b + 108) * q^26 + (76*b - 43) * q^27 + (-56*b + 70) * q^28 + (-24*b - 13) * q^29 + (180*b - 60) * q^31 + (196*b - 336) * q^32 + (-4*b - 249) * q^33 + (-151*b - 12) * q^34 + (32*b - 68) * q^36 + (-60*b - 282) * q^37 + (194*b - 160) * q^38 + (96*b - 7) * q^39 + (-124*b - 164) * q^41 + (105*b - 28) * q^42 + (68*b + 130) * q^43 + (376*b - 582) * q^44 + (150*b + 352) * q^46 + (-132*b + 175) * q^47 + (-240*b + 684) * q^48 + 49 * q^49 + (-144*b - 377) * q^51 + (240*b - 314) * q^52 + (128*b + 28) * q^53 + (-347*b + 324) * q^54 + (238*b - 168) * q^56 + (-28*b + 334) * q^57 + (83*b + 4) * q^58 - 616 * q^59 + (108*b + 168) * q^61 + (-780*b + 600) * q^62 + (56*b + 42) * q^63 + (-352*b + 1064) * q^64 + (-233*b + 988) * q^66 + (-64*b + 76) * q^67 + (240*b - 454) * q^68 + (556*b + 666) * q^69 - 952 * q^71 + (12*b + 400) * q^72 + (-344*b - 338) * q^73 + (-42*b + 1008) * q^74 + (-584*b + 884) * q^76 + (224*b - 49) * q^77 + (-391*b + 220) * q^78 + (-248*b + 507) * q^79 + (-120*b - 727) * q^81 + (332*b + 408) * q^82 + (600*b + 188) * q^83 + (-224*b + 378) * q^84 + (-142*b - 384) * q^86 + (76*b + 205) * q^87 + (-1006*b + 2344) * q^88 + (-44*b - 108) * q^89 + (28*b - 175) * q^91 + (296*b - 132) * q^92 + (60*b - 1380) * q^93 + (703*b - 964) * q^94 + (1148*b - 1232) * q^96 + (220*b - 1371) * q^97 + (49*b - 196) * q^98 + (136*b + 470) * q^99
$\operatorname{Tr}(f)(q)$	$=$	2 * q - 8 * q^2 - 2 * q^3 + 20 * q^4 - 8 * q^6 + 14 * q^7 - 48 * q^8 + 12 * q^9 - 14 * q^11 + 108 * q^12 - 50 * q^13 - 56 * q^14 + 168 * q^16 + 50 * q^17 - 16 * q^18 + 36 * q^19 - 14 * q^21 + 184 * q^22 - 244 * q^23 - 496 * q^24 + 216 * q^26 - 86 * q^27 + 140 * q^28 - 26 * q^29 - 120 * q^31 - 672 * q^32 - 498 * q^33 - 24 * q^34 - 136 * q^36 - 564 * q^37 - 320 * q^38 - 14 * q^39 - 328 * q^41 - 56 * q^42 + 260 * q^43 - 1164 * q^44 + 704 * q^46 + 350 * q^47 + 1368 * q^48 + 98 * q^49 - 754 * q^51 - 628 * q^52 + 56 * q^53 + 648 * q^54 - 336 * q^56 + 668 * q^57 + 8 * q^58 - 1232 * q^59 + 336 * q^61 + 1200 * q^62 + 84 * q^63 + 2128 * q^64 + 1976 * q^66 + 152 * q^67 - 908 * q^68 + 1332 * q^69 - 1904 * q^71 + 800 * q^72 - 676 * q^73 + 2016 * q^74 + 1768 * q^76 - 98 * q^77 + 440 * q^78 + 1014 * q^79 - 1454 * q^81 + 816 * q^82 + 376 * q^83 + 756 * q^84 - 768 * q^86 + 410 * q^87 + 4688 * q^88 - 216 * q^89 - 350 * q^91 - 264 * q^92 - 2760 * q^93 - 1928 * q^94 - 2464 * q^96 - 2742 * q^97 - 392 * q^98 + 940 * 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

−1.41421
1.41421

−5.41421

4.65685

21.3137

0

−25.2132

7.00000

−72.0833

−5.31371

0

1.2

−2.58579

−6.65685

−1.31371

0

17.2132

7.00000

24.0833

17.3137

0

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	175.4.a.c		2
3.b	odd	2	1		1575.4.a.z		2
5.b	even	2	1		35.4.a.b	✓	2
5.c	odd	4	2		175.4.b.c		4
7.b	odd	2	1		1225.4.a.m		2
15.d	odd	2	1		315.4.a.f		2
20.d	odd	2	1		560.4.a.r		2
35.c	odd	2	1		245.4.a.k		2
35.i	odd	6	2		245.4.e.i		4
35.j	even	6	2		245.4.e.h		4
40.e	odd	2	1		2240.4.a.bo		2
40.f	even	2	1		2240.4.a.bn		2
105.g	even	2	1		2205.4.a.u		2

    

By twisted newform orbit
Twist	Min	Dim	Char	Parity	Ord	Mult	Type
35.4.a.b	✓	2	5.b	even	2	1
175.4.a.c		2	1.a	even	1	1	trivial
175.4.b.c		4	5.c	odd	4	2
245.4.a.k		2	35.c	odd	2	1
245.4.e.h		4	35.j	even	6	2
245.4.e.i		4	35.i	odd	6	2
315.4.a.f		2	15.d	odd	2	1
560.4.a.r		2	20.d	odd	2	1
1225.4.a.m		2	7.b	odd	2	1
1575.4.a.z		2	3.b	odd	2	1
2205.4.a.u		2	105.g	even	2	1
2240.4.a.bn		2	40.f	even	2	1
2240.4.a.bo		2	40.e	odd	2	1

Hecke kernels

This newform subspace can be constructed as the kernel of the linear operator $T_{2}^{2} + 8T_{2} + 14$ acting on $S_{4}^{\mathrm{new}}(\Gamma_0(175))$.

Hecke characteristic polynomials

$p$	$F_p(T)$
$2$	$T^{2} + 8T + 14$
$3$	$T^{2} + 2T - 31$
$5$	$T^{2}$
$7$	$(T - 7)^{2}$
$11$	$T^{2} + 14T - 1999$