Space of modular forms of level 175, weight 8, and Character 175.b

• Label: 175.8.b
• Level: $175$
• Weight: $8$
• Character orbit: 175.b
• Rep. character: $\chi_{175}(99,\cdot)$
• Character field: $\Q$
• Dimension: $62$
• Newform subspaces: $8$
• Sturm bound: $160$
• Trace bound: $4$

Defining parameters

Level:	$N$	$=$	$175 = 5^{2} \cdot 7$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	175.b (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$5$
Character field:			$\Q$
Newform subspaces:			$8$
Sturm bound:			$160$
Trace bound:			$4$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{8}(175, [\chi])$.

	Total	New	Old
Modular forms	146	62	84
Cusp forms	134	62	72
Eisenstein series	12	0	12

Trace form

62 * q - 3736 * q^4 - 216 * q^6 - 39114 * q^9 - 16556 * q^11 + 10976 * q^14 + 241032 * q^16 + 92840 * q^19 + 19208 * q^21 - 595700 * q^24 + 214284 * q^26 - 371140 * q^29 + 1079644 * q^31 + 224888 * q^34 + 1507812 * q^36 + 2427052 * q^39 - 1649656 * q^41 - 475242 * q^44 - 7705286 * q^46 - 7294238 * q^49 - 1478836 * q^51 - 11167580 * q^54 - 956970 * q^56 - 8268340 * q^59 + 2621904 * q^61 - 25530846 * q^64 + 45621428 * q^66 + 11264892 * q^69 - 4023656 * q^71 + 23927058 * q^74 - 9332740 * q^76 - 2383980 * q^79 + 23252662 * q^81 - 7288064 * q^84 - 48314346 * q^86 - 24913680 * q^89 - 14503412 * q^91 + 97282468 * q^94 + 106266924 * q^96 - 31535248 * q^99

Decomposition of $S_{8}^{\mathrm{new}}(175, [\chi])$ into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
175.8.b.a	$175$	$8$	175.b	5.b	$2$	$2$	$2$	$54.667$	$\Q(\sqrt{-1})$	None					7.8.a.a	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+6 i q^{2}-42 i q^{3}+92 q^{4}+252 q^{6}+\cdots$
175.8.b.b	$175$	$8$	175.b	5.b	$2$	$4$	$4$	$54.667$	$\Q(i, \sqrt{865})$	None					7.8.a.b	$2$	$0$	$0$	$0$	$0$	$0$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-\beta _{2})q^{2}+(2\beta _{1}-46\beta _{2})q^{3}+(-92+\cdots)q^{4}+\cdots$
175.8.b.c	$175$	$8$	175.b	5.b	$2$	$4$	$4$	$54.667$	$\Q(i, \sqrt{11})$	None					35.8.a.a	$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(8\beta _{1}+\beta _{3})q^{2}+(15\beta _{1}+6\beta _{3})q^{3}+\cdots$
175.8.b.d	$175$	$8$	175.b	5.b	$2$	$6$	$6$	$54.667$	$\mathbb{Q}[x]/(x^{6} + \cdots)$	None					35.8.a.b	$2$	$0$	$0$	$0$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+8\beta _{2})q^{2}+(-2\beta _{1}-17\beta _{2}-\beta _{5})q^{3}+\cdots$
175.8.b.e	$175$	$8$	175.b	5.b	$2$	$8$	$8$	$54.667$	$\mathbb{Q}[x]/(x^{8} - \cdots)$	None					35.8.a.c	$2$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\beta _{2}-\beta _{4})q^{2}+(9\beta _{2}+\beta _{4}+2\beta _{5}+\cdots)q^{3}+\cdots$
175.8.b.f	$175$	$8$	175.b	5.b	$2$	$10$	$10$	$54.667$	$\mathbb{Q}[x]/(x^{10} + \cdots)$	None					35.8.a.d	$2$	$0$	$0$	$0$	$0$	$0$	$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}-2\beta _{5})q^{2}+(13\beta _{5}-\beta _{7})q^{3}+(-111+\cdots)q^{4}+\cdots$
175.8.b.g	$175$	$8$	175.b	5.b	$2$	$12$	$12$	$54.667$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None		✓			175.8.a.g	$2$	$0$	$0$	$0$	$0$	$0$	$2^{9}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+\beta _{7})q^{2}+(\beta _{1}+5\beta _{7}+\beta _{8})q^{3}+\cdots$
175.8.b.h	$175$	$8$	175.b	5.b	$2$	$16$	$16$	$54.667$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None		✓	✓		175.8.a.i	$2$	$0$	$0$	$0$	$0$	$0$	$2^{9}\cdot 5^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\beta _{1}+2\beta _{9})q^{2}+(-7\beta _{9}-\beta _{10})q^{3}+\cdots$

Decomposition of $S_{8}^{\mathrm{old}}(175, [\chi])$ into lower level spaces

$S_{8}^{\mathrm{old}}(175, [\chi]) \simeq$ $S_{8}^{\mathrm{new}}(5, [\chi])$$^{\oplus 4}$$\oplus$$S_{8}^{\mathrm{new}}(25, [\chi])$$^{\oplus 2}$$\oplus$$S_{8}^{\mathrm{new}}(35, [\chi])$$^{\oplus 2}$