Space of modular forms of level 75, weight 8, and Character 75.g

• Label: 75.8.g
• Level: $75$
• Weight: $8$
• Character orbit: 75.g
• Rep. character: $\chi_{75}(16,\cdot)$
• Character field: $\Q(\zeta_{5})$
• Dimension: $136$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	75.g (of order \(5\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{5})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(75, [\chi])\).

	Total	New	Old
Modular forms	288	136	152
Cusp forms	272	136	136
Eisenstein series	16	0	16

Trace form

136 * q + 16 * q^2 - 2048 * q^4 - 390 * q^5 + 432 * q^6 - 2136 * q^7 + 66 * q^8 - 24786 * q^9 - 7590 * q^10 - 11586 * q^11 - 15336 * q^12 + 21684 * q^13 + 17628 * q^14 + 3780 * q^15 - 115540 * q^16 - 88570 * q^17 - 46656 * q^18 + 76118 * q^19 + 360400 * q^20 + 37044 * q^21 + 381810 * q^22 + 209268 * q^23 - 331776 * q^24 - 201860 * q^25 - 506348 * q^26 + 801012 * q^28 - 93364 * q^29 + 809460 * q^30 + 338346 * q^31 - 1614036 * q^32 - 732078 * q^33 + 32704 * q^34 + 540570 * q^35 - 1492992 * q^36 + 716104 * q^37 + 370162 * q^38 + 474552 * q^39 - 4659340 * q^40 + 2827146 * q^41 + 390852 * q^42 + 6080896 * q^43 + 5477666 * q^44 - 284310 * q^45 - 2592924 * q^46 - 4557232 * q^47 - 1418256 * q^48 + 13340080 * q^49 - 542080 * q^50 - 4244832 * q^51 + 7252940 * q^52 + 5047668 * q^53 + 314928 * q^54 + 5511830 * q^55 - 8259300 * q^56 + 2671488 * q^57 - 3966526 * q^58 - 3378948 * q^59 - 10350990 * q^60 + 5383940 * q^61 - 29690962 * q^62 - 121014 * q^63 - 1135622 * q^64 - 2112900 * q^65 + 80136 * q^66 - 10273120 * q^67 + 14657528 * q^68 + 2532708 * q^69 + 5942540 * q^70 - 271288 * q^71 + 48114 * q^72 - 11174592 * q^73 - 5572692 * q^74 - 955800 * q^75 - 31445632 * q^76 + 12339688 * q^77 - 17011080 * q^78 + 16588380 * q^79 + 7162160 * q^80 - 18068994 * q^81 + 83708328 * q^82 - 6271538 * q^83 - 15423048 * q^84 - 38746410 * q^85 + 1176084 * q^86 - 9875304 * q^87 + 7217486 * q^88 + 10375968 * q^89 + 18064620 * q^90 + 19989246 * q^91 + 8329414 * q^92 + 41715864 * q^93 + 47876802 * q^94 + 80483760 * q^95 - 23936796 * q^96 - 55782260 * q^97 - 103930284 * q^98 + 5630796 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(75, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
75.8.g.a	$75$	$8$	75.g	25.d	$5$	$68$	$17$	$23.429$		None		✓			75.8.g.a	$2$	$0$	\(0\)	\(459\)	\(-900\)	\(1676\)		$\mathrm{SU}(2)[C_{5}]$
75.8.g.b	$75$	$8$	75.g	25.d	$5$	$68$	$17$	$23.429$		None		✓			75.8.g.b	$2$	$0$	\(16\)	\(-459\)	\(510\)	\(-3812\)		$\mathrm{SU}(2)[C_{5}]$

Decomposition of \(S_{8}^{\mathrm{old}}(75, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(75, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)