Space of modular forms of level 74, weight 8, and Character 74.f

• Label: 74.8.f
• Level: $74$
• Weight: $8$
• Character orbit: 74.f
• Rep. character: $\chi_{74}(7,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $126$
• Newform subspaces: $2$
• Sturm bound: $76$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$74 = 2 \cdot 37$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	74.f (of order $9$ and degree $6$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$37$
Character field:			$\Q(\zeta_{9})$
Newform subspaces:			$2$
Sturm bound:			$76$
Trace bound:			$1$

Dimensions

The following table gives the dimensions of various subspaces of $M_{8}(74, [\chi])$.

	Total	New	Old
Modular forms	414	126	288
Cusp forms	390	126	264
Eisenstein series	24	0	24

Trace form

126 * q - 78 * q^3 - 165 * q^5 - 1836 * q^7 + 1536 * q^8 + 6474 * q^9 + 6000 * q^10 + 7986 * q^11 - 4992 * q^12 + 162 * q^13 + 13488 * q^14 - 20820 * q^15 - 31161 * q^17 + 100110 * q^19 - 10560 * q^20 + 223326 * q^21 - 281268 * q^23 + 580365 * q^25 + 423144 * q^26 - 183378 * q^27 - 183168 * q^28 - 45786 * q^29 + 471744 * q^30 + 2356632 * q^31 - 211578 * q^33 - 660840 * q^34 - 2404590 * q^35 + 4758912 * q^36 - 837798 * q^37 - 2253696 * q^38 + 2828730 * q^39 + 1108992 * q^40 + 3754767 * q^41 + 1879968 * q^42 + 3145584 * q^43 - 290688 * q^44 - 1217670 * q^45 - 2751216 * q^46 - 1014978 * q^47 + 9445032 * q^49 - 517392 * q^50 - 3165696 * q^52 + 1414668 * q^53 - 481824 * q^54 + 6336630 * q^55 + 1362612 * q^57 - 3855288 * q^58 + 12206724 * q^59 - 13094106 * q^61 + 106848 * q^62 - 4170054 * q^63 - 16515072 * q^64 - 1081131 * q^65 - 8160150 * q^67 + 2505984 * q^68 - 4236810 * q^69 + 5959968 * q^70 - 25073952 * q^71 - 24545946 * q^73 + 16320504 * q^74 + 19727244 * q^75 + 6407040 * q^76 + 3167172 * q^77 - 17599056 * q^78 - 15728478 * q^79 + 3489792 * q^80 - 7684584 * q^81 + 161472 * q^82 + 32153040 * q^83 + 7112448 * q^84 - 17537505 * q^85 + 22501344 * q^86 - 85975716 * q^87 - 559104 * q^88 - 40498248 * q^89 - 76965432 * q^90 + 3337950 * q^91 + 12584832 * q^92 - 48769896 * q^93 - 38896320 * q^94 + 56656764 * q^95 - 11198520 * q^97 + 49143840 * q^98 + 26364066 * q^99

Decomposition of $S_{8}^{\mathrm{new}}(74, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
74.8.f.a	$74$	$8$	74.f	37.f	$9$	$60$	$10$	$23.116$		None		✓			74.8.f.a	$2$	$0$	$0$	$-39$	$-624$	$-918$		$\mathrm{SU}(2)[C_{9}]$
74.8.f.b	$74$	$8$	74.f	37.f	$9$	$66$	$11$	$23.116$		None		✓	✓		74.8.f.b	$2$	$0$	$0$	$-39$	$459$	$-918$		$\mathrm{SU}(2)[C_{9}]$

Decomposition of $S_{8}^{\mathrm{old}}(74, [\chi])$ into lower level spaces

$S_{8}^{\mathrm{old}}(74, [\chi]) \simeq$ $S_{8}^{\mathrm{new}}(37, [\chi])$$^{\oplus 2}$