Space of modular forms of level 72, weight 5, and Character 72.m

• Label: 72.5.m
• Level: $72$
• Weight: $5$
• Character orbit: 72.m
• Rep. character: $\chi_{72}(41,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	$N$	$=$	$72 = 2^{3} \cdot 3^{2}$
Weight:	$k$	$=$	$5$
Character orbit:	$[\chi]$	$=$	72.m (of order $6$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$9$
Character field:			$\Q(\zeta_{6})$
Newform subspaces:			$1$
Sturm bound:			$60$
Trace bound:			$0$

Dimensions

The following table gives the dimensions of various subspaces of $M_{5}(72, [\chi])$.

	Total	New	Old
Modular forms	104	24	80
Cusp forms	88	24	64
Eisenstein series	16	0	16

Trace form

24 * q + 4 * q^3 - 100 * q^9 + 252 * q^11 - 80 * q^15 - 408 * q^19 + 24 * q^21 + 720 * q^23 + 1500 * q^25 - 1280 * q^27 + 2376 * q^29 - 1104 * q^31 - 1412 * q^33 - 4184 * q^39 + 1980 * q^41 + 1476 * q^43 - 4696 * q^45 + 4536 * q^47 - 6084 * q^49 - 7828 * q^51 + 2544 * q^55 - 1204 * q^57 + 10332 * q^59 + 2784 * q^61 + 9072 * q^63 + 17280 * q^65 - 2604 * q^67 + 5680 * q^69 + 5112 * q^73 - 15412 * q^75 - 28368 * q^77 + 3480 * q^79 - 26548 * q^81 - 23400 * q^83 + 7392 * q^85 - 3192 * q^87 - 14208 * q^91 + 39488 * q^93 + 57528 * q^95 - 4020 * q^97 + 50744 * q^99

Decomposition of $S_{5}^{\mathrm{new}}(72, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.5.m.a	$72$	$5$	72.m	9.d	$6$	$24$	$12$	$7.443$		None		✓	✓	✓	72.5.m.a	$2$	$0$	$0$	$4$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$

Decomposition of $S_{5}^{\mathrm{old}}(72, [\chi])$ into lower level spaces

$S_{5}^{\mathrm{old}}(72, [\chi]) \simeq$ $S_{5}^{\mathrm{new}}(9, [\chi])$$^{\oplus 4}$$\oplus$$S_{5}^{\mathrm{new}}(18, [\chi])$$^{\oplus 3}$$\oplus$$S_{5}^{\mathrm{new}}(36, [\chi])$$^{\oplus 2}$