Space of modular forms of level 72, weight 8, and Character 72.i

• Label: 72.8.i
• Level: $72$
• Weight: $8$
• Character orbit: 72.i
• Rep. character: $\chi_{72}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $42$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	72.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(72, [\chi])\).

	Total	New	Old
Modular forms	176	42	134
Cusp forms	160	42	118
Eisenstein series	16	0	16

Trace form

42 * q + 13 * q^3 - 250 * q^5 - 2431 * q^9 + 7805 * q^11 - 25838 * q^15 + 75262 * q^17 + 2094 * q^19 - 96276 * q^21 + 1148 * q^23 - 328125 * q^25 - 527888 * q^27 - 50316 * q^29 - 161286 * q^31 + 80299 * q^33 - 530028 * q^35 + 438850 * q^39 - 563049 * q^41 + 288243 * q^43 - 1163194 * q^45 - 1185840 * q^47 - 2795967 * q^49 - 38887 * q^51 - 1994128 * q^53 + 1177332 * q^55 + 3461069 * q^57 + 2220851 * q^59 - 1288482 * q^61 - 2650194 * q^63 + 3228818 * q^65 + 1084569 * q^67 - 5179742 * q^69 + 14147128 * q^71 + 4804146 * q^73 - 4179055 * q^75 + 3459684 * q^77 + 1809366 * q^79 + 2996381 * q^81 + 12576862 * q^83 - 302748 * q^85 + 9009912 * q^87 + 33871596 * q^89 - 12907428 * q^91 - 18593230 * q^93 + 2834944 * q^95 + 19656147 * q^97 + 23546180 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(72, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.8.i.a	$72$	$8$	72.i	9.c	$3$	$20$	$10$	$22.492$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			72.8.i.a	$2$	$0$	\(0\)	\(57\)	\(-125\)	\(1245\)	$2^{48}\cdot 3^{30}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(3+\beta _{5})q^{3}+(13\beta _{2}-\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{5}+\cdots\)
72.8.i.b	$72$	$8$	72.i	9.c	$3$	$22$	$11$	$22.492$		None		✓	✓		72.8.i.b	$2$	$0$	\(0\)	\(-44\)	\(-125\)	\(-1245\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{8}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(72, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(18, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 2}\)