Space of modular forms of level 72, weight 4, and Character 72.i

• Label: 72.4.i
• Level: $72$
• Weight: $4$
• Character orbit: 72.i
• Rep. character: $\chi_{72}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
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:			\(48\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(72, [\chi])\).

	Total	New	Old
Modular forms	80	18	62
Cusp forms	64	18	46
Eisenstein series	16	0	16

Trace form

18 * q + q^3 - 10 * q^5 + 29 * q^9 + 41 * q^11 + 82 * q^15 + 22 * q^17 - 90 * q^19 + 228 * q^21 - 52 * q^23 - 225 * q^25 + 160 * q^27 - 132 * q^29 + 90 * q^31 - 353 * q^33 - 828 * q^35 - 518 * q^39 - 549 * q^41 - 297 * q^43 + 446 * q^45 + 648 * q^47 - 243 * q^49 + 941 * q^51 + 1568 * q^53 + 612 * q^55 + 1889 * q^57 + 1223 * q^59 - 18 * q^61 + 462 * q^63 - 1342 * q^65 - 387 * q^67 - 3710 * q^69 - 2312 * q^71 + 1242 * q^73 - 2875 * q^75 - 1644 * q^77 + 126 * q^79 + 1025 * q^81 + 2446 * q^83 - 828 * q^85 + 3696 * q^87 + 6252 * q^89 + 1980 * q^91 + 3746 * q^93 + 3304 * q^95 - 369 * q^97 - 3340 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(72, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.4.i.a	$72$	$4$	72.i	9.c	$3$	$8$	$4$	$4.248$	8.0.5206055409.1	None		✓			72.4.i.a	$2$	$0$	\(0\)	\(-3\)	\(-5\)	\(3\)	$2^{6}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{5}q^{3}+(2\beta _{1}-\beta _{2}+\beta _{4})q^{5}+(1+\beta _{2}+\cdots)q^{7}+\cdots\)
72.4.i.b	$72$	$4$	72.i	9.c	$3$	$10$	$5$	$4.248$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		✓	✓		72.4.i.b	$2$	$0$	\(0\)	\(4\)	\(-5\)	\(-3\)	$2^{8}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{4}q^{3}+(-1+\beta _{1}+\beta _{8})q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

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