Space of modular forms of level 72, weight 2, and Character 72.i

• Label: 72.2.i
• Level: $72$
• Weight: $2$
• Character orbit: 72.i
• Rep. character: $\chi_{72}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(72, [\chi])\).

	Total	New	Old
Modular forms	32	6	26
Cusp forms	16	6	10
Eisenstein series	16	0	16

Trace form

6 * q + q^3 + 2 * q^5 - q^9 - 7 * q^11 - 14 * q^15 - 14 * q^17 + 6 * q^19 - 12 * q^21 - 4 * q^23 - 3 * q^25 + 16 * q^27 + 12 * q^29 - 6 * q^31 + 13 * q^33 + 36 * q^35 + 34 * q^39 + 9 * q^41 - 9 * q^43 + 2 * q^45 - 9 * q^49 - 19 * q^51 - 16 * q^53 - 12 * q^55 - 13 * q^57 - 25 * q^59 - 6 * q^61 - 18 * q^63 + 14 * q^65 - 3 * q^67 + 22 * q^69 - 8 * q^71 - 18 * q^73 - 19 * q^75 + 12 * q^77 + 6 * q^79 + 11 * q^81 - 26 * q^83 + 12 * q^85 - 24 * q^87 - 12 * q^89 + 12 * q^91 - 10 * q^93 + 16 * q^95 + 21 * q^97 + 20 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(72, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
72.2.i.a	$72$	$2$	72.i	9.c	$3$	$2$	$1$	$0.575$	\(\Q(\sqrt{-3}) \)	None		✓			72.2.i.a	$2$	$0$	\(0\)	\(0\)	\(1\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+3\zeta_{6}q^{7}+\cdots\)
72.2.i.b	$72$	$2$	72.i	9.c	$3$	$4$	$2$	$0.575$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None		✓	✓		72.2.i.b	$2$	$0$	\(0\)	\(1\)	\(1\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{3}+(\beta _{1}-\beta _{2}-2\beta _{3})q^{5}+(1-2\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(72, [\chi])\) into lower level spaces

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