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

• Label: 72.2.n
• Level: $72$
• Weight: $2$
• Character orbit: 72.n
• Rep. character: $\chi_{72}(13,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $20$
• 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.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 72 \)
Character field:			\(\Q(\zeta_{6})\)
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	28	28	0
Cusp forms	20	20	0
Eisenstein series	8	8	0

Trace form

20 * q - q^2 - q^4 - q^6 - 2 * q^7 - 10 * q^8 - 4 * q^9 - 8 * q^10 - 16 * q^12 + 8 * q^14 - 10 * q^15 - q^16 - 8 * q^17 + 16 * q^18 - 16 * q^20 - 5 * q^22 - 14 * q^23 - 5 * q^24 + 20 * q^26 + 4 * q^28 + 34 * q^30 - 2 * q^31 + 19 * q^32 - 18 * q^33 - 9 * q^34 + 27 * q^36 + 25 * q^38 + 2 * q^39 - 2 * q^40 + 2 * q^41 + 8 * q^42 + 42 * q^44 - 12 * q^46 + 18 * q^47 + 39 * q^48 - 25 * q^50 - 47 * q^54 - 28 * q^55 + 26 * q^56 + 4 * q^57 - 14 * q^58 + 6 * q^60 - 68 * q^62 + 50 * q^63 + 26 * q^64 - 22 * q^65 - 72 * q^66 - 39 * q^68 - 16 * q^70 + 48 * q^71 - 65 * q^72 - 8 * q^73 - 34 * q^74 + 9 * q^76 - 2 * q^78 - 2 * q^79 - 96 * q^80 - 8 * q^81 + 18 * q^82 - 76 * q^84 + 29 * q^86 + 42 * q^87 + 19 * q^88 + 8 * q^89 + 52 * q^90 - 30 * q^92 + 40 * q^95 - 26 * q^96 - 2 * q^97 + 102 * q^98

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.n.a	$72$	$2$	72.n	72.n	$6$	$4$	$2$	$0.575$	\(\Q(\zeta_{12})\)	None		✓			72.2.n.a	$4$	$0$	\(-2\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
72.2.n.b	$72$	$2$	72.n	72.n	$6$	$16$	$8$	$0.575$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		72.2.n.b	$4$	$0$	\(1\)	\(0\)	\(0\)	\(6\)	$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{2}+(-\beta _{3}-\beta _{10})q^{3}+(\beta _{8}-\beta _{13}+\cdots)q^{4}+\cdots\)