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

• Label: 72.2.l
• Level: $72$
• Weight: $2$
• Character orbit: 72.l
• Rep. character: $\chi_{72}(11,\cdot)$
• 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.l (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 - 3 * q^2 - 4 * q^3 - q^4 - 7 * q^6 - 4 * q^9 - 6 * q^11 + 2 * q^12 - 18 * q^14 - q^16 - 16 * q^18 - 8 * q^19 + 18 * q^20 - 5 * q^22 + 29 * q^24 - 4 * q^25 - 16 * q^27 - 12 * q^28 + 12 * q^30 + 27 * q^32 - 2 * q^33 - 5 * q^34 + 23 * q^36 + 21 * q^38 - 12 * q^40 - 18 * q^41 + 42 * q^42 - 2 * q^43 + 12 * q^46 - 19 * q^48 - 4 * q^49 + 51 * q^50 + 28 * q^51 - 18 * q^52 + 35 * q^54 - 66 * q^56 - 20 * q^57 + 12 * q^58 + 30 * q^59 - 72 * q^60 + 2 * q^64 - 6 * q^65 - 32 * q^66 - 2 * q^67 - 45 * q^68 + 18 * q^70 - 37 * q^72 - 8 * q^73 - 60 * q^74 + 68 * q^75 - 11 * q^76 - 72 * q^78 + 8 * q^81 + 10 * q^82 + 54 * q^83 + 12 * q^84 - 87 * q^86 - 5 * q^88 - 66 * q^90 - 36 * q^91 + 84 * q^92 + 24 * q^94 + 74 * q^96 - 2 * q^97 + 10 * 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.l.a	$72$	$2$	72.l	72.l	$6$	$4$	$2$	$0.575$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	\(\Q(\sqrt{-2}) \)		✓			72.2.l.a	$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+\beta _{1}q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
72.2.l.b	$72$	$2$	72.l	72.l	$6$	$16$	$8$	$0.575$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		✓	✓		72.2.l.b	$4$	$0$	\(-3\)	\(-6\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{2}+(-\beta _{3}+\beta _{6})q^{3}+(-1-\beta _{1}+\cdots)q^{4}+\cdots\)