Space of modular forms of level 216 and weight 2

• Label: 216.2
• Level: 216
• Weight: 2
• Dimension: 544
• Nonzero newspaces: 9
• Newform subspaces: 20
• Sturm bound: 5184
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 20 \)
Sturm bound:			\(5184\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(216))\).

	Total	New	Old
Modular forms	1476	608	868
Cusp forms	1117	544	573
Eisenstein series	359	64	295

Trace form

544 * q - 8 * q^2 - 12 * q^3 - 14 * q^4 - 2 * q^5 - 12 * q^6 - 14 * q^7 - 2 * q^8 - 24 * q^9 - 6 * q^10 + 4 * q^11 - 12 * q^12 + 10 * q^13 - 2 * q^14 - 10 * q^16 + 10 * q^17 - 12 * q^18 + 2 * q^19 - 14 * q^20 + 12 * q^21 - 34 * q^22 + 18 * q^23 - 30 * q^24 - 17 * q^25 - 50 * q^26 - 27 * q^27 - 76 * q^28 - 30 * q^29 - 60 * q^30 - 34 * q^31 - 118 * q^32 - 33 * q^33 - 62 * q^34 - 90 * q^35 - 72 * q^36 - 30 * q^37 - 118 * q^38 - 48 * q^39 - 74 * q^40 - 38 * q^41 - 72 * q^42 - 50 * q^43 - 102 * q^44 - 54 * q^45 - 50 * q^46 - 84 * q^47 - 30 * q^48 + 5 * q^49 - 68 * q^50 - 72 * q^51 - 26 * q^52 - 20 * q^53 - 12 * q^54 - 58 * q^55 + 70 * q^56 - 69 * q^57 + 26 * q^58 - 95 * q^59 + 48 * q^60 - 14 * q^61 + 122 * q^62 - 108 * q^63 + 46 * q^64 - 82 * q^65 + 78 * q^66 - 70 * q^67 + 150 * q^68 - 48 * q^69 + 110 * q^70 - 130 * q^71 + 72 * q^72 - 42 * q^73 + 154 * q^74 - 78 * q^75 + 110 * q^76 - 24 * q^77 + 102 * q^78 - 58 * q^79 + 174 * q^80 - 36 * q^81 + 8 * q^82 - 70 * q^83 + 54 * q^84 - 4 * q^85 + 106 * q^86 - 18 * q^87 - 10 * q^88 + 25 * q^89 + 126 * q^90 - 36 * q^91 + 54 * q^92 + 72 * q^93 - 42 * q^94 + 40 * q^95 + 144 * q^96 - 42 * q^97 + 114 * q^98 + 126 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
216.2.a	\(\chi_{216}(1, \cdot)\)	216.2.a.a	1	1
		216.2.a.b	1
		216.2.a.c	1
		216.2.a.d	1
216.2.c	\(\chi_{216}(215, \cdot)\)	None	0	1
216.2.d	\(\chi_{216}(109, \cdot)\)	216.2.d.a	4	1
		216.2.d.b	4
		216.2.d.c	8
216.2.f	\(\chi_{216}(107, \cdot)\)	216.2.f.a	8	1
		216.2.f.b	8
216.2.i	\(\chi_{216}(73, \cdot)\)	216.2.i.a	2	2
		216.2.i.b	4
216.2.l	\(\chi_{216}(35, \cdot)\)	216.2.l.a	4	2
		216.2.l.b	16
216.2.n	\(\chi_{216}(37, \cdot)\)	216.2.n.a	4	2
		216.2.n.b	16
216.2.o	\(\chi_{216}(71, \cdot)\)	None	0	2
216.2.q	\(\chi_{216}(25, \cdot)\)	216.2.q.a	24	6
		216.2.q.b	30
216.2.t	\(\chi_{216}(13, \cdot)\)	216.2.t.a	204	6
216.2.v	\(\chi_{216}(11, \cdot)\)	216.2.v.a	12	6
		216.2.v.b	192
216.2.w	\(\chi_{216}(23, \cdot)\)	None	0	6

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(216))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(216)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)