Space of modular forms of level 66 and weight 2

• Label: 66.2
• Level: 66
• Weight: 2
• Dimension: 31
• Nonzero newspaces: 4
• Newform subspaces: 9
• Sturm bound: 480
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 9 \)
Sturm bound:			\(480\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(66))\).

	Total	New	Old
Modular forms	160	31	129
Cusp forms	81	31	50
Eisenstein series	79	0	79

Trace form

31 * q + q^2 + q^3 + q^4 + 6 * q^5 - 4 * q^6 - 12 * q^7 + q^8 - 19 * q^9 - 14 * q^10 - 9 * q^11 - 9 * q^12 - 6 * q^13 - 12 * q^14 - 24 * q^15 + q^16 - 22 * q^17 - 4 * q^18 - 10 * q^19 + 6 * q^20 - 12 * q^21 + 11 * q^22 + 4 * q^23 + 6 * q^24 - 9 * q^25 + 14 * q^26 + 31 * q^27 + 8 * q^28 + 10 * q^29 + 36 * q^30 + 12 * q^31 + q^32 + 56 * q^33 + 18 * q^34 + 28 * q^35 + 6 * q^36 + 38 * q^37 + 20 * q^38 + 24 * q^39 + 6 * q^40 + 22 * q^41 + 18 * q^42 - 16 * q^43 - 9 * q^44 + 6 * q^45 - 16 * q^46 - 32 * q^47 + q^48 - 63 * q^49 - 9 * q^50 - 37 * q^51 - 26 * q^52 - 6 * q^53 - 9 * q^54 - 34 * q^55 + 8 * q^56 + 15 * q^57 - 50 * q^58 - 14 * q^60 - 38 * q^61 - 28 * q^62 - 2 * q^63 + q^64 - 36 * q^65 - 49 * q^66 - 32 * q^67 - 22 * q^68 - 6 * q^69 - 32 * q^70 - 8 * q^71 - 19 * q^72 - 6 * q^73 - 2 * q^74 - 14 * q^75 + 8 * q^77 - 26 * q^78 + 20 * q^79 - 14 * q^80 - 39 * q^81 + 32 * q^82 + 24 * q^83 + 8 * q^84 + 48 * q^85 - 16 * q^86 + 30 * q^87 - 9 * q^88 + 30 * q^89 + 16 * q^90 + 152 * q^91 + 24 * q^92 + 2 * q^93 + 88 * q^94 + 60 * q^95 + q^96 + 68 * q^97 + 57 * q^98 + 41 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)

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
66.2.a	\(\chi_{66}(1, \cdot)\)	66.2.a.a	1	1
		66.2.a.b	1
		66.2.a.c	1
66.2.b	\(\chi_{66}(65, \cdot)\)	66.2.b.a	2	1
		66.2.b.b	2
66.2.e	\(\chi_{66}(25, \cdot)\)	66.2.e.a	4	4
		66.2.e.b	4
66.2.h	\(\chi_{66}(17, \cdot)\)	66.2.h.a	8	4
		66.2.h.b	8

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(66))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(66)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 1}\)