Space of modular forms of level 66 and weight 4

• Label: 66.4
• Level: 66
• Weight: 4
• Dimension: 88
• Nonzero newspaces: 4
• Newform subspaces: 11
• Sturm bound: 960
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 66 = 2 \cdot 3 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 4 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(960\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(66))\).

	Total	New	Old
Modular forms	400	88	312
Cusp forms	320	88	232
Eisenstein series	80	0	80

Trace form

88 * q + 4 * q^2 + 6 * q^3 - 8 * q^4 - 12 * q^5 - 62 * q^6 - 8 * q^7 + 16 * q^8 + 142 * q^9 + 224 * q^10 + 188 * q^11 + 104 * q^12 + 4 * q^13 - 104 * q^14 - 374 * q^15 - 32 * q^16 - 368 * q^17 - 194 * q^18 + 410 * q^19 - 48 * q^20 + 324 * q^21 + 24 * q^22 + 44 * q^23 + 152 * q^24 + 538 * q^25 + 152 * q^26 - 6 * q^27 + 128 * q^28 - 760 * q^29 - 852 * q^30 - 1204 * q^31 + 64 * q^32 - 1899 * q^33 - 504 * q^34 - 388 * q^35 - 172 * q^36 - 508 * q^37 + 80 * q^38 + 988 * q^39 + 96 * q^40 + 656 * q^41 + 332 * q^42 - 2156 * q^43 - 1168 * q^44 + 1542 * q^45 - 48 * q^46 + 692 * q^47 + 96 * q^48 + 2834 * q^49 + 1004 * q^50 + 1389 * q^51 + 1616 * q^52 + 2724 * q^53 + 432 * q^54 + 2468 * q^55 - 256 * q^56 + 1625 * q^57 + 3480 * q^58 + 3360 * q^59 + 624 * q^60 - 1244 * q^61 - 3112 * q^62 - 5612 * q^63 - 128 * q^64 - 7176 * q^65 - 2992 * q^66 - 8448 * q^67 - 1472 * q^68 - 3232 * q^69 - 2064 * q^70 + 2096 * q^71 + 1264 * q^72 + 944 * q^73 + 3816 * q^74 + 6261 * q^75 + 1360 * q^76 + 4292 * q^77 + 2504 * q^78 + 5240 * q^79 + 1088 * q^80 + 11978 * q^81 + 7228 * q^82 + 3024 * q^83 + 2256 * q^84 + 10112 * q^85 - 1048 * q^86 + 180 * q^87 - 1024 * q^88 - 3120 * q^89 - 5324 * q^90 - 16524 * q^91 - 1344 * q^92 - 13558 * q^93 - 9664 * q^94 - 9600 * q^95 - 192 * q^96 - 10978 * q^97 - 348 * q^98 - 7998 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)

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
66.4.a	\(\chi_{66}(1, \cdot)\)	66.4.a.a	1	1
		66.4.a.b	1
		66.4.a.c	2
66.4.b	\(\chi_{66}(65, \cdot)\)	66.4.b.a	6	1
		66.4.b.b	6
66.4.e	\(\chi_{66}(25, \cdot)\)	66.4.e.a	4	4
		66.4.e.b	4
		66.4.e.c	8
		66.4.e.d	8
66.4.h	\(\chi_{66}(17, \cdot)\)	66.4.h.a	24	4
		66.4.h.b	24

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(66))\) into lower level spaces

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