Space of modular forms of level 264 and weight 4

• Label: 264.4
• Level: 264
• Weight: 4
• Dimension: 2356
• Nonzero newspaces: 12
• Sturm bound: 15360
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 264 = 2^{3} \cdot 3 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(15360\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(264))\).

	Total	New	Old
Modular forms	6000	2428	3572
Cusp forms	5520	2356	3164
Eisenstein series	480	72	408

Trace form

2356 * q - 4 * q^2 - 12 * q^3 - 60 * q^4 - 28 * q^5 + 18 * q^6 - 28 * q^7 + 152 * q^8 + 74 * q^9 - 92 * q^10 + 28 * q^11 + 92 * q^12 + 148 * q^13 + 200 * q^14 + 236 * q^15 + 172 * q^16 - 288 * q^17 - 342 * q^18 - 598 * q^19 - 112 * q^20 - 276 * q^21 - 468 * q^22 - 1052 * q^23 - 1074 * q^24 - 422 * q^25 - 112 * q^26 + 204 * q^27 - 372 * q^28 + 976 * q^29 + 224 * q^30 + 2472 * q^31 - 1284 * q^32 - 877 * q^33 - 1136 * q^34 - 1068 * q^35 + 1006 * q^36 - 60 * q^37 + 2852 * q^38 + 1190 * q^39 + 6352 * q^40 + 1184 * q^41 + 2988 * q^42 + 1676 * q^43 + 4868 * q^44 + 978 * q^45 + 1624 * q^46 + 2196 * q^47 - 2072 * q^48 - 502 * q^49 - 3800 * q^50 - 3511 * q^51 - 6408 * q^52 + 260 * q^53 - 1142 * q^54 - 5992 * q^55 - 5312 * q^56 - 2833 * q^57 + 1592 * q^58 - 1192 * q^59 + 6324 * q^60 + 436 * q^61 + 4216 * q^62 + 3286 * q^63 + 3084 * q^64 + 5560 * q^65 - 1362 * q^66 + 4104 * q^67 - 5952 * q^68 + 2072 * q^69 - 3256 * q^70 - 5704 * q^71 - 4878 * q^72 - 7760 * q^73 + 6364 * q^74 - 2915 * q^75 + 3452 * q^76 - 2052 * q^77 + 4516 * q^78 + 3132 * q^79 - 2596 * q^80 - 4962 * q^81 - 676 * q^82 + 16416 * q^83 + 3422 * q^84 + 7424 * q^85 - 12080 * q^86 + 9180 * q^87 - 25284 * q^88 + 6032 * q^89 - 10458 * q^90 + 12752 * q^91 - 14176 * q^92 + 7830 * q^93 - 24596 * q^94 - 2544 * q^95 - 14088 * q^96 + 5770 * q^97 - 1648 * q^98 - 5620 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(264))\)

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
264.4.a	\(\chi_{264}(1, \cdot)\)	264.4.a.a	1	1
		264.4.a.b	1
		264.4.a.c	1
		264.4.a.d	1
		264.4.a.e	2
		264.4.a.f	2
		264.4.a.g	2
		264.4.a.h	3
		264.4.a.i	3
264.4.b	\(\chi_{264}(65, \cdot)\)	264.4.b.a	18	1
		264.4.b.b	18
264.4.d	\(\chi_{264}(23, \cdot)\)	None	0	1
264.4.f	\(\chi_{264}(133, \cdot)\)	264.4.f.a	2	1
		264.4.f.b	28
		264.4.f.c	30
264.4.h	\(\chi_{264}(43, \cdot)\)	264.4.h.a	36	1
		264.4.h.b	36
264.4.k	\(\chi_{264}(155, \cdot)\)	n/a	120	1
264.4.m	\(\chi_{264}(197, \cdot)\)	n/a	140	1
264.4.o	\(\chi_{264}(175, \cdot)\)	None	0	1
264.4.q	\(\chi_{264}(25, \cdot)\)	264.4.q.a	16	4
		264.4.q.b	16
		264.4.q.c	20
		264.4.q.d	20
264.4.s	\(\chi_{264}(7, \cdot)\)	None	0	4
264.4.u	\(\chi_{264}(29, \cdot)\)	n/a	560	4
264.4.w	\(\chi_{264}(59, \cdot)\)	n/a	560	4
264.4.z	\(\chi_{264}(19, \cdot)\)	n/a	288	4
264.4.bb	\(\chi_{264}(37, \cdot)\)	n/a	288	4
264.4.bd	\(\chi_{264}(47, \cdot)\)	None	0	4
264.4.bf	\(\chi_{264}(17, \cdot)\)	n/a	144	4

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(264))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(264)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 1}\)