Space of modular forms of level 756 and weight 4

• Label: 756.4
• Level: 756
• Weight: 4
• Dimension: 20448
• Nonzero newspaces: 32
• Sturm bound: 124416
• Trace bound: 21

Defining parameters

Level:	\( N \)	=	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(124416\)
Trace bound:			\(21\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(756))\).

	Total	New	Old
Modular forms	47556	20768	26788
Cusp forms	45756	20448	25308
Eisenstein series	1800	320	1480

Trace form

20448 * q - 18 * q^2 - 16 * q^4 - 48 * q^5 - 24 * q^6 + 28 * q^7 - 30 * q^8 + 48 * q^9 - 128 * q^10 + 276 * q^11 + 210 * q^12 - 108 * q^13 - 171 * q^14 - 468 * q^15 - 304 * q^16 - 720 * q^17 - 738 * q^18 - 88 * q^19 - 936 * q^20 - 48 * q^21 - 474 * q^22 + 480 * q^23 + 564 * q^24 + 1690 * q^25 + 24 * q^26 - 54 * q^27 - 90 * q^28 - 96 * q^29 + 378 * q^30 + 464 * q^31 + 4212 * q^32 - 1914 * q^33 + 2308 * q^34 - 1074 * q^35 + 2040 * q^36 - 2244 * q^37 + 1818 * q^38 - 132 * q^39 - 932 * q^40 - 2532 * q^41 - 2610 * q^42 + 2048 * q^43 - 7644 * q^44 + 1884 * q^45 - 3504 * q^46 + 3744 * q^47 + 834 * q^48 + 108 * q^49 + 3516 * q^50 + 6516 * q^51 - 1892 * q^52 + 4056 * q^53 + 8880 * q^54 - 720 * q^55 + 1953 * q^56 - 1230 * q^57 - 4952 * q^58 - 4158 * q^59 - 1968 * q^60 + 516 * q^61 - 3798 * q^62 - 7842 * q^63 + 242 * q^64 - 5484 * q^65 - 6222 * q^66 + 5324 * q^67 + 534 * q^68 - 1680 * q^69 + 1539 * q^70 + 3432 * q^71 + 9012 * q^72 + 7296 * q^73 + 22902 * q^74 + 6996 * q^75 + 12144 * q^76 + 9942 * q^77 + 5880 * q^78 - 3856 * q^79 + 8070 * q^80 - 7656 * q^81 + 412 * q^82 - 13140 * q^83 - 6360 * q^84 - 16036 * q^85 - 24966 * q^86 - 9648 * q^87 - 16008 * q^88 - 29454 * q^89 + 2172 * q^90 - 4906 * q^91 - 10062 * q^92 - 17208 * q^93 - 14688 * q^94 + 1368 * q^95 - 1200 * q^96 + 10176 * q^97 - 11304 * q^98 + 10152 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(756))\)

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
756.4.a	\(\chi_{756}(1, \cdot)\)	756.4.a.a	1	1
		756.4.a.b	1
		756.4.a.c	1
		756.4.a.d	1
		756.4.a.e	2
		756.4.a.f	2
		756.4.a.g	2
		756.4.a.h	2
		756.4.a.i	2
		756.4.a.j	2
		756.4.a.k	4
		756.4.a.l	4
756.4.b	\(\chi_{756}(55, \cdot)\)	n/a	192	1
756.4.e	\(\chi_{756}(323, \cdot)\)	n/a	144	1
756.4.f	\(\chi_{756}(377, \cdot)\)	756.4.f.a	2	1
		756.4.f.b	2
		756.4.f.c	4
		756.4.f.d	8
		756.4.f.e	16
756.4.i	\(\chi_{756}(37, \cdot)\)	756.4.i.a	48	2
756.4.j	\(\chi_{756}(253, \cdot)\)	756.4.j.a	18	2
		756.4.j.b	18
756.4.k	\(\chi_{756}(109, \cdot)\)	756.4.k.a	2	2
		756.4.k.b	2
		756.4.k.c	4
		756.4.k.d	4
		756.4.k.e	4
		756.4.k.f	16
		756.4.k.g	16
		756.4.k.h	16
756.4.l	\(\chi_{756}(289, \cdot)\)	756.4.l.a	48	2
756.4.n	\(\chi_{756}(19, \cdot)\)	n/a	280	2
756.4.o	\(\chi_{756}(179, \cdot)\)	n/a	280	2
756.4.t	\(\chi_{756}(269, \cdot)\)	756.4.t.a	2	2
		756.4.t.b	2
		756.4.t.c	12
		756.4.t.d	16
		756.4.t.e	32
756.4.w	\(\chi_{756}(341, \cdot)\)	756.4.w.a	48	2
756.4.x	\(\chi_{756}(125, \cdot)\)	756.4.x.a	48	2
756.4.ba	\(\chi_{756}(71, \cdot)\)	n/a	216	2
756.4.bb	\(\chi_{756}(611, \cdot)\)	n/a	280	2
756.4.be	\(\chi_{756}(107, \cdot)\)	n/a	384	2
756.4.bf	\(\chi_{756}(271, \cdot)\)	n/a	384	2
756.4.bi	\(\chi_{756}(307, \cdot)\)	n/a	280	2
756.4.bj	\(\chi_{756}(451, \cdot)\)	n/a	280	2
756.4.bm	\(\chi_{756}(17, \cdot)\)	756.4.bm.a	48	2
756.4.bo	\(\chi_{756}(85, \cdot)\)	n/a	324	6
756.4.bp	\(\chi_{756}(193, \cdot)\)	n/a	432	6
756.4.bq	\(\chi_{756}(25, \cdot)\)	n/a	432	6
756.4.bs	\(\chi_{756}(11, \cdot)\)	n/a	2568	6
756.4.bt	\(\chi_{756}(103, \cdot)\)	n/a	2568	6
756.4.bx	\(\chi_{756}(41, \cdot)\)	n/a	432	6
756.4.ca	\(\chi_{756}(173, \cdot)\)	n/a	432	6
756.4.cc	\(\chi_{756}(139, \cdot)\)	n/a	2568	6
756.4.cd	\(\chi_{756}(31, \cdot)\)	n/a	2568	6
756.4.cf	\(\chi_{756}(155, \cdot)\)	n/a	1944	6
756.4.ci	\(\chi_{756}(95, \cdot)\)	n/a	2568	6
756.4.ck	\(\chi_{756}(5, \cdot)\)	n/a	432	6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(756))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(756)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(378))\)\(^{\oplus 2}\)