Space of modular forms of level 600 and weight 6

• Label: 600.6
• Level: 600
• Weight: 6
• Dimension: 18581
• Nonzero newspaces: 18
• Sturm bound: 115200
• Trace bound: 8

Defining parameters

Level:	\( N \)	=	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 18 \)
Sturm bound:			\(115200\)
Trace bound:			\(8\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(600))\).

	Total	New	Old
Modular forms	48672	18745	29927
Cusp forms	47328	18581	28747
Eisenstein series	1344	164	1180

Trace form

18581 * q + 2 * q^2 - 23 * q^3 - 68 * q^4 - 82 * q^5 + 158 * q^6 + 108 * q^7 + 68 * q^8 - 917 * q^9 - 32 * q^10 - 60 * q^11 + 1444 * q^12 + 4610 * q^13 - 7300 * q^14 - 2488 * q^15 - 3272 * q^16 - 3942 * q^17 + 15378 * q^18 + 9592 * q^19 + 13640 * q^20 + 10904 * q^21 + 4024 * q^22 - 8736 * q^23 - 33360 * q^24 - 4738 * q^25 - 54200 * q^26 - 2987 * q^27 - 7352 * q^28 + 40962 * q^29 + 9748 * q^30 - 36708 * q^31 + 98232 * q^32 - 21484 * q^33 + 123668 * q^34 - 9552 * q^35 + 3320 * q^36 + 91524 * q^37 - 153784 * q^38 + 61598 * q^39 - 118512 * q^40 + 32162 * q^41 - 56912 * q^42 - 80456 * q^43 + 89680 * q^44 - 1490 * q^45 + 227488 * q^46 - 112824 * q^47 + 146612 * q^48 + 71169 * q^49 + 40360 * q^50 + 184594 * q^51 - 278120 * q^52 + 84020 * q^53 + 102314 * q^54 - 151456 * q^55 + 10808 * q^56 - 304168 * q^57 + 77468 * q^58 - 16268 * q^59 - 209372 * q^60 + 224058 * q^61 + 25300 * q^62 - 62624 * q^63 - 366296 * q^64 + 223326 * q^65 + 253636 * q^66 + 157696 * q^67 + 464272 * q^68 - 150552 * q^69 + 399496 * q^70 + 136304 * q^71 + 390968 * q^72 - 227618 * q^73 - 311840 * q^74 - 272328 * q^75 - 698920 * q^76 + 507360 * q^77 - 791596 * q^78 - 587828 * q^79 - 492880 * q^80 - 6045 * q^81 - 2312148 * q^82 - 1076348 * q^83 + 137684 * q^84 + 487198 * q^85 + 1134808 * q^86 + 1342650 * q^87 + 4323144 * q^88 - 1144340 * q^89 + 1287788 * q^90 + 1469144 * q^91 + 1623552 * q^92 - 99960 * q^93 - 1111840 * q^94 - 848576 * q^95 - 1547540 * q^96 + 432910 * q^97 - 5210310 * q^98 - 994852 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(600))\)

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
600.6.a	\(\chi_{600}(1, \cdot)\)	600.6.a.a	1	1
		600.6.a.b	1
		600.6.a.c	1
		600.6.a.d	1
		600.6.a.e	1
		600.6.a.f	1
		600.6.a.g	1
		600.6.a.h	1
		600.6.a.i	1
		600.6.a.j	2
		600.6.a.k	2
		600.6.a.l	2
		600.6.a.m	2
		600.6.a.n	2
		600.6.a.o	2
		600.6.a.p	3
		600.6.a.q	3
		600.6.a.r	3
		600.6.a.s	3
		600.6.a.t	3
		600.6.a.u	3
		600.6.a.v	4
		600.6.a.w	4
600.6.b	\(\chi_{600}(251, \cdot)\)	n/a	374	1
600.6.d	\(\chi_{600}(349, \cdot)\)	n/a	180	1
600.6.f	\(\chi_{600}(49, \cdot)\)	600.6.f.a	2	1
		600.6.f.b	2
		600.6.f.c	2
		600.6.f.d	2
		600.6.f.e	2
		600.6.f.f	2
		600.6.f.g	2
		600.6.f.h	2
		600.6.f.i	2
		600.6.f.j	4
		600.6.f.k	4
		600.6.f.l	4
		600.6.f.m	4
		600.6.f.n	6
		600.6.f.o	6
600.6.h	\(\chi_{600}(551, \cdot)\)	None	0	1
600.6.k	\(\chi_{600}(301, \cdot)\)	n/a	190	1
600.6.m	\(\chi_{600}(299, \cdot)\)	n/a	356	1
600.6.o	\(\chi_{600}(599, \cdot)\)	None	0	1
600.6.r	\(\chi_{600}(257, \cdot)\)	n/a	180	2
600.6.s	\(\chi_{600}(7, \cdot)\)	None	0	2
600.6.v	\(\chi_{600}(43, \cdot)\)	n/a	360	2
600.6.w	\(\chi_{600}(293, \cdot)\)	n/a	712	2
600.6.y	\(\chi_{600}(121, \cdot)\)	n/a	304	4
600.6.ba	\(\chi_{600}(71, \cdot)\)	None	0	4
600.6.bc	\(\chi_{600}(169, \cdot)\)	n/a	296	4
600.6.be	\(\chi_{600}(109, \cdot)\)	n/a	1200	4
600.6.bg	\(\chi_{600}(11, \cdot)\)	n/a	2384	4
600.6.bi	\(\chi_{600}(119, \cdot)\)	None	0	4
600.6.bk	\(\chi_{600}(59, \cdot)\)	n/a	2384	4
600.6.bm	\(\chi_{600}(61, \cdot)\)	n/a	1200	4
600.6.bp	\(\chi_{600}(53, \cdot)\)	n/a	4768	8
600.6.bq	\(\chi_{600}(67, \cdot)\)	n/a	2400	8
600.6.bt	\(\chi_{600}(103, \cdot)\)	None	0	8
600.6.bu	\(\chi_{600}(17, \cdot)\)	n/a	1200	8

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(600))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(600)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 16}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(600))\)\(^{\oplus 1}\)