Space of modular forms of level 300 and weight 8

• Label: 300.8
• Level: 300
• Weight: 8
• Dimension: 6736
• Nonzero newspaces: 12
• Sturm bound: 38400
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(38400\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(300))\).

	Total	New	Old
Modular forms	17080	6820	10260
Cusp forms	16520	6736	9784
Eisenstein series	560	84	476

Trace form

6736 * q - 52 * q^3 + 20 * q^4 - 62 * q^5 - 10 * q^6 + 4096 * q^7 - 4008 * q^8 - 346 * q^9 - 7200 * q^10 + 3904 * q^11 + 22710 * q^12 + 4140 * q^13 - 21386 * q^15 - 193796 * q^16 - 23280 * q^17 + 99462 * q^18 + 10680 * q^19 + 113980 * q^20 + 28408 * q^21 - 233044 * q^22 - 99080 * q^23 - 639908 * q^24 - 485066 * q^25 + 426016 * q^26 + 404 * q^27 + 372172 * q^28 + 455668 * q^29 + 617194 * q^30 - 298928 * q^31 - 71080 * q^32 - 781456 * q^33 - 2083460 * q^34 + 1322164 * q^35 + 239718 * q^36 - 980002 * q^37 + 3201484 * q^38 + 3343880 * q^39 + 7556664 * q^40 + 115396 * q^41 - 7018886 * q^42 - 3609608 * q^43 - 11667740 * q^44 - 3630678 * q^45 - 2244156 * q^46 - 440960 * q^47 + 7722460 * q^48 + 7245820 * q^49 + 19849636 * q^50 + 1170076 * q^51 - 4293240 * q^52 - 478994 * q^53 - 10972648 * q^54 - 9191272 * q^55 - 9913144 * q^56 - 11657372 * q^57 - 10146888 * q^58 - 6470272 * q^59 + 13912194 * q^60 + 5163116 * q^61 + 41147364 * q^62 + 16020902 * q^63 - 26840032 * q^64 - 1266570 * q^65 + 12712478 * q^66 + 1469416 * q^67 - 16086304 * q^68 - 26800106 * q^69 - 28995132 * q^70 - 3409680 * q^71 - 36026914 * q^72 - 40562332 * q^73 + 34552998 * q^75 + 56556216 * q^76 + 30509568 * q^77 + 27024792 * q^78 + 20783336 * q^79 + 20744156 * q^80 + 82578902 * q^81 + 6315756 * q^82 + 1939880 * q^83 - 77045402 * q^84 + 86829454 * q^85 - 40903256 * q^86 + 40794750 * q^87 + 19146572 * q^88 - 163926070 * q^89 + 63153230 * q^90 - 1125616 * q^91 + 107917816 * q^92 - 20370854 * q^93 + 52454876 * q^94 - 22332080 * q^95 - 23213902 * q^96 + 186365996 * q^97 - 166380584 * q^98 + 16539552 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(300))\)

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
300.8.a	\(\chi_{300}(1, \cdot)\)	300.8.a.a	1	1
		300.8.a.b	1
		300.8.a.c	1
		300.8.a.d	1
		300.8.a.e	1
		300.8.a.f	1
		300.8.a.g	1
		300.8.a.h	1
		300.8.a.i	2
		300.8.a.j	2
		300.8.a.k	2
		300.8.a.l	2
		300.8.a.m	3
		300.8.a.n	3
300.8.d	\(\chi_{300}(49, \cdot)\)	300.8.d.a	2	1
		300.8.d.b	2
		300.8.d.c	2
		300.8.d.d	2
		300.8.d.e	2
		300.8.d.f	2
		300.8.d.g	4
		300.8.d.h	6
300.8.e	\(\chi_{300}(251, \cdot)\)	n/a	260	1
300.8.h	\(\chi_{300}(299, \cdot)\)	n/a	248	1
300.8.i	\(\chi_{300}(257, \cdot)\)	300.8.i.a	4	2
		300.8.i.b	4
		300.8.i.c	16
		300.8.i.d	28
		300.8.i.e	32
300.8.j	\(\chi_{300}(7, \cdot)\)	n/a	252	2
300.8.m	\(\chi_{300}(61, \cdot)\)	n/a	144	4
300.8.n	\(\chi_{300}(11, \cdot)\)	n/a	1664	4
300.8.o	\(\chi_{300}(109, \cdot)\)	n/a	136	4
300.8.r	\(\chi_{300}(59, \cdot)\)	n/a	1664	4
300.8.w	\(\chi_{300}(67, \cdot)\)	n/a	1680	8
300.8.x	\(\chi_{300}(17, \cdot)\)	n/a	560	8

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

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