Space of modular forms of level 300 and weight 4

• Label: 300.4
• Level: 300
• Weight: 4
• Dimension: 2863
• Nonzero newspaces: 12
• Sturm bound: 19200
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(19200\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(300))\).

	Total	New	Old
Modular forms	7480	2947	4533
Cusp forms	6920	2863	4057
Eisenstein series	560	84	476

Trace form

2863 * q + 11 * q^3 - 12 * q^4 + 38 * q^5 - 10 * q^6 - 56 * q^7 - 168 * q^8 - 43 * q^9 - 160 * q^10 - 76 * q^11 - 42 * q^12 + 262 * q^13 + 4 * q^15 + 508 * q^16 + 18 * q^17 + 198 * q^18 - 260 * q^19 + 380 * q^20 - 452 * q^21 + 812 * q^22 - 568 * q^23 + 220 * q^24 - 1166 * q^25 - 736 * q^26 + 611 * q^27 - 2036 * q^28 + 302 * q^29 - 86 * q^30 + 480 * q^31 - 680 * q^32 + 1784 * q^33 + 892 * q^34 + 1784 * q^35 - 186 * q^36 + 208 * q^37 - 916 * q^38 - 2470 * q^39 - 1736 * q^40 + 554 * q^41 + 346 * q^42 - 2076 * q^43 + 2660 * q^44 + 462 * q^45 + 4 * q^46 + 1472 * q^47 + 4060 * q^48 + 3019 * q^49 + 5636 * q^50 + 106 * q^51 + 1480 * q^52 + 2000 * q^53 + 1544 * q^54 + 3688 * q^55 + 3784 * q^56 + 4264 * q^57 + 664 * q^58 + 292 * q^59 - 6366 * q^60 - 26 * q^61 - 7356 * q^62 - 2356 * q^63 - 12000 * q^64 - 4710 * q^65 - 5794 * q^66 - 4292 * q^67 - 8864 * q^68 - 3044 * q^69 - 5052 * q^70 - 3720 * q^71 + 734 * q^72 - 2614 * q^73 + 1428 * q^75 - 648 * q^76 + 2496 * q^77 + 4728 * q^78 - 2096 * q^79 + 4636 * q^80 + 5093 * q^81 + 23916 * q^82 - 668 * q^83 + 20518 * q^84 - 4506 * q^85 + 10856 * q^86 + 6198 * q^87 + 14924 * q^88 - 440 * q^89 + 3470 * q^90 + 12896 * q^91 - 2824 * q^92 + 13108 * q^93 - 7972 * q^94 + 6320 * q^95 + 626 * q^96 + 17818 * q^97 - 20584 * q^98 - 1692 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(300))\)

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
300.4.a	\(\chi_{300}(1, \cdot)\)	300.4.a.a	1	1
		300.4.a.b	1
		300.4.a.c	1
		300.4.a.d	1
		300.4.a.e	1
		300.4.a.f	1
		300.4.a.g	1
		300.4.a.h	1
		300.4.a.i	1
300.4.d	\(\chi_{300}(49, \cdot)\)	300.4.d.a	2	1
		300.4.d.b	2
		300.4.d.c	2
		300.4.d.d	2
		300.4.d.e	2
300.4.e	\(\chi_{300}(251, \cdot)\)	n/a	108	1
300.4.h	\(\chi_{300}(299, \cdot)\)	n/a	104	1
300.4.i	\(\chi_{300}(257, \cdot)\)	300.4.i.a	4	2
		300.4.i.b	4
		300.4.i.c	4
		300.4.i.d	8
		300.4.i.e	8
		300.4.i.f	8
300.4.j	\(\chi_{300}(7, \cdot)\)	n/a	108	2
300.4.m	\(\chi_{300}(61, \cdot)\)	300.4.m.a	32	4
		300.4.m.b	32
300.4.n	\(\chi_{300}(11, \cdot)\)	n/a	704	4
300.4.o	\(\chi_{300}(109, \cdot)\)	300.4.o.a	56	4
300.4.r	\(\chi_{300}(59, \cdot)\)	n/a	704	4
300.4.w	\(\chi_{300}(67, \cdot)\)	n/a	720	8
300.4.x	\(\chi_{300}(17, \cdot)\)	n/a	240	8

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

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