Space of modular forms of level 300 and weight 3

• Label: 300.3
• Level: 300
• Weight: 3
• Dimension: 1895
• Nonzero newspaces: 12
• Newform subspaces: 39
• Sturm bound: 14400
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 39 \)
Sturm bound:			\(14400\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(300))\).

	Total	New	Old
Modular forms	5080	1975	3105
Cusp forms	4520	1895	2625
Eisenstein series	560	80	480

Trace form

1895 * q - 2 * q^2 + q^3 - 24 * q^4 - 12 * q^5 - 28 * q^6 - 54 * q^7 - 8 * q^8 - 57 * q^9 + 32 * q^11 + 66 * q^12 - 34 * q^13 + 216 * q^14 + 14 * q^15 + 172 * q^16 - 120 * q^17 + 44 * q^18 - 94 * q^19 - 20 * q^20 + 154 * q^21 - 76 * q^22 + 40 * q^23 + 184 * q^25 - 228 * q^26 + 169 * q^27 - 52 * q^28 + 308 * q^29 - 6 * q^30 + 58 * q^31 + 248 * q^32 + 72 * q^33 + 280 * q^34 + 164 * q^35 - 198 * q^36 - 74 * q^37 + 524 * q^38 - 54 * q^39 + 664 * q^40 - 28 * q^41 + 74 * q^42 + 274 * q^43 + 92 * q^44 + 272 * q^45 - 492 * q^46 + 160 * q^47 - 512 * q^48 + 117 * q^49 - 364 * q^50 + 368 * q^51 - 888 * q^52 - 220 * q^53 - 678 * q^54 - 272 * q^55 - 584 * q^56 - 322 * q^57 - 1388 * q^58 - 800 * q^59 - 1006 * q^60 - 474 * q^61 - 1260 * q^62 - 176 * q^63 - 552 * q^64 - 120 * q^65 + 678 * q^66 - 414 * q^67 + 488 * q^68 - 14 * q^69 + 468 * q^70 + 160 * q^71 + 1214 * q^72 + 1110 * q^73 + 828 * q^74 + 98 * q^75 + 1304 * q^76 + 688 * q^77 + 1160 * q^78 + 1138 * q^79 + 356 * q^80 - 97 * q^81 + 328 * q^82 + 1120 * q^83 - 298 * q^84 + 1904 * q^85 - 384 * q^86 + 70 * q^87 - 1780 * q^88 + 784 * q^89 - 970 * q^90 - 540 * q^91 - 2264 * q^92 - 1208 * q^93 - 2900 * q^94 - 80 * q^95 - 1918 * q^96 - 1274 * q^97 - 1594 * q^98 - 1120 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(300))\)

We only show spaces with odd 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
300.3.b	\(\chi_{300}(149, \cdot)\)	300.3.b.a	2	1
		300.3.b.b	2
		300.3.b.c	4
		300.3.b.d	4
300.3.c	\(\chi_{300}(151, \cdot)\)	300.3.c.a	2	1
		300.3.c.b	2
		300.3.c.c	2
		300.3.c.d	8
		300.3.c.e	8
		300.3.c.f	8
		300.3.c.g	8
300.3.f	\(\chi_{300}(199, \cdot)\)	300.3.f.a	4	1
		300.3.f.b	16
		300.3.f.c	16
300.3.g	\(\chi_{300}(101, \cdot)\)	300.3.g.a	1	1
		300.3.g.b	1
		300.3.g.c	1
		300.3.g.d	2
		300.3.g.e	2
		300.3.g.f	2
		300.3.g.g	2
		300.3.g.h	2
300.3.k	\(\chi_{300}(157, \cdot)\)	300.3.k.a	4	2
		300.3.k.b	4
		300.3.k.c	4
300.3.l	\(\chi_{300}(107, \cdot)\)	300.3.l.a	4	2
		300.3.l.b	4
		300.3.l.c	4
		300.3.l.d	4
		300.3.l.e	8
		300.3.l.f	8
		300.3.l.g	40
		300.3.l.h	64
300.3.p	\(\chi_{300}(31, \cdot)\)	300.3.p.a	240	4
300.3.q	\(\chi_{300}(29, \cdot)\)	300.3.q.a	80	4
300.3.s	\(\chi_{300}(41, \cdot)\)	300.3.s.a	80	4
300.3.t	\(\chi_{300}(19, \cdot)\)	300.3.t.a	240	4
300.3.u	\(\chi_{300}(23, \cdot)\)	300.3.u.a	928	8
300.3.v	\(\chi_{300}(13, \cdot)\)	300.3.v.a	80	8

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(300))\) into lower level spaces

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