Space of modular forms of level 450 and weight 3

• Label: 450.3
• Level: 450
• Weight: 3
• Dimension: 2628
• Nonzero newspaces: 12
• Sturm bound: 32400
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(32400\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(450))\).

	Total	New	Old
Modular forms	11248	2628	8620
Cusp forms	10352	2628	7724
Eisenstein series	896	0	896

Trace form

2628 * q + 4 * q^2 - 12 * q^6 - 14 * q^7 - 8 * q^8 - 68 * q^9 - 54 * q^10 - 142 * q^11 - 20 * q^12 - 70 * q^13 + 36 * q^14 + 24 * q^15 + 16 * q^16 + 120 * q^17 + 104 * q^18 + 48 * q^19 + 56 * q^20 + 54 * q^21 + 84 * q^22 - 110 * q^23 - 18 * q^25 + 64 * q^26 - 96 * q^27 + 120 * q^28 + 218 * q^29 + 326 * q^31 + 24 * q^32 + 598 * q^33 + 150 * q^34 + 704 * q^35 + 268 * q^36 - 148 * q^37 + 296 * q^38 + 1018 * q^39 - 12 * q^40 + 322 * q^41 + 208 * q^42 - 262 * q^43 - 80 * q^45 + 200 * q^46 - 578 * q^47 - 104 * q^48 - 78 * q^49 - 242 * q^50 - 1224 * q^51 + 92 * q^52 - 944 * q^53 - 924 * q^54 + 640 * q^55 - 152 * q^56 - 1168 * q^57 + 76 * q^58 + 706 * q^59 + 448 * q^60 + 490 * q^61 + 1216 * q^62 + 1734 * q^63 - 48 * q^64 + 2282 * q^65 + 120 * q^66 + 958 * q^67 + 632 * q^68 + 1018 * q^69 + 744 * q^70 + 640 * q^71 - 96 * q^72 + 252 * q^73 + 72 * q^74 + 544 * q^75 - 120 * q^76 + 70 * q^77 - 336 * q^78 - 1498 * q^79 + 772 * q^81 - 916 * q^82 - 2054 * q^83 - 864 * q^84 - 2580 * q^85 - 876 * q^86 - 2110 * q^87 - 328 * q^88 - 4550 * q^89 - 1984 * q^90 - 1420 * q^91 - 1220 * q^92 - 2234 * q^93 - 956 * q^94 - 1352 * q^95 - 80 * q^96 + 130 * q^97 - 988 * q^98 - 2114 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(450))\)

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
450.3.b	\(\chi_{450}(449, \cdot)\)	450.3.b.a	4	1
		450.3.b.b	4
		450.3.b.c	4
450.3.d	\(\chi_{450}(251, \cdot)\)	450.3.d.a	2	1
		450.3.d.b	2
		450.3.d.c	2
		450.3.d.d	2
		450.3.d.e	2
		450.3.d.f	2
		450.3.d.g	2
450.3.g	\(\chi_{450}(307, \cdot)\)	450.3.g.a	2	2
		450.3.g.b	2
		450.3.g.c	2
		450.3.g.d	2
		450.3.g.e	2
		450.3.g.f	4
		450.3.g.g	4
		450.3.g.h	4
		450.3.g.i	4
		450.3.g.j	4
450.3.i	\(\chi_{450}(101, \cdot)\)	450.3.i.a	4	2
		450.3.i.b	4
		450.3.i.c	4
		450.3.i.d	16
		450.3.i.e	16
		450.3.i.f	16
		450.3.i.g	16
450.3.k	\(\chi_{450}(149, \cdot)\)	450.3.k.a	8	2
		450.3.k.b	32
		450.3.k.c	32
450.3.m	\(\chi_{450}(89, \cdot)\)	450.3.m.a	80	4
450.3.n	\(\chi_{450}(71, \cdot)\)	450.3.n.a	32	4
		450.3.n.b	48
450.3.o	\(\chi_{450}(7, \cdot)\)	n/a	144	4
450.3.r	\(\chi_{450}(37, \cdot)\)	n/a	200	8
450.3.t	\(\chi_{450}(11, \cdot)\)	n/a	480	8
450.3.u	\(\chi_{450}(29, \cdot)\)	n/a	480	8
450.3.x	\(\chi_{450}(13, \cdot)\)	n/a	960	16

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(450)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)