Space of modular forms of level 450 and weight 4

• Label: 450.4
• Level: 450
• Weight: 4
• Dimension: 3940
• Nonzero newspaces: 12
• Sturm bound: 43200
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(43200\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(450))\).

	Total	New	Old
Modular forms	16648	3940	12708
Cusp forms	15752	3940	11812
Eisenstein series	896	0	896

Trace form

3940 * q + 3 * q^3 + 5 * q^5 - 18 * q^6 + 4 * q^7 - 24 * q^8 + 151 * q^9 + 46 * q^10 - 13 * q^11 - 104 * q^12 - 638 * q^13 - 604 * q^14 - 336 * q^15 - 128 * q^16 - 212 * q^17 + 92 * q^18 + 814 * q^19 + 176 * q^20 + 1548 * q^21 + 534 * q^22 + 1112 * q^23 - 24 * q^24 - 1603 * q^25 - 620 * q^26 - 1104 * q^27 - 368 * q^28 - 2782 * q^29 - 894 * q^31 + 160 * q^32 - 2867 * q^33 + 2272 * q^34 + 164 * q^35 - 380 * q^36 + 3929 * q^37 + 858 * q^38 + 3610 * q^39 - 72 * q^40 + 5463 * q^41 + 4048 * q^42 - 2955 * q^43 - 200 * q^44 + 3520 * q^45 - 3928 * q^46 + 4268 * q^47 + 880 * q^48 - 795 * q^49 + 798 * q^50 + 519 * q^51 + 712 * q^52 - 4563 * q^53 - 3462 * q^54 + 820 * q^55 - 1904 * q^56 - 11461 * q^57 + 2760 * q^58 - 11915 * q^59 - 4352 * q^60 - 1128 * q^61 - 9336 * q^62 - 11010 * q^63 + 576 * q^64 - 2963 * q^65 + 336 * q^66 + 6343 * q^67 + 2820 * q^68 + 9382 * q^69 + 9024 * q^70 + 2256 * q^71 - 24 * q^72 + 14164 * q^73 + 13748 * q^74 + 14584 * q^75 + 844 * q^76 + 11940 * q^77 + 7572 * q^78 + 3166 * q^79 + 80 * q^80 + 2491 * q^81 + 768 * q^82 + 7822 * q^83 - 408 * q^84 - 6475 * q^85 + 5098 * q^86 + 9932 * q^87 + 5016 * q^88 + 3845 * q^89 - 12544 * q^90 + 5108 * q^91 - 5952 * q^92 + 8854 * q^93 + 4196 * q^94 - 1492 * q^95 - 128 * q^96 - 14801 * q^97 - 8166 * q^98 - 8480 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(450))\)

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
450.4.a	\(\chi_{450}(1, \cdot)\)	450.4.a.a	1	1
		450.4.a.b	1
		450.4.a.c	1
		450.4.a.d	1
		450.4.a.e	1
		450.4.a.f	1
		450.4.a.g	1
		450.4.a.h	1
		450.4.a.i	1
		450.4.a.j	1
		450.4.a.k	1
		450.4.a.l	1
		450.4.a.m	1
		450.4.a.n	1
		450.4.a.o	1
		450.4.a.p	1
		450.4.a.q	1
		450.4.a.r	1
		450.4.a.s	1
		450.4.a.t	1
		450.4.a.u	2
		450.4.a.v	2
450.4.c	\(\chi_{450}(199, \cdot)\)	450.4.c.a	2	1
		450.4.c.b	2
		450.4.c.c	2
		450.4.c.d	2
		450.4.c.e	2
		450.4.c.f	2
		450.4.c.g	2
		450.4.c.h	2
		450.4.c.i	2
		450.4.c.j	2
		450.4.c.k	2
450.4.e	\(\chi_{450}(151, \cdot)\)	n/a	114	2
450.4.f	\(\chi_{450}(107, \cdot)\)	450.4.f.a	4	2
		450.4.f.b	4
		450.4.f.c	4
		450.4.f.d	8
		450.4.f.e	8
		450.4.f.f	8
450.4.h	\(\chi_{450}(91, \cdot)\)	n/a	148	4
450.4.j	\(\chi_{450}(49, \cdot)\)	n/a	108	2
450.4.l	\(\chi_{450}(19, \cdot)\)	n/a	152	4
450.4.p	\(\chi_{450}(257, \cdot)\)	n/a	216	4
450.4.q	\(\chi_{450}(31, \cdot)\)	n/a	720	8
450.4.s	\(\chi_{450}(17, \cdot)\)	n/a	240	8
450.4.v	\(\chi_{450}(79, \cdot)\)	n/a	720	8
450.4.w	\(\chi_{450}(23, \cdot)\)	n/a	1440	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces

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