Space of modular forms of level 450 and weight 2

• Label: 450.2
• Level: 450
• Weight: 2
• Dimension: 1313
• Nonzero newspaces: 12
• Newform subspaces: 63
• Sturm bound: 21600
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 63 \)
Sturm bound:			\(21600\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(450))\).

	Total	New	Old
Modular forms	5848	1313	4535
Cusp forms	4953	1313	3640
Eisenstein series	895	0	895

Trace form

1313 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 5 * q^5 + 3 * q^6 - 18 * q^7 + 19 * q^9 + 11 * q^10 + 43 * q^11 + 16 * q^12 + 34 * q^13 + 46 * q^14 + 24 * q^15 - 3 * q^16 + 74 * q^17 + 26 * q^18 + 62 * q^19 + 16 * q^20 + 54 * q^21 + 51 * q^22 + 94 * q^23 - 3 * q^24 + 67 * q^25 - 4 * q^26 + 48 * q^27 + 8 * q^28 + 70 * q^29 + 44 * q^31 + 2 * q^32 + 7 * q^33 + 8 * q^34 + 4 * q^35 - 29 * q^36 + 81 * q^37 - 87 * q^38 - 128 * q^39 + 3 * q^40 - 105 * q^41 - 128 * q^42 + 17 * q^43 - 46 * q^44 - 80 * q^45 + 36 * q^46 - 98 * q^47 - 29 * q^48 + 30 * q^49 - 57 * q^50 - 87 * q^51 - 14 * q^52 - 87 * q^53 - 87 * q^54 + 60 * q^55 - 34 * q^56 - 61 * q^57 - 50 * q^58 - 31 * q^59 - 32 * q^60 - 104 * q^61 - 156 * q^62 - 84 * q^63 - 253 * q^65 - 24 * q^66 - 189 * q^67 - 117 * q^68 - 152 * q^69 - 216 * q^70 - 24 * q^71 + 3 * q^72 - 190 * q^73 - 212 * q^74 - 296 * q^75 - 31 * q^76 - 474 * q^77 - 126 * q^78 - 188 * q^79 - 5 * q^80 - 137 * q^81 - 178 * q^82 - 436 * q^83 - 78 * q^84 - 185 * q^85 - 43 * q^86 - 214 * q^87 + 11 * q^88 - 239 * q^89 - 64 * q^90 + 24 * q^91 - 6 * q^92 - 104 * q^93 + 38 * q^94 + 28 * q^95 + 16 * q^96 + 123 * q^97 + 72 * q^98 - 14 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)

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
450.2.a	\(\chi_{450}(1, \cdot)\)	450.2.a.a	1	1
		450.2.a.b	1
		450.2.a.c	1
		450.2.a.d	1
		450.2.a.e	1
		450.2.a.f	1
		450.2.a.g	1
450.2.c	\(\chi_{450}(199, \cdot)\)	450.2.c.a	2	1
		450.2.c.b	2
		450.2.c.c	2
		450.2.c.d	2
450.2.e	\(\chi_{450}(151, \cdot)\)	450.2.e.a	2	2
		450.2.e.b	2
		450.2.e.c	2
		450.2.e.d	2
		450.2.e.e	2
		450.2.e.f	2
		450.2.e.g	2
		450.2.e.h	2
		450.2.e.i	2
		450.2.e.j	4
		450.2.e.k	4
		450.2.e.l	4
		450.2.e.m	4
		450.2.e.n	4
450.2.f	\(\chi_{450}(107, \cdot)\)	450.2.f.a	4	2
		450.2.f.b	4
		450.2.f.c	4
450.2.h	\(\chi_{450}(91, \cdot)\)	450.2.h.a	4	4
		450.2.h.b	4
		450.2.h.c	4
		450.2.h.d	8
		450.2.h.e	8
		450.2.h.f	12
		450.2.h.g	12
450.2.j	\(\chi_{450}(49, \cdot)\)	450.2.j.a	4	2
		450.2.j.b	4
		450.2.j.c	4
		450.2.j.d	4
		450.2.j.e	4
		450.2.j.f	8
		450.2.j.g	8
450.2.l	\(\chi_{450}(19, \cdot)\)	450.2.l.a	8	4
		450.2.l.b	8
		450.2.l.c	16
		450.2.l.d	16
450.2.p	\(\chi_{450}(257, \cdot)\)	450.2.p.a	8	4
		450.2.p.b	8
		450.2.p.c	8
		450.2.p.d	8
		450.2.p.e	8
		450.2.p.f	8
		450.2.p.g	8
		450.2.p.h	16
450.2.q	\(\chi_{450}(31, \cdot)\)	450.2.q.a	8	8
		450.2.q.b	112
		450.2.q.c	120
450.2.s	\(\chi_{450}(17, \cdot)\)	450.2.s.a	16	8
		450.2.s.b	16
		450.2.s.c	16
		450.2.s.d	32
450.2.v	\(\chi_{450}(79, \cdot)\)	450.2.v.a	240	8
450.2.w	\(\chi_{450}(23, \cdot)\)	450.2.w.a	480	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces

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