Space of modular forms of level 450 and weight 7

• Label: 450.7
• Level: 450
• Weight: 7
• Dimension: 7880
• Nonzero newspaces: 12
• Sturm bound: 75600
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 7 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(75600\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(\Gamma_1(450))\).

	Total	New	Old
Modular forms	32848	7880	24968
Cusp forms	31952	7880	24072
Eisenstein series	896	0	896

Trace form

7880 * q - 16 * q^2 - 42 * q^3 + 128 * q^4 - 180 * q^5 - 144 * q^6 + 664 * q^7 + 512 * q^8 + 4750 * q^9 + 3096 * q^10 - 9782 * q^11 - 7808 * q^12 - 11540 * q^13 - 4752 * q^14 + 14784 * q^15 + 8192 * q^16 + 70620 * q^17 + 6752 * q^18 - 14372 * q^19 - 30464 * q^20 - 68436 * q^21 - 88464 * q^22 + 149864 * q^23 - 6144 * q^24 + 48942 * q^25 - 34048 * q^26 - 43008 * q^27 + 67072 * q^28 + 146692 * q^29 + 216928 * q^31 - 24576 * q^32 + 706126 * q^33 - 39384 * q^34 - 172856 * q^35 - 277184 * q^36 - 294932 * q^37 + 27040 * q^38 + 740764 * q^39 - 29952 * q^40 + 1258862 * q^41 + 964672 * q^42 + 9094 * q^43 - 471680 * q^45 + 486624 * q^46 - 2210860 * q^47 - 468992 * q^48 + 1801260 * q^49 - 219832 * q^50 + 446226 * q^51 - 115328 * q^52 + 2223296 * q^53 + 2564400 * q^54 - 1370040 * q^55 + 402944 * q^56 - 809194 * q^57 - 439344 * q^58 + 541178 * q^59 + 974848 * q^60 - 303932 * q^61 - 3925504 * q^62 - 3748728 * q^63 - 458752 * q^64 - 1758998 * q^65 + 960672 * q^66 + 3707326 * q^67 + 4577728 * q^68 + 8255272 * q^69 + 6874464 * q^70 - 4650400 * q^71 - 374784 * q^72 - 3076880 * q^73 - 2197152 * q^74 - 5883296 * q^75 - 638528 * q^76 - 15475432 * q^77 - 7119168 * q^78 - 4944308 * q^79 + 184320 * q^80 + 1687750 * q^81 - 2891952 * q^82 + 7155764 * q^83 + 3192576 * q^84 + 8758140 * q^85 - 785040 * q^86 + 17051900 * q^87 - 26112 * q^88 + 25795850 * q^89 + 7083776 * q^90 + 7317056 * q^91 - 5316352 * q^92 - 22650032 * q^93 - 207888 * q^94 - 9516712 * q^95 - 966656 * q^96 - 8905598 * q^97 - 15855248 * q^98 - 8167916 * q^99

Decomposition of \(S_{7}^{\mathrm{new}}(\Gamma_1(450))\)

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
450.7.b	\(\chi_{450}(449, \cdot)\)	450.7.b.a	4	1
		450.7.b.b	8
		450.7.b.c	8
		450.7.b.d	8
		450.7.b.e	8
450.7.d	\(\chi_{450}(251, \cdot)\)	450.7.d.a	2	1
		450.7.d.b	4
		450.7.d.c	4
		450.7.d.d	4
		450.7.d.e	4
		450.7.d.f	4
		450.7.d.g	4
		450.7.d.h	6
		450.7.d.i	6
450.7.g	\(\chi_{450}(307, \cdot)\)	450.7.g.a	2	2
		450.7.g.b	2
		450.7.g.c	2
		450.7.g.d	4
		450.7.g.e	4
		450.7.g.f	4
		450.7.g.g	4
		450.7.g.h	4
		450.7.g.i	4
		450.7.g.j	4
		450.7.g.k	4
		450.7.g.l	4
		450.7.g.m	4
		450.7.g.n	4
		450.7.g.o	4
		450.7.g.p	6
		450.7.g.q	6
		450.7.g.r	8
		450.7.g.s	8
		450.7.g.t	8
450.7.i	\(\chi_{450}(101, \cdot)\)	n/a	228	2
450.7.k	\(\chi_{450}(149, \cdot)\)	n/a	216	2
450.7.m	\(\chi_{450}(89, \cdot)\)	n/a	240	4
450.7.n	\(\chi_{450}(71, \cdot)\)	n/a	240	4
450.7.o	\(\chi_{450}(7, \cdot)\)	n/a	432	4
450.7.r	\(\chi_{450}(37, \cdot)\)	n/a	600	8
450.7.t	\(\chi_{450}(11, \cdot)\)	n/a	1440	8
450.7.u	\(\chi_{450}(29, \cdot)\)	n/a	1440	8
450.7.x	\(\chi_{450}(13, \cdot)\)	n/a	2880	16

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

Decomposition of \(S_{7}^{\mathrm{old}}(\Gamma_1(450))\) into lower level spaces

\( S_{7}^{\mathrm{old}}(\Gamma_1(450)) \cong \) \(S_{7}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 9}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 2}\)