Space of modular forms of level 225 and weight 4

• Label: 225.4
• Level: 225
• Weight: 4
• Dimension: 3848
• Nonzero newspaces: 12
• Newform subspaces: 54
• Sturm bound: 14400
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 54 \)
Sturm bound:			\(14400\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(225))\).

	Total	New	Old
Modular forms	5624	4033	1591
Cusp forms	5176	3848	1328
Eisenstein series	448	185	263

Trace form

3848 * q - 17 * q^2 - 27 * q^3 - 51 * q^4 - 21 * q^5 - 31 * q^6 - 21 * q^7 - 84 * q^8 - 107 * q^9 - 190 * q^10 - 104 * q^11 + 76 * q^12 + 379 * q^13 + 846 * q^14 + 136 * q^15 + 673 * q^16 + 188 * q^17 + 192 * q^18 - 668 * q^19 - 870 * q^20 - 1155 * q^21 - 2085 * q^22 - 1219 * q^23 - 691 * q^24 + 957 * q^25 + 1716 * q^26 + 648 * q^27 + 4066 * q^28 + 2977 * q^29 + 1128 * q^30 + 1811 * q^31 + 2833 * q^32 + 2398 * q^33 - 1665 * q^34 - 352 * q^35 + 1591 * q^36 - 3419 * q^37 - 6191 * q^38 - 2337 * q^39 - 4092 * q^40 - 4994 * q^41 - 7318 * q^42 + 110 * q^43 - 5226 * q^44 - 2292 * q^45 + 1066 * q^46 - 5401 * q^47 - 9373 * q^48 - 771 * q^49 + 1556 * q^50 - 743 * q^51 + 5610 * q^52 + 5587 * q^53 + 8623 * q^54 + 1758 * q^55 + 14556 * q^56 + 9219 * q^57 + 6636 * q^58 + 11504 * q^59 + 13940 * q^60 + 5945 * q^61 + 13472 * q^62 + 8571 * q^63 + 4666 * q^64 + 3373 * q^65 + 826 * q^66 - 2766 * q^67 - 8827 * q^68 - 5309 * q^69 - 14730 * q^70 - 4990 * q^71 - 10125 * q^72 - 16790 * q^73 - 17512 * q^74 - 6592 * q^75 - 14203 * q^76 - 9057 * q^77 - 1302 * q^78 - 4239 * q^79 - 15350 * q^80 - 2783 * q^81 - 3380 * q^82 - 12275 * q^83 - 17254 * q^84 - 1189 * q^85 - 20915 * q^86 - 13601 * q^87 + 4749 * q^88 - 11235 * q^89 - 1016 * q^90 - 660 * q^91 - 4184 * q^92 - 13589 * q^93 + 15078 * q^94 + 4330 * q^95 - 8912 * q^96 + 18464 * q^97 + 14200 * q^98 - 663 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.4.a	\(\chi_{225}(1, \cdot)\)	225.4.a.a	1	1
		225.4.a.b	1
		225.4.a.c	1
		225.4.a.d	1
		225.4.a.e	1
		225.4.a.f	1
		225.4.a.g	1
		225.4.a.h	1
		225.4.a.i	2
		225.4.a.j	2
		225.4.a.k	2
		225.4.a.l	2
		225.4.a.m	2
		225.4.a.n	2
		225.4.a.o	2
225.4.b	\(\chi_{225}(199, \cdot)\)	225.4.b.a	2	1
		225.4.b.b	2
		225.4.b.c	2
		225.4.b.d	2
		225.4.b.e	2
		225.4.b.f	2
		225.4.b.g	2
		225.4.b.h	4
		225.4.b.i	4
225.4.e	\(\chi_{225}(76, \cdot)\)	225.4.e.a	4	2
		225.4.e.b	4
		225.4.e.c	6
		225.4.e.d	14
		225.4.e.e	24
		225.4.e.f	24
		225.4.e.g	32
225.4.f	\(\chi_{225}(107, \cdot)\)	225.4.f.a	4	2
		225.4.f.b	4
		225.4.f.c	12
		225.4.f.d	16
225.4.h	\(\chi_{225}(46, \cdot)\)	225.4.h.a	28	4
		225.4.h.b	28
		225.4.h.c	28
		225.4.h.d	64
225.4.k	\(\chi_{225}(49, \cdot)\)	225.4.k.a	8	2
		225.4.k.b	8
		225.4.k.c	12
		225.4.k.d	28
		225.4.k.e	48
225.4.m	\(\chi_{225}(19, \cdot)\)	225.4.m.a	24	4
		225.4.m.b	56
		225.4.m.c	64
225.4.p	\(\chi_{225}(32, \cdot)\)	225.4.p.a	48	4
		225.4.p.b	64
		225.4.p.c	96
225.4.q	\(\chi_{225}(16, \cdot)\)	225.4.q.a	704	8
225.4.s	\(\chi_{225}(8, \cdot)\)	225.4.s.a	240	8
225.4.u	\(\chi_{225}(4, \cdot)\)	225.4.u.a	704	8
225.4.w	\(\chi_{225}(2, \cdot)\)	225.4.w.a	1408	16

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(225)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)