Space of modular forms of level 225 and weight 5

• Label: 225.5
• Level: 225
• Weight: 5
• Dimension: 5162
• Nonzero newspaces: 12
• Sturm bound: 18000
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(18000\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(225))\).

	Total	New	Old
Modular forms	7424	5346	2078
Cusp forms	6976	5162	1814
Eisenstein series	448	184	264

Trace form

5162 * q - 21 * q^2 - 27 * q^3 - 11 * q^4 - 66 * q^5 - 139 * q^6 + 38 * q^7 + 354 * q^8 + 355 * q^9 - 320 * q^10 - 771 * q^11 - 974 * q^12 - 1608 * q^13 - 1152 * q^14 + 316 * q^15 + 4673 * q^16 + 4632 * q^17 + 4068 * q^18 + 1584 * q^19 - 990 * q^20 + 2472 * q^21 - 6647 * q^22 - 9420 * q^23 - 9961 * q^24 - 3258 * q^25 - 13548 * q^26 - 4770 * q^27 + 5634 * q^28 + 2238 * q^29 + 2328 * q^30 + 7480 * q^31 + 20337 * q^32 + 175 * q^33 + 25887 * q^34 + 3228 * q^35 + 14023 * q^36 + 226 * q^37 + 20055 * q^38 + 16110 * q^39 - 18052 * q^40 - 5337 * q^41 + 20348 * q^42 - 17451 * q^43 - 22080 * q^44 - 1092 * q^45 + 20034 * q^46 + 1440 * q^47 - 43435 * q^48 + 8491 * q^49 - 17934 * q^50 - 40823 * q^51 - 12780 * q^52 - 46698 * q^53 - 51269 * q^54 - 8962 * q^55 - 29016 * q^56 + 18543 * q^57 - 946 * q^58 + 3789 * q^59 - 50620 * q^60 + 29832 * q^61 + 35400 * q^62 + 37938 * q^63 + 90958 * q^64 + 82818 * q^65 + 64354 * q^66 + 88859 * q^67 + 191499 * q^68 + 63958 * q^69 + 110550 * q^70 + 5202 * q^71 - 36069 * q^72 - 29220 * q^73 - 167622 * q^74 - 77152 * q^75 - 66499 * q^76 - 77730 * q^77 - 9444 * q^78 - 87450 * q^79 - 182910 * q^80 + 118699 * q^81 - 83020 * q^82 + 20526 * q^83 + 121250 * q^84 - 54644 * q^85 + 133683 * q^86 + 76480 * q^87 + 65301 * q^88 + 47220 * q^89 + 96664 * q^90 - 906 * q^91 - 96798 * q^92 - 112118 * q^93 - 114282 * q^94 - 145050 * q^95 - 406688 * q^96 - 48585 * q^97 - 326574 * q^98 - 168822 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.5.c	\(\chi_{225}(26, \cdot)\)	225.5.c.a	2	1
		225.5.c.b	4
		225.5.c.c	6
		225.5.c.d	6
		225.5.c.e	8
225.5.d	\(\chi_{225}(224, \cdot)\)	225.5.d.a	4	1
		225.5.d.b	8
		225.5.d.c	12
225.5.g	\(\chi_{225}(82, \cdot)\)	225.5.g.a	2	2
		225.5.g.b	2
		225.5.g.c	2
		225.5.g.d	4
		225.5.g.e	4
		225.5.g.f	4
		225.5.g.g	4
		225.5.g.h	4
		225.5.g.i	4
		225.5.g.j	4
		225.5.g.k	4
		225.5.g.l	4
		225.5.g.m	8
		225.5.g.n	8
225.5.i	\(\chi_{225}(74, \cdot)\)	n/a	140	2
225.5.j	\(\chi_{225}(101, \cdot)\)	n/a	146	2
225.5.l	\(\chi_{225}(44, \cdot)\)	n/a	160	4
225.5.n	\(\chi_{225}(71, \cdot)\)	n/a	160	4
225.5.o	\(\chi_{225}(7, \cdot)\)	n/a	280	4
225.5.r	\(\chi_{225}(28, \cdot)\)	n/a	392	8
225.5.t	\(\chi_{225}(11, \cdot)\)	n/a	944	8
225.5.v	\(\chi_{225}(14, \cdot)\)	n/a	944	8
225.5.x	\(\chi_{225}(13, \cdot)\)	n/a	1888	16

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

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