Space of modular forms of level 225 and weight 3

• Label: 225.3
• Level: 225
• Weight: 3
• Dimension: 2534
• Nonzero newspaces: 12
• Newform subspaces: 32
• Sturm bound: 10800
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 32 \)
Sturm bound:			\(10800\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(225))\).

	Total	New	Old
Modular forms	3824	2718	1106
Cusp forms	3376	2534	842
Eisenstein series	448	184	264

Trace form

2534 * q - 25 * q^2 - 27 * q^3 - 23 * q^4 - 26 * q^5 - 31 * q^6 - 24 * q^7 + 42 * q^8 + 7 * q^9 - 10 * q^10 + 55 * q^11 + 46 * q^12 + 14 * q^13 - 44 * q^15 - 91 * q^16 - 96 * q^17 - 120 * q^18 - 96 * q^19 + 50 * q^20 - 30 * q^21 + 253 * q^22 + 190 * q^23 + 83 * q^24 + 72 * q^25 + 276 * q^26 + 126 * q^27 - 102 * q^28 - 28 * q^29 - 72 * q^30 - 338 * q^31 - 947 * q^32 - 383 * q^33 - 779 * q^34 - 532 * q^35 - 1265 * q^36 - 242 * q^37 - 957 * q^38 - 768 * q^39 + 168 * q^40 - 379 * q^41 - 496 * q^42 + 311 * q^43 + 320 * q^44 + 108 * q^45 + 402 * q^46 + 862 * q^47 + 1145 * q^48 + 833 * q^49 + 796 * q^50 + 961 * q^51 + 408 * q^52 + 1118 * q^53 + 1375 * q^54 - 322 * q^55 + 888 * q^56 + 759 * q^57 - 698 * q^58 - 409 * q^59 - 700 * q^60 - 538 * q^61 - 2464 * q^62 - 1032 * q^63 - 2986 * q^64 - 1672 * q^65 - 1034 * q^66 - 1407 * q^67 - 2993 * q^68 - 1244 * q^69 - 1410 * q^70 - 1454 * q^71 - 2289 * q^72 - 1072 * q^73 - 2454 * q^74 - 832 * q^75 + 513 * q^76 - 1232 * q^77 - 2052 * q^78 + 1020 * q^79 + 1210 * q^80 - 1145 * q^81 + 2232 * q^82 + 936 * q^83 + 50 * q^84 + 2216 * q^85 + 559 * q^86 + 682 * q^87 + 4545 * q^88 + 2970 * q^89 + 2104 * q^90 + 1162 * q^91 + 4782 * q^92 + 1708 * q^93 + 1342 * q^94 + 1310 * q^95 + 2872 * q^96 + 149 * q^97 + 3366 * q^98 + 2544 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.3.c	\(\chi_{225}(26, \cdot)\)	225.3.c.a	2	1
		225.3.c.b	2
		225.3.c.c	4
		225.3.c.d	4
225.3.d	\(\chi_{225}(224, \cdot)\)	225.3.d.a	4	1
		225.3.d.b	8
225.3.g	\(\chi_{225}(82, \cdot)\)	225.3.g.a	4	2
		225.3.g.b	4
		225.3.g.c	4
		225.3.g.d	4
		225.3.g.e	4
		225.3.g.f	4
		225.3.g.g	4
225.3.i	\(\chi_{225}(74, \cdot)\)	225.3.i.a	4	2
		225.3.i.b	32
		225.3.i.c	32
225.3.j	\(\chi_{225}(101, \cdot)\)	225.3.j.a	2	2
		225.3.j.b	16
		225.3.j.c	16
		225.3.j.d	16
		225.3.j.e	20
225.3.l	\(\chi_{225}(44, \cdot)\)	225.3.l.a	80	4
225.3.n	\(\chi_{225}(71, \cdot)\)	225.3.n.a	80	4
225.3.o	\(\chi_{225}(7, \cdot)\)	225.3.o.a	32	4
		225.3.o.b	40
		225.3.o.c	64
225.3.r	\(\chi_{225}(28, \cdot)\)	225.3.r.a	32	8
		225.3.r.b	80
		225.3.r.c	80
225.3.t	\(\chi_{225}(11, \cdot)\)	225.3.t.a	464	8
225.3.v	\(\chi_{225}(14, \cdot)\)	225.3.v.a	464	8
225.3.x	\(\chi_{225}(13, \cdot)\)	225.3.x.a	928	16

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

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