Space of modular forms of level 225 and weight 2

• Label: 225.2
• Level: 225
• Weight: 2
• Dimension: 1221
• Nonzero newspaces: 12
• Newform subspaces: 34
• Sturm bound: 7200
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 34 \)
Sturm bound:			\(7200\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(225))\).

	Total	New	Old
Modular forms	2024	1406	618
Cusp forms	1577	1221	356
Eisenstein series	447	185	262

Trace form

1221 * q - 16 * q^2 - 24 * q^3 - 8 * q^4 - 21 * q^5 - 40 * q^6 - 6 * q^7 - 24 * q^8 - 32 * q^9 - 75 * q^10 - 46 * q^11 - 56 * q^12 - 26 * q^13 - 54 * q^14 - 44 * q^15 - 56 * q^16 - 44 * q^17 - 72 * q^18 - 70 * q^19 - 90 * q^20 - 72 * q^21 - 86 * q^22 - 74 * q^23 - 112 * q^24 - 63 * q^25 - 132 * q^26 - 72 * q^27 - 166 * q^28 - 94 * q^29 - 72 * q^30 - 58 * q^31 - 91 * q^32 - 56 * q^33 - 83 * q^34 - 32 * q^35 - 8 * q^36 - 99 * q^37 - 28 * q^38 + 24 * q^39 - 57 * q^40 + 26 * q^41 + 32 * q^42 - 6 * q^43 + 36 * q^44 - 12 * q^45 - 142 * q^46 + 10 * q^47 + 80 * q^48 - 91 * q^49 - 89 * q^50 - 80 * q^51 - 144 * q^52 - 79 * q^53 - 32 * q^54 - 142 * q^55 - 66 * q^56 - 72 * q^57 - 152 * q^58 - 128 * q^59 + 20 * q^60 - 66 * q^61 - 68 * q^62 - 60 * q^63 + 22 * q^64 + 53 * q^65 - 128 * q^66 + 42 * q^67 + 190 * q^68 - 20 * q^69 + 150 * q^70 - 62 * q^71 + 192 * q^72 + 34 * q^73 + 304 * q^74 + 128 * q^75 + 52 * q^76 + 234 * q^77 + 240 * q^78 + 114 * q^79 + 425 * q^80 + 88 * q^81 + 170 * q^82 + 284 * q^83 + 344 * q^84 + 21 * q^85 + 266 * q^86 + 148 * q^87 + 90 * q^88 + 177 * q^89 + 184 * q^90 - 86 * q^91 + 182 * q^92 + 100 * q^93 - 182 * q^94 - 70 * q^95 + 136 * q^96 - 174 * q^97 + 56 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.2.a	\(\chi_{225}(1, \cdot)\)	225.2.a.a	1	1
		225.2.a.b	1
		225.2.a.c	1
		225.2.a.d	1
		225.2.a.e	1
		225.2.a.f	2
225.2.b	\(\chi_{225}(199, \cdot)\)	225.2.b.a	2	1
		225.2.b.b	2
		225.2.b.c	2
225.2.e	\(\chi_{225}(76, \cdot)\)	225.2.e.a	2	2
		225.2.e.b	6
		225.2.e.c	8
		225.2.e.d	8
		225.2.e.e	8
225.2.f	\(\chi_{225}(107, \cdot)\)	225.2.f.a	4	2
		225.2.f.b	8
225.2.h	\(\chi_{225}(46, \cdot)\)	225.2.h.a	4	4
		225.2.h.b	4
		225.2.h.c	8
		225.2.h.d	12
		225.2.h.e	16
225.2.k	\(\chi_{225}(49, \cdot)\)	225.2.k.a	4	2
		225.2.k.b	12
		225.2.k.c	16
225.2.m	\(\chi_{225}(19, \cdot)\)	225.2.m.a	8	4
		225.2.m.b	16
		225.2.m.c	24
225.2.p	\(\chi_{225}(32, \cdot)\)	225.2.p.a	16	4
		225.2.p.b	16
		225.2.p.c	32
225.2.q	\(\chi_{225}(16, \cdot)\)	225.2.q.a	224	8
225.2.s	\(\chi_{225}(8, \cdot)\)	225.2.s.a	80	8
225.2.u	\(\chi_{225}(4, \cdot)\)	225.2.u.a	224	8
225.2.w	\(\chi_{225}(2, \cdot)\)	225.2.w.a	448	16

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

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