Space of modular forms of level 225 and weight 8

• Label: 225.8
• Level: 225
• Weight: 8
• Dimension: 9102
• Nonzero newspaces: 12
• Sturm bound: 28800
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 8 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(28800\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_1(225))\).

	Total	New	Old
Modular forms	12824	9287	3537
Cusp forms	12376	9102	3274
Eisenstein series	448	185	263

Trace form

9102 * q - 49 * q^2 - 347 * q^4 - 51 * q^5 - 1273 * q^6 + 3838 * q^7 + 612 * q^8 + 9598 * q^9 + 40 * q^10 - 36934 * q^11 - 18596 * q^12 + 31912 * q^13 + 80538 * q^14 + 25156 * q^15 - 52855 * q^16 - 72602 * q^17 - 160668 * q^18 - 155106 * q^19 - 295350 * q^20 + 163392 * q^21 + 921033 * q^22 + 36874 * q^23 - 654883 * q^24 - 80253 * q^25 - 748824 * q^26 + 527832 * q^27 + 1024098 * q^28 + 1560308 * q^29 + 869928 * q^30 - 273542 * q^31 - 1814503 * q^32 + 156802 * q^33 - 1488985 * q^34 - 2906432 * q^35 - 1084085 * q^36 - 1635459 * q^37 + 7595483 * q^38 + 6044148 * q^39 + 3490268 * q^40 - 4017742 * q^41 - 6204286 * q^42 - 58438 * q^43 - 10654866 * q^44 - 3480492 * q^45 - 1268510 * q^46 + 6118558 * q^47 + 11158523 * q^48 + 7604516 * q^49 + 14868346 * q^50 + 5958568 * q^51 - 19675990 * q^52 - 17369455 * q^53 - 17726783 * q^54 - 3816222 * q^55 - 22590708 * q^56 - 2129010 * q^57 + 13699132 * q^58 + 58805896 * q^59 + 15350900 * q^60 + 14011988 * q^61 - 7613816 * q^62 - 19998816 * q^63 - 25814486 * q^64 - 8768497 * q^65 - 22819694 * q^66 - 17878166 * q^67 + 16580017 * q^68 + 6344248 * q^69 + 15203190 * q^70 + 40228954 * q^71 + 26901219 * q^72 + 14609140 * q^73 - 40562948 * q^74 - 89237632 * q^75 + 1093161 * q^76 - 55432590 * q^77 - 13095714 * q^78 - 12179242 * q^79 + 159664010 * q^80 + 47140846 * q^81 + 9032364 * q^82 + 129030188 * q^83 + 157730114 * q^84 + 75563191 * q^85 - 59944849 * q^86 - 108501320 * q^87 - 16373859 * q^88 - 155759187 * q^89 - 168867896 * q^90 + 62555874 * q^91 + 5224976 * q^92 + 38192656 * q^93 - 153038638 * q^94 - 24364390 * q^95 + 117666976 * q^96 - 113737438 * q^97 + 151207274 * q^98 + 52811244 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.8.a	\(\chi_{225}(1, \cdot)\)	225.8.a.a	1	1
		225.8.a.b	1
		225.8.a.c	1
		225.8.a.d	1
		225.8.a.e	1
		225.8.a.f	1
		225.8.a.g	1
		225.8.a.h	1
		225.8.a.i	1
		225.8.a.j	1
		225.8.a.k	2
		225.8.a.l	2
		225.8.a.m	2
		225.8.a.n	2
		225.8.a.o	2
		225.8.a.p	2
		225.8.a.q	2
		225.8.a.r	2
		225.8.a.s	2
		225.8.a.t	2
		225.8.a.u	2
		225.8.a.v	2
		225.8.a.w	2
		225.8.a.x	3
		225.8.a.y	3
		225.8.a.z	4
		225.8.a.ba	4
		225.8.a.bb	4
225.8.b	\(\chi_{225}(199, \cdot)\)	225.8.b.a	2	1
		225.8.b.b	2
		225.8.b.c	2
		225.8.b.d	2
		225.8.b.e	2
		225.8.b.f	2
		225.8.b.g	2
		225.8.b.h	2
		225.8.b.i	2
		225.8.b.j	4
		225.8.b.k	4
		225.8.b.l	4
		225.8.b.m	4
		225.8.b.n	4
		225.8.b.o	4
		225.8.b.p	4
		225.8.b.q	6
225.8.e	\(\chi_{225}(76, \cdot)\)	n/a	260	2
225.8.f	\(\chi_{225}(107, \cdot)\)	225.8.f.a	4	2
		225.8.f.b	16
		225.8.f.c	24
		225.8.f.d	40
225.8.h	\(\chi_{225}(46, \cdot)\)	n/a	348	4
225.8.k	\(\chi_{225}(49, \cdot)\)	n/a	248	2
225.8.m	\(\chi_{225}(19, \cdot)\)	n/a	344	4
225.8.p	\(\chi_{225}(32, \cdot)\)	n/a	496	4
225.8.q	\(\chi_{225}(16, \cdot)\)	n/a	1664	8
225.8.s	\(\chi_{225}(8, \cdot)\)	n/a	560	8
225.8.u	\(\chi_{225}(4, \cdot)\)	n/a	1664	8
225.8.w	\(\chi_{225}(2, \cdot)\)	n/a	3328	16

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

Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

\( S_{8}^{\mathrm{old}}(\Gamma_1(225)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)