Space of modular forms of level 225 and weight 6

• Label: 225.6
• Level: 225
• Weight: 6
• Dimension: 6474
• Nonzero newspaces: 12
• Sturm bound: 21600
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	=	\( 6 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(21600\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(225))\).

	Total	New	Old
Modular forms	9224	6659	2565
Cusp forms	8776	6474	2302
Eisenstein series	448	185	263

Trace form

6474 * q - 17 * q^2 - 36 * q^3 + 37 * q^4 + 39 * q^5 + 131 * q^6 - 418 * q^7 - 1212 * q^8 - 686 * q^9 + 2300 * q^10 + 3298 * q^11 + 2188 * q^12 - 4330 * q^13 - 13782 * q^14 - 2204 * q^15 - 6935 * q^16 + 458 * q^17 + 708 * q^18 + 21926 * q^19 + 16890 * q^20 + 4470 * q^21 + 6469 * q^22 + 12650 * q^23 + 25877 * q^24 - 8823 * q^25 - 40080 * q^26 - 30384 * q^27 - 63070 * q^28 - 24674 * q^29 - 32472 * q^30 - 31438 * q^31 + 1897 * q^32 + 62644 * q^33 + 52455 * q^34 + 11408 * q^35 - 58469 * q^36 + 136395 * q^37 - 15809 * q^38 - 48396 * q^39 + 36188 * q^40 - 60032 * q^41 + 109250 * q^42 + 10906 * q^43 + 229422 * q^44 + 63108 * q^45 - 340750 * q^46 - 151858 * q^47 + 8795 * q^48 + 34192 * q^49 - 56674 * q^50 + 28924 * q^51 + 420498 * q^52 + 34723 * q^53 - 254171 * q^54 + 105218 * q^55 - 283860 * q^56 - 212370 * q^57 - 450052 * q^58 - 26608 * q^59 + 288020 * q^60 - 306110 * q^61 - 496504 * q^62 - 237336 * q^63 - 838422 * q^64 - 521387 * q^65 + 127522 * q^66 + 229826 * q^67 + 658313 * q^68 + 366838 * q^69 + 786630 * q^70 + 282602 * q^71 + 1508883 * q^72 + 129416 * q^73 + 617324 * q^74 + 471488 * q^75 - 502695 * q^76 - 177192 * q^77 - 1148058 * q^78 + 470838 * q^79 - 842870 * q^80 - 432038 * q^81 - 1191188 * q^82 - 1066232 * q^83 - 714982 * q^84 - 659899 * q^85 + 424099 * q^86 + 47032 * q^87 - 1247619 * q^88 + 913695 * q^89 + 1828744 * q^90 + 494202 * q^91 + 4844416 * q^92 + 2009878 * q^93 + 477234 * q^94 + 33370 * q^95 - 102392 * q^96 - 26636 * q^97 - 2909162 * q^98 - 2214624 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(225))\)

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
225.6.a	\(\chi_{225}(1, \cdot)\)	225.6.a.a	1	1
		225.6.a.b	1
		225.6.a.c	1
		225.6.a.d	1
		225.6.a.e	1
		225.6.a.f	1
		225.6.a.g	1
		225.6.a.h	1
		225.6.a.i	2
		225.6.a.j	2
		225.6.a.k	2
		225.6.a.l	2
		225.6.a.m	2
		225.6.a.n	2
		225.6.a.o	2
		225.6.a.p	2
		225.6.a.q	2
		225.6.a.r	2
		225.6.a.s	2
		225.6.a.t	2
		225.6.a.u	2
		225.6.a.v	4
225.6.b	\(\chi_{225}(199, \cdot)\)	225.6.b.a	2	1
		225.6.b.b	2
		225.6.b.c	2
		225.6.b.d	2
		225.6.b.e	2
		225.6.b.f	2
		225.6.b.g	4
		225.6.b.h	4
		225.6.b.i	4
		225.6.b.j	4
		225.6.b.k	4
		225.6.b.l	4
225.6.e	\(\chi_{225}(76, \cdot)\)	n/a	184	2
225.6.f	\(\chi_{225}(107, \cdot)\)	225.6.f.a	16	2
		225.6.f.b	20
		225.6.f.c	24
225.6.h	\(\chi_{225}(46, \cdot)\)	n/a	244	4
225.6.k	\(\chi_{225}(49, \cdot)\)	n/a	176	2
225.6.m	\(\chi_{225}(19, \cdot)\)	n/a	248	4
225.6.p	\(\chi_{225}(32, \cdot)\)	n/a	352	4
225.6.q	\(\chi_{225}(16, \cdot)\)	n/a	1184	8
225.6.s	\(\chi_{225}(8, \cdot)\)	n/a	400	8
225.6.u	\(\chi_{225}(4, \cdot)\)	n/a	1184	8
225.6.w	\(\chi_{225}(2, \cdot)\)	n/a	2368	16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(225))\) into lower level spaces

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