Space of modular forms of level 825 and weight 3

• Label: 825.3
• Level: 825
• Weight: 3
• Dimension: 32258
• Nonzero newspaces: 42
• Sturm bound: 144000
• Trace bound: 10

Defining parameters

Level:	\( N \)	=	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 42 \)
Sturm bound:			\(144000\)
Trace bound:			\(10\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(825))\).

	Total	New	Old
Modular forms	49120	32994	16126
Cusp forms	46880	32258	14622
Eisenstein series	2240	736	1504

Trace form

32258 * q - 16 * q^2 - 61 * q^3 - 122 * q^4 - 8 * q^5 - 121 * q^6 - 152 * q^7 + 8 * q^8 + 9 * q^9 - 72 * q^10 + 42 * q^11 + 42 * q^12 - 60 * q^13 + 10 * q^14 - 92 * q^15 - 154 * q^16 + 110 * q^17 - 123 * q^18 + 58 * q^19 + 488 * q^20 + 46 * q^21 + 190 * q^22 + 344 * q^23 + 493 * q^24 - 128 * q^25 + 442 * q^26 + 206 * q^27 - 476 * q^28 - 240 * q^29 - 628 * q^30 - 690 * q^31 - 1424 * q^32 - 522 * q^33 - 1612 * q^34 - 520 * q^35 - 393 * q^36 + 38 * q^37 + 686 * q^38 + 234 * q^39 + 2336 * q^40 + 296 * q^41 + 1768 * q^42 + 2496 * q^43 + 3570 * q^44 + 652 * q^45 + 3040 * q^46 + 2462 * q^47 + 2506 * q^48 + 2348 * q^49 + 608 * q^50 + 965 * q^51 - 208 * q^52 + 114 * q^53 - 366 * q^54 - 924 * q^55 - 2280 * q^56 - 1471 * q^57 - 5308 * q^58 - 2650 * q^59 - 4308 * q^60 - 2696 * q^61 - 4768 * q^62 - 2914 * q^63 - 8154 * q^64 - 1864 * q^65 - 3032 * q^66 - 3738 * q^67 - 4816 * q^68 - 3141 * q^69 - 1640 * q^70 - 1608 * q^71 - 2144 * q^72 - 1308 * q^73 - 730 * q^74 + 188 * q^75 + 1116 * q^76 - 394 * q^77 + 520 * q^78 + 1088 * q^79 + 328 * q^80 + 413 * q^81 + 4482 * q^82 + 2306 * q^83 + 5834 * q^84 + 4224 * q^85 + 2744 * q^86 + 3944 * q^87 + 4154 * q^88 + 3380 * q^89 + 4528 * q^90 + 5460 * q^91 + 10206 * q^92 + 5875 * q^93 + 10908 * q^94 + 3808 * q^95 + 7620 * q^96 + 5592 * q^97 + 9488 * q^98 + 3815 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(825))\)

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
825.3.b	\(\chi_{825}(76, \cdot)\)	825.3.b.a	4	1
		825.3.b.b	16
		825.3.b.c	16
		825.3.b.d	16
		825.3.b.e	24
825.3.e	\(\chi_{825}(551, \cdot)\)	n/a	126	1
825.3.g	\(\chi_{825}(749, \cdot)\)	n/a	120	1
825.3.h	\(\chi_{825}(274, \cdot)\)	825.3.h.a	8	1
		825.3.h.b	32
		825.3.h.c	32
825.3.i	\(\chi_{825}(232, \cdot)\)	n/a	120	2
825.3.l	\(\chi_{825}(32, \cdot)\)	n/a	280	2
825.3.t	\(\chi_{825}(71, \cdot)\)	n/a	944	4
825.3.u	\(\chi_{825}(316, \cdot)\)	n/a	480	4
825.3.w	\(\chi_{825}(89, \cdot)\)	n/a	800	4
825.3.y	\(\chi_{825}(349, \cdot)\)	n/a	288	4
825.3.z	\(\chi_{825}(19, \cdot)\)	n/a	480	4
825.3.ba	\(\chi_{825}(409, \cdot)\)	n/a	480	4
825.3.bb	\(\chi_{825}(79, \cdot)\)	n/a	480	4
825.3.bc	\(\chi_{825}(14, \cdot)\)	n/a	944	4
825.3.be	\(\chi_{825}(179, \cdot)\)	n/a	944	4
825.3.bg	\(\chi_{825}(344, \cdot)\)	n/a	944	4
825.3.bh	\(\chi_{825}(224, \cdot)\)	n/a	560	4
825.3.bk	\(\chi_{825}(109, \cdot)\)	n/a	480	4
825.3.bm	\(\chi_{825}(241, \cdot)\)	n/a	480	4
825.3.bn	\(\chi_{825}(146, \cdot)\)	n/a	944	4
825.3.bp	\(\chi_{825}(26, \cdot)\)	n/a	584	4
825.3.bq	\(\chi_{825}(86, \cdot)\)	n/a	944	4
825.3.bt	\(\chi_{825}(191, \cdot)\)	n/a	944	4
825.3.bw	\(\chi_{825}(46, \cdot)\)	n/a	480	4
825.3.bz	\(\chi_{825}(211, \cdot)\)	n/a	480	4
825.3.ca	\(\chi_{825}(151, \cdot)\)	n/a	304	4
825.3.cc	\(\chi_{825}(61, \cdot)\)	n/a	480	4
825.3.cd	\(\chi_{825}(56, \cdot)\)	n/a	800	4
825.3.cf	\(\chi_{825}(139, \cdot)\)	n/a	480	4
825.3.ch	\(\chi_{825}(104, \cdot)\)	n/a	944	4
825.3.cj	\(\chi_{825}(167, \cdot)\)	n/a	1888	8
825.3.ck	\(\chi_{825}(202, \cdot)\)	n/a	960	8
825.3.cn	\(\chi_{825}(148, \cdot)\)	n/a	960	8
825.3.co	\(\chi_{825}(98, \cdot)\)	n/a	1888	8
825.3.cp	\(\chi_{825}(68, \cdot)\)	n/a	1120	8
825.3.cq	\(\chi_{825}(17, \cdot)\)	n/a	1888	8
825.3.cr	\(\chi_{825}(2, \cdot)\)	n/a	1888	8
825.3.da	\(\chi_{825}(82, \cdot)\)	n/a	576	8
825.3.db	\(\chi_{825}(37, \cdot)\)	n/a	960	8
825.3.dc	\(\chi_{825}(58, \cdot)\)	n/a	960	8
825.3.dd	\(\chi_{825}(67, \cdot)\)	n/a	800	8
825.3.de	\(\chi_{825}(248, \cdot)\)	n/a	1888	8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(825))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(825)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(275))\)\(^{\oplus 2}\)