Space of modular forms of level 880 and weight 3

• Label: 880.3
• Level: 880
• Weight: 3
• Dimension: 23122
• Nonzero newspaces: 28
• Sturm bound: 138240
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(138240\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(880))\).

	Total	New	Old
Modular forms	47200	23606	23594
Cusp forms	44960	23122	21838
Eisenstein series	2240	484	1756

Trace form

23122 * q - 32 * q^2 - 26 * q^3 - 56 * q^4 - 71 * q^5 - 120 * q^6 - 34 * q^7 - 8 * q^8 + 26 * q^9 + 28 * q^10 - 114 * q^11 + 144 * q^12 - 46 * q^13 + 24 * q^14 - 129 * q^15 - 248 * q^16 - 222 * q^17 - 320 * q^18 + 106 * q^19 - 212 * q^20 - 136 * q^21 - 136 * q^22 + 288 * q^23 + 168 * q^24 + 57 * q^25 + 296 * q^26 + 466 * q^27 + 456 * q^28 + 302 * q^29 + 636 * q^30 + 62 * q^31 + 568 * q^32 - 270 * q^33 + 272 * q^34 - 377 * q^35 + 88 * q^36 - 206 * q^37 + 248 * q^38 - 1262 * q^39 - 124 * q^40 - 238 * q^41 - 600 * q^42 - 592 * q^43 - 272 * q^44 - 566 * q^45 - 872 * q^46 - 258 * q^47 - 1272 * q^48 - 526 * q^49 - 732 * q^50 + 942 * q^51 - 456 * q^52 + 530 * q^53 - 472 * q^54 + 427 * q^55 - 880 * q^56 + 390 * q^57 - 728 * q^58 + 810 * q^59 - 620 * q^60 - 14 * q^61 - 600 * q^62 + 1304 * q^63 - 488 * q^64 + 296 * q^65 - 544 * q^66 + 872 * q^67 - 808 * q^68 + 552 * q^69 - 392 * q^70 + 1070 * q^71 + 1504 * q^72 + 2194 * q^73 + 1328 * q^74 + 1375 * q^75 + 2296 * q^76 + 1282 * q^77 + 3680 * q^78 + 770 * q^79 + 2120 * q^80 + 1522 * q^81 + 3608 * q^82 + 470 * q^83 + 3864 * q^84 - 647 * q^85 + 2200 * q^86 - 972 * q^87 + 104 * q^88 - 892 * q^89 + 1316 * q^90 - 2482 * q^91 - 168 * q^92 - 3098 * q^93 - 1512 * q^94 - 2445 * q^95 - 1832 * q^96 - 2222 * q^97 - 3128 * q^98 - 2322 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(880))\)

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
880.3.d	\(\chi_{880}(681, \cdot)\)	None	0	1
880.3.e	\(\chi_{880}(111, \cdot)\)	880.3.e.a	16	1
		880.3.e.b	24
880.3.h	\(\chi_{880}(199, \cdot)\)	None	0	1
880.3.i	\(\chi_{880}(769, \cdot)\)	880.3.i.a	2	1
		880.3.i.b	2
		880.3.i.c	2
		880.3.i.d	4
		880.3.i.e	4
		880.3.i.f	4
		880.3.i.g	8
		880.3.i.h	8
		880.3.i.i	36
880.3.j	\(\chi_{880}(241, \cdot)\)	880.3.j.a	8	1
		880.3.j.b	8
		880.3.j.c	8
		880.3.j.d	24
880.3.k	\(\chi_{880}(551, \cdot)\)	None	0	1
880.3.n	\(\chi_{880}(639, \cdot)\)	880.3.n.a	20	1
		880.3.n.b	40
880.3.o	\(\chi_{880}(329, \cdot)\)	None	0	1
880.3.q	\(\chi_{880}(43, \cdot)\)	n/a	568	2
880.3.r	\(\chi_{880}(573, \cdot)\)	n/a	480	2
880.3.u	\(\chi_{880}(419, \cdot)\)	n/a	480	2
880.3.x	\(\chi_{880}(109, \cdot)\)	n/a	568	2
880.3.y	\(\chi_{880}(527, \cdot)\)	n/a	144	2
880.3.ba	\(\chi_{880}(177, \cdot)\)	n/a	120	2
880.3.bc	\(\chi_{880}(617, \cdot)\)	None	0	2
880.3.be	\(\chi_{880}(87, \cdot)\)	None	0	2
880.3.bg	\(\chi_{880}(21, \cdot)\)	n/a	384	2
880.3.bj	\(\chi_{880}(331, \cdot)\)	n/a	320	2
880.3.bm	\(\chi_{880}(483, \cdot)\)	n/a	568	2
880.3.bn	\(\chi_{880}(133, \cdot)\)	n/a	480	2
880.3.bq	\(\chi_{880}(249, \cdot)\)	None	0	4
880.3.br	\(\chi_{880}(159, \cdot)\)	n/a	288	4
880.3.bu	\(\chi_{880}(71, \cdot)\)	None	0	4
880.3.bv	\(\chi_{880}(161, \cdot)\)	n/a	192	4
880.3.bw	\(\chi_{880}(129, \cdot)\)	n/a	280	4
880.3.bx	\(\chi_{880}(119, \cdot)\)	None	0	4
880.3.ca	\(\chi_{880}(31, \cdot)\)	n/a	192	4
880.3.cb	\(\chi_{880}(41, \cdot)\)	None	0	4
880.3.ce	\(\chi_{880}(53, \cdot)\)	n/a	2272	8
880.3.cf	\(\chi_{880}(83, \cdot)\)	n/a	2272	8
880.3.cj	\(\chi_{880}(91, \cdot)\)	n/a	1536	8
880.3.ck	\(\chi_{880}(61, \cdot)\)	n/a	1536	8
880.3.cn	\(\chi_{880}(137, \cdot)\)	None	0	8
880.3.cp	\(\chi_{880}(7, \cdot)\)	None	0	8
880.3.cr	\(\chi_{880}(63, \cdot)\)	n/a	576	8
880.3.ct	\(\chi_{880}(97, \cdot)\)	n/a	560	8
880.3.cv	\(\chi_{880}(29, \cdot)\)	n/a	2272	8
880.3.cw	\(\chi_{880}(59, \cdot)\)	n/a	2272	8
880.3.da	\(\chi_{880}(37, \cdot)\)	n/a	2272	8
880.3.db	\(\chi_{880}(123, \cdot)\)	n/a	2272	8

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

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(880))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(880)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 10}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 5}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 2}\)