Space of modular forms of level 3040 and weight 2

• Label: 3040.2
• Level: 3040
• Weight: 2
• Dimension: 140748
• Nonzero newspaces: 60
• Sturm bound: 1105920
• Trace bound: 77

Defining parameters

Level:	\( N \)	=	\( 3040 = 2^{5} \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(1105920\)
Trace bound:			\(77\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3040))\).

	Total	New	Old
Modular forms	281088	142788	138300
Cusp forms	271873	140748	131125
Eisenstein series	9215	2040	7175

Trace form

140748 * q - 128 * q^2 - 100 * q^3 - 128 * q^4 - 196 * q^5 - 384 * q^6 - 100 * q^7 - 128 * q^8 - 196 * q^9 - 176 * q^10 - 292 * q^11 - 64 * q^12 - 104 * q^13 - 64 * q^14 - 138 * q^15 - 304 * q^16 - 48 * q^17 - 48 * q^18 - 100 * q^19 - 376 * q^20 - 384 * q^21 - 80 * q^22 - 68 * q^23 - 176 * q^24 - 296 * q^25 - 464 * q^26 + 20 * q^27 - 208 * q^28 - 152 * q^29 - 256 * q^30 - 180 * q^31 - 208 * q^32 - 248 * q^33 - 176 * q^34 - 50 * q^35 - 496 * q^36 - 56 * q^37 - 120 * q^38 - 56 * q^39 - 168 * q^40 - 464 * q^41 - 48 * q^42 - 4 * q^43 + 32 * q^44 - 76 * q^45 - 256 * q^46 - 36 * q^47 + 80 * q^48 - 20 * q^49 - 112 * q^50 - 276 * q^51 - 96 * q^52 + 8 * q^53 - 80 * q^54 - 170 * q^55 - 336 * q^56 - 224 * q^57 - 288 * q^58 - 220 * q^59 - 328 * q^60 - 296 * q^61 - 208 * q^62 - 308 * q^63 - 368 * q^64 - 564 * q^65 - 736 * q^66 - 308 * q^67 - 272 * q^68 - 192 * q^69 - 504 * q^70 - 484 * q^71 - 512 * q^72 - 336 * q^73 - 416 * q^74 - 304 * q^75 - 536 * q^76 - 400 * q^77 - 576 * q^78 - 204 * q^79 - 520 * q^80 - 404 * q^81 - 448 * q^82 - 20 * q^83 - 656 * q^84 - 352 * q^85 - 720 * q^86 + 36 * q^87 - 464 * q^88 - 272 * q^89 - 648 * q^90 - 164 * q^91 - 560 * q^92 - 368 * q^93 - 304 * q^94 - 98 * q^95 - 1056 * q^96 - 304 * q^97 - 304 * q^98 + 116 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3040))\)

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
3040.2.a	\(\chi_{3040}(1, \cdot)\)	3040.2.a.a	1	1
		3040.2.a.b	1
		3040.2.a.c	1
		3040.2.a.d	1
		3040.2.a.e	2
		3040.2.a.f	2
		3040.2.a.g	2
		3040.2.a.h	2
		3040.2.a.i	3
		3040.2.a.j	3
		3040.2.a.k	3
		3040.2.a.l	3
		3040.2.a.m	3
		3040.2.a.n	3
		3040.2.a.o	3
		3040.2.a.p	3
		3040.2.a.q	4
		3040.2.a.r	4
		3040.2.a.s	4
		3040.2.a.t	4
		3040.2.a.u	5
		3040.2.a.v	5
		3040.2.a.w	5
		3040.2.a.x	5
3040.2.d	\(\chi_{3040}(609, \cdot)\)	n/a	108	1
3040.2.e	\(\chi_{3040}(911, \cdot)\)	3040.2.e.a	80	1
3040.2.f	\(\chi_{3040}(1521, \cdot)\)	3040.2.f.a	28	1
		3040.2.f.b	44
3040.2.g	\(\chi_{3040}(3039, \cdot)\)	n/a	120	1
3040.2.j	\(\chi_{3040}(2431, \cdot)\)	3040.2.j.a	4	1
		3040.2.j.b	4
		3040.2.j.c	4
		3040.2.j.d	8
		3040.2.j.e	20
		3040.2.j.f	40
3040.2.k	\(\chi_{3040}(2129, \cdot)\)	n/a	108	1
3040.2.p	\(\chi_{3040}(1519, \cdot)\)	n/a	116	1
3040.2.q	\(\chi_{3040}(961, \cdot)\)	n/a	160	2
3040.2.r	\(\chi_{3040}(2393, \cdot)\)	None	0	2
3040.2.t	\(\chi_{3040}(1863, \cdot)\)	None	0	2
3040.2.w	\(\chi_{3040}(759, \cdot)\)	None	0	2
3040.2.y	\(\chi_{3040}(761, \cdot)\)	None	0	2
3040.2.bb	\(\chi_{3040}(113, \cdot)\)	n/a	232	2
3040.2.bc	\(\chi_{3040}(1407, \cdot)\)	n/a	216	2
3040.2.bd	\(\chi_{3040}(417, \cdot)\)	n/a	240	2
3040.2.be	\(\chi_{3040}(1103, \cdot)\)	n/a	216	2
3040.2.bi	\(\chi_{3040}(1369, \cdot)\)	None	0	2
3040.2.bk	\(\chi_{3040}(151, \cdot)\)	None	0	2
3040.2.bl	\(\chi_{3040}(343, \cdot)\)	None	0	2
3040.2.bn	\(\chi_{3040}(873, \cdot)\)	None	0	2
3040.2.bp	\(\chi_{3040}(49, \cdot)\)	n/a	232	2
3040.2.bq	\(\chi_{3040}(31, \cdot)\)	n/a	160	2
3040.2.bv	\(\chi_{3040}(559, \cdot)\)	n/a	232	2
3040.2.by	\(\chi_{3040}(1551, \cdot)\)	n/a	160	2
3040.2.bz	\(\chi_{3040}(1569, \cdot)\)	n/a	240	2
3040.2.ca	\(\chi_{3040}(639, \cdot)\)	n/a	240	2
3040.2.cb	\(\chi_{3040}(881, \cdot)\)	n/a	160	2
3040.2.ce	\(\chi_{3040}(37, \cdot)\)	n/a	1904	4
3040.2.cf	\(\chi_{3040}(1027, \cdot)\)	n/a	1728	4
3040.2.ck	\(\chi_{3040}(531, \cdot)\)	n/a	1280	4
3040.2.cl	\(\chi_{3040}(381, \cdot)\)	n/a	1152	4
3040.2.co	\(\chi_{3040}(229, \cdot)\)	n/a	1728	4
3040.2.cp	\(\chi_{3040}(379, \cdot)\)	n/a	1904	4
3040.2.cq	\(\chi_{3040}(267, \cdot)\)	n/a	1728	4
3040.2.cr	\(\chi_{3040}(797, \cdot)\)	n/a	1904	4
3040.2.cu	\(\chi_{3040}(161, \cdot)\)	n/a	480	6
3040.2.cv	\(\chi_{3040}(217, \cdot)\)	None	0	4
3040.2.cx	\(\chi_{3040}(7, \cdot)\)	None	0	4
3040.2.da	\(\chi_{3040}(121, \cdot)\)	None	0	4
3040.2.dc	\(\chi_{3040}(1319, \cdot)\)	None	0	4
3040.2.dd	\(\chi_{3040}(753, \cdot)\)	n/a	464	4
3040.2.de	\(\chi_{3040}(543, \cdot)\)	n/a	480	4
3040.2.dj	\(\chi_{3040}(673, \cdot)\)	n/a	480	4
3040.2.dk	\(\chi_{3040}(463, \cdot)\)	n/a	464	4
3040.2.dm	\(\chi_{3040}(711, \cdot)\)	None	0	4
3040.2.do	\(\chi_{3040}(729, \cdot)\)	None	0	4
3040.2.dp	\(\chi_{3040}(87, \cdot)\)	None	0	4
3040.2.dr	\(\chi_{3040}(297, \cdot)\)	None	0	4
3040.2.dt	\(\chi_{3040}(79, \cdot)\)	n/a	696	6
3040.2.dy	\(\chi_{3040}(81, \cdot)\)	n/a	480	6
3040.2.dz	\(\chi_{3040}(319, \cdot)\)	n/a	720	6
3040.2.ec	\(\chi_{3040}(289, \cdot)\)	n/a	720	6
3040.2.ed	\(\chi_{3040}(431, \cdot)\)	n/a	480	6
3040.2.ee	\(\chi_{3040}(831, \cdot)\)	n/a	480	6
3040.2.ef	\(\chi_{3040}(529, \cdot)\)	n/a	696	6
3040.2.ei	\(\chi_{3040}(387, \cdot)\)	n/a	3808	8
3040.2.ej	\(\chi_{3040}(597, \cdot)\)	n/a	3808	8
3040.2.eo	\(\chi_{3040}(179, \cdot)\)	n/a	3808	8
3040.2.ep	\(\chi_{3040}(349, \cdot)\)	n/a	3808	8
3040.2.es	\(\chi_{3040}(501, \cdot)\)	n/a	2560	8
3040.2.et	\(\chi_{3040}(331, \cdot)\)	n/a	2560	8
3040.2.eu	\(\chi_{3040}(293, \cdot)\)	n/a	3808	8
3040.2.ev	\(\chi_{3040}(83, \cdot)\)	n/a	3808	8
3040.2.ey	\(\chi_{3040}(9, \cdot)\)	None	0	12
3040.2.ez	\(\chi_{3040}(71, \cdot)\)	None	0	12
3040.2.fe	\(\chi_{3040}(33, \cdot)\)	n/a	1440	12
3040.2.ff	\(\chi_{3040}(47, \cdot)\)	n/a	1392	12
3040.2.fi	\(\chi_{3040}(23, \cdot)\)	None	0	12
3040.2.fj	\(\chi_{3040}(393, \cdot)\)	None	0	12
3040.2.fm	\(\chi_{3040}(793, \cdot)\)	None	0	12
3040.2.fn	\(\chi_{3040}(263, \cdot)\)	None	0	12
3040.2.fq	\(\chi_{3040}(337, \cdot)\)	n/a	1392	12
3040.2.fr	\(\chi_{3040}(63, \cdot)\)	n/a	1440	12
3040.2.fs	\(\chi_{3040}(441, \cdot)\)	None	0	12
3040.2.ft	\(\chi_{3040}(279, \cdot)\)	None	0	12
3040.2.fy	\(\chi_{3040}(53, \cdot)\)	n/a	11424	24
3040.2.fz	\(\chi_{3040}(187, \cdot)\)	n/a	11424	24
3040.2.ga	\(\chi_{3040}(61, \cdot)\)	n/a	7680	24
3040.2.gb	\(\chi_{3040}(59, \cdot)\)	n/a	11424	24
3040.2.gc	\(\chi_{3040}(149, \cdot)\)	n/a	11424	24
3040.2.gd	\(\chi_{3040}(51, \cdot)\)	n/a	7680	24
3040.2.gk	\(\chi_{3040}(43, \cdot)\)	n/a	11424	24
3040.2.gl	\(\chi_{3040}(13, \cdot)\)	n/a	11424	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3040))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1520))\)\(^{\oplus 2}\)