Space of modular forms of level 1860 and weight 4

• Label: 1860.4
• Level: 1860
• Weight: 4
• Dimension: 110304
• Nonzero newspaces: 48
• Sturm bound: 737280
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1860 = 2^{2} \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(737280\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1860))\).

	Total	New	Old
Modular forms	278880	111008	167872
Cusp forms	274080	110304	163776
Eisenstein series	4800	704	4096

Trace form

110304 * q + 20 * q^3 - 76 * q^4 + 40 * q^5 - 154 * q^6 - 32 * q^7 - 168 * q^8 - 92 * q^9 - 210 * q^10 + 32 * q^11 + 298 * q^12 + 32 * q^13 - 100 * q^15 - 308 * q^16 - 568 * q^17 - 542 * q^18 - 800 * q^19 + 760 * q^20 - 524 * q^21 + 1492 * q^22 - 1032 * q^23 + 1074 * q^24 + 1956 * q^25 - 736 * q^26 + 692 * q^27 - 2796 * q^28 + 3120 * q^29 - 662 * q^30 + 3456 * q^31 - 680 * q^32 + 1108 * q^33 + 1812 * q^34 + 440 * q^35 + 326 * q^36 - 3200 * q^37 + 4064 * q^38 - 3060 * q^39 + 5318 * q^40 - 3056 * q^41 + 1746 * q^42 - 3800 * q^43 - 2170 * q^45 - 6596 * q^46 - 672 * q^47 + 7380 * q^48 + 12528 * q^49 + 4282 * q^50 + 6268 * q^51 + 2640 * q^52 + 1232 * q^53 - 1520 * q^54 + 760 * q^55 - 13796 * q^56 - 6736 * q^57 - 20816 * q^58 - 5080 * q^59 - 15752 * q^60 - 22872 * q^61 - 20288 * q^62 - 8080 * q^63 - 17956 * q^64 - 14060 * q^65 - 18988 * q^66 - 7016 * q^67 - 16844 * q^68 - 2384 * q^69 - 6224 * q^70 + 2160 * q^71 + 14004 * q^72 + 10824 * q^73 + 28500 * q^74 + 5560 * q^75 + 49384 * q^76 + 24840 * q^77 + 24688 * q^78 - 560 * q^79 + 9272 * q^80 + 180 * q^81 + 3956 * q^82 + 2688 * q^83 + 8498 * q^84 + 20980 * q^85 + 896 * q^86 + 3032 * q^87 - 1676 * q^88 + 640 * q^89 + 7515 * q^90 + 10496 * q^91 + 5776 * q^92 - 12508 * q^93 + 9976 * q^94 + 3600 * q^95 + 11216 * q^96 - 17104 * q^97 + 6576 * q^98 - 8220 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1860))\)

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
1860.4.a	\(\chi_{1860}(1, \cdot)\)	1860.4.a.a	1	1
		1860.4.a.b	5
		1860.4.a.c	6
		1860.4.a.d	7
		1860.4.a.e	7
		1860.4.a.f	8
		1860.4.a.g	8
		1860.4.a.h	9
		1860.4.a.i	9
1860.4.f	\(\chi_{1860}(991, \cdot)\)	n/a	384	1
1860.4.g	\(\chi_{1860}(1489, \cdot)\)	1860.4.g.a	46	1
		1860.4.g.b	46
1860.4.h	\(\chi_{1860}(311, \cdot)\)	n/a	720	1
1860.4.i	\(\chi_{1860}(929, \cdot)\)	n/a	192	1
1860.4.n	\(\chi_{1860}(1799, \cdot)\)	n/a	1080	1
1860.4.o	\(\chi_{1860}(1301, \cdot)\)	n/a	128	1
1860.4.p	\(\chi_{1860}(619, \cdot)\)	n/a	576	1
1860.4.q	\(\chi_{1860}(1141, \cdot)\)	n/a	128	2
1860.4.r	\(\chi_{1860}(497, \cdot)\)	n/a	360	2
1860.4.s	\(\chi_{1860}(433, \cdot)\)	n/a	192	2
1860.4.t	\(\chi_{1860}(743, \cdot)\)	n/a	2288	2
1860.4.u	\(\chi_{1860}(187, \cdot)\)	n/a	1080	2
1860.4.z	\(\chi_{1860}(481, \cdot)\)	n/a	256	4
1860.4.ba	\(\chi_{1860}(739, \cdot)\)	n/a	1152	2
1860.4.bb	\(\chi_{1860}(161, \cdot)\)	n/a	256	2
1860.4.bc	\(\chi_{1860}(1079, \cdot)\)	n/a	2288	2
1860.4.bh	\(\chi_{1860}(1049, \cdot)\)	n/a	384	2
1860.4.bi	\(\chi_{1860}(191, \cdot)\)	n/a	1536	2
1860.4.bj	\(\chi_{1860}(769, \cdot)\)	n/a	192	2
1860.4.bk	\(\chi_{1860}(1111, \cdot)\)	n/a	768	2
1860.4.bp	\(\chi_{1860}(139, \cdot)\)	n/a	2304	4
1860.4.bq	\(\chi_{1860}(401, \cdot)\)	n/a	512	4
1860.4.br	\(\chi_{1860}(419, \cdot)\)	n/a	4576	4
1860.4.bw	\(\chi_{1860}(29, \cdot)\)	n/a	768	4
1860.4.bx	\(\chi_{1860}(791, \cdot)\)	n/a	3072	4
1860.4.by	\(\chi_{1860}(109, \cdot)\)	n/a	384	4
1860.4.bz	\(\chi_{1860}(91, \cdot)\)	n/a	1536	4
1860.4.ci	\(\chi_{1860}(67, \cdot)\)	n/a	2304	4
1860.4.cj	\(\chi_{1860}(347, \cdot)\)	n/a	4576	4
1860.4.ck	\(\chi_{1860}(37, \cdot)\)	n/a	384	4
1860.4.cl	\(\chi_{1860}(377, \cdot)\)	n/a	768	4
1860.4.cm	\(\chi_{1860}(121, \cdot)\)	n/a	512	8
1860.4.cr	\(\chi_{1860}(163, \cdot)\)	n/a	4608	8
1860.4.cs	\(\chi_{1860}(23, \cdot)\)	n/a	9152	8
1860.4.ct	\(\chi_{1860}(277, \cdot)\)	n/a	768	8
1860.4.cu	\(\chi_{1860}(233, \cdot)\)	n/a	1536	8
1860.4.cz	\(\chi_{1860}(331, \cdot)\)	n/a	3072	8
1860.4.da	\(\chi_{1860}(49, \cdot)\)	n/a	768	8
1860.4.db	\(\chi_{1860}(71, \cdot)\)	n/a	6144	8
1860.4.dc	\(\chi_{1860}(269, \cdot)\)	n/a	1536	8
1860.4.dh	\(\chi_{1860}(59, \cdot)\)	n/a	9152	8
1860.4.di	\(\chi_{1860}(641, \cdot)\)	n/a	1024	8
1860.4.dj	\(\chi_{1860}(79, \cdot)\)	n/a	4608	8
1860.4.dk	\(\chi_{1860}(113, \cdot)\)	n/a	3072	16
1860.4.dl	\(\chi_{1860}(13, \cdot)\)	n/a	1536	16
1860.4.dm	\(\chi_{1860}(83, \cdot)\)	n/a	18304	16
1860.4.dn	\(\chi_{1860}(7, \cdot)\)	n/a	9216	16

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1860))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1860)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(124))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(372))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(620))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(930))\)\(^{\oplus 2}\)