Space of modular forms of level 1840 and weight 4

• Label: 1840.4
• Level: 1840
• Weight: 4
• Dimension: 155654
• Nonzero newspaces: 28
• Sturm bound: 811008
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(811008\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1840))\).

	Total	New	Old
Modular forms	306592	156790	149802
Cusp forms	301664	155654	146010
Eisenstein series	4928	1136	3792

Trace form

155654 * q - 80 * q^2 - 46 * q^3 - 40 * q^4 - 153 * q^5 - 360 * q^6 - 150 * q^7 - 248 * q^8 - 58 * q^9 - 252 * q^10 + 74 * q^11 + 328 * q^12 + 174 * q^13 + 680 * q^14 - 327 * q^15 + 888 * q^16 - 186 * q^17 + 624 * q^18 - 794 * q^19 - 508 * q^20 - 1010 * q^21 - 2424 * q^22 - 32 * q^23 - 3552 * q^24 - 345 * q^25 - 1288 * q^26 + 854 * q^27 + 24 * q^28 - 670 * q^29 - 908 * q^30 + 1410 * q^31 + 2440 * q^32 + 442 * q^33 + 2824 * q^34 + 1417 * q^35 + 840 * q^36 + 1862 * q^37 - 856 * q^38 + 1526 * q^39 + 3452 * q^40 + 1518 * q^41 + 2488 * q^42 - 2750 * q^43 + 5528 * q^44 + 1518 * q^45 + 1824 * q^46 - 4088 * q^47 + 2776 * q^48 - 482 * q^49 - 3844 * q^50 - 6238 * q^51 - 8504 * q^52 - 5674 * q^53 - 9032 * q^54 - 2635 * q^55 - 2184 * q^56 - 4006 * q^57 - 40 * q^58 + 5190 * q^59 + 524 * q^60 + 3726 * q^61 - 392 * q^62 + 1162 * q^63 + 9704 * q^64 - 4237 * q^65 + 11240 * q^66 - 2422 * q^67 + 2344 * q^68 + 1510 * q^69 + 1656 * q^70 + 1538 * q^71 - 1224 * q^72 + 4238 * q^73 - 10504 * q^74 + 25347 * q^75 - 13720 * q^76 + 9962 * q^77 - 26696 * q^78 + 9298 * q^79 - 18052 * q^80 + 12230 * q^81 - 14696 * q^82 + 3798 * q^83 - 10168 * q^84 - 45 * q^85 + 10088 * q^86 - 15934 * q^87 + 4808 * q^88 - 11678 * q^89 + 11116 * q^90 - 24076 * q^91 + 6216 * q^92 - 38388 * q^93 + 1608 * q^94 - 20151 * q^95 + 6744 * q^96 - 20594 * q^97 + 8320 * q^98 - 20646 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1840))\)

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
1840.4.a	\(\chi_{1840}(1, \cdot)\)	1840.4.a.a	1	1
		1840.4.a.b	1
		1840.4.a.c	1
		1840.4.a.d	1
		1840.4.a.e	1
		1840.4.a.f	1
		1840.4.a.g	1
		1840.4.a.h	2
		1840.4.a.i	2
		1840.4.a.j	3
		1840.4.a.k	4
		1840.4.a.l	4
		1840.4.a.m	4
		1840.4.a.n	5
		1840.4.a.o	5
		1840.4.a.p	5
		1840.4.a.q	5
		1840.4.a.r	6
		1840.4.a.s	6
		1840.4.a.t	6
		1840.4.a.u	6
		1840.4.a.v	8
		1840.4.a.w	8
		1840.4.a.x	8
		1840.4.a.y	9
		1840.4.a.z	9
		1840.4.a.ba	10
		1840.4.a.bb	10
1840.4.b	\(\chi_{1840}(919, \cdot)\)	None	0	1
1840.4.e	\(\chi_{1840}(369, \cdot)\)	n/a	198	1
1840.4.f	\(\chi_{1840}(921, \cdot)\)	None	0	1
1840.4.i	\(\chi_{1840}(1471, \cdot)\)	n/a	144	1
1840.4.j	\(\chi_{1840}(1289, \cdot)\)	None	0	1
1840.4.m	\(\chi_{1840}(1839, \cdot)\)	n/a	216	1
1840.4.n	\(\chi_{1840}(551, \cdot)\)	None	0	1
1840.4.r	\(\chi_{1840}(413, \cdot)\)	n/a	1720	2
1840.4.t	\(\chi_{1840}(1243, \cdot)\)	n/a	1584	2
1840.4.u	\(\chi_{1840}(91, \cdot)\)	n/a	1152	2
1840.4.x	\(\chi_{1840}(461, \cdot)\)	n/a	1056	2
1840.4.y	\(\chi_{1840}(1057, \cdot)\)	n/a	428	2
1840.4.ba	\(\chi_{1840}(47, \cdot)\)	n/a	396	2
1840.4.bd	\(\chi_{1840}(967, \cdot)\)	None	0	2
1840.4.bf	\(\chi_{1840}(137, \cdot)\)	None	0	2
1840.4.bg	\(\chi_{1840}(829, \cdot)\)	n/a	1584	2
1840.4.bj	\(\chi_{1840}(459, \cdot)\)	n/a	1720	2
1840.4.bk	\(\chi_{1840}(323, \cdot)\)	n/a	1584	2
1840.4.bm	\(\chi_{1840}(1333, \cdot)\)	n/a	1720	2
1840.4.bo	\(\chi_{1840}(81, \cdot)\)	n/a	1440	10
1840.4.br	\(\chi_{1840}(471, \cdot)\)	None	0	10
1840.4.bs	\(\chi_{1840}(79, \cdot)\)	n/a	2160	10
1840.4.bv	\(\chi_{1840}(9, \cdot)\)	None	0	10
1840.4.bw	\(\chi_{1840}(111, \cdot)\)	n/a	1440	10
1840.4.bz	\(\chi_{1840}(41, \cdot)\)	None	0	10
1840.4.ca	\(\chi_{1840}(49, \cdot)\)	n/a	2140	10
1840.4.cd	\(\chi_{1840}(199, \cdot)\)	None	0	10
1840.4.cf	\(\chi_{1840}(53, \cdot)\)	n/a	17200	20
1840.4.ch	\(\chi_{1840}(3, \cdot)\)	n/a	17200	20
1840.4.cj	\(\chi_{1840}(19, \cdot)\)	n/a	17200	20
1840.4.ck	\(\chi_{1840}(29, \cdot)\)	n/a	17200	20
1840.4.cm	\(\chi_{1840}(57, \cdot)\)	None	0	20
1840.4.co	\(\chi_{1840}(87, \cdot)\)	None	0	20
1840.4.cr	\(\chi_{1840}(127, \cdot)\)	n/a	4320	20
1840.4.ct	\(\chi_{1840}(17, \cdot)\)	n/a	4280	20
1840.4.cv	\(\chi_{1840}(101, \cdot)\)	n/a	11520	20
1840.4.cw	\(\chi_{1840}(11, \cdot)\)	n/a	11520	20
1840.4.cy	\(\chi_{1840}(123, \cdot)\)	n/a	17200	20
1840.4.da	\(\chi_{1840}(37, \cdot)\)	n/a	17200	20

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1840))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1840)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(920))\)\(^{\oplus 2}\)