Space of modular forms of level 1840 and weight 2

• Label: 1840.2
• Level: 1840
• Weight: 2
• Dimension: 51506
• Nonzero newspaces: 28
• Sturm bound: 405504
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 1840 = 2^{4} \cdot 5 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(405504\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1840))\).

	Total	New	Old
Modular forms	103840	52642	51198
Cusp forms	98913	51506	47407
Eisenstein series	4927	1136	3791

Trace form

51506 * q - 80 * q^2 - 62 * q^3 - 72 * q^4 - 149 * q^5 - 216 * q^6 - 54 * q^7 - 56 * q^8 - 14 * q^9 - 116 * q^10 - 166 * q^11 - 88 * q^12 - 90 * q^13 - 88 * q^14 - 55 * q^15 - 264 * q^16 - 162 * q^17 - 64 * q^18 - 10 * q^19 - 108 * q^20 - 242 * q^21 - 72 * q^22 - 48 * q^23 - 160 * q^24 - 13 * q^25 - 216 * q^26 - 74 * q^27 - 104 * q^28 - 70 * q^29 - 188 * q^30 - 254 * q^31 - 120 * q^32 - 230 * q^33 - 184 * q^34 - 119 * q^35 - 376 * q^36 - 146 * q^37 - 232 * q^38 - 106 * q^39 - 292 * q^40 - 122 * q^41 - 232 * q^42 - 46 * q^43 - 200 * q^44 - 190 * q^45 - 288 * q^46 - 56 * q^47 - 168 * q^48 - 166 * q^49 - 228 * q^50 - 126 * q^51 - 152 * q^52 - 98 * q^53 - 168 * q^54 - 59 * q^55 - 264 * q^56 + 58 * q^57 - 120 * q^58 - 10 * q^59 - 52 * q^60 - 330 * q^61 - 8 * q^62 - 118 * q^63 - 24 * q^64 - 197 * q^65 - 88 * q^66 - 166 * q^67 + 40 * q^68 - 122 * q^69 - 88 * q^70 - 286 * q^71 + 184 * q^72 + 22 * q^73 + 104 * q^74 - 245 * q^75 - 56 * q^76 - 6 * q^77 + 184 * q^78 - 110 * q^79 + 60 * q^80 - 126 * q^81 + 56 * q^82 - 106 * q^83 + 200 * q^84 - 13 * q^85 - 104 * q^86 + 98 * q^87 + 136 * q^88 + 202 * q^89 + 116 * q^90 + 20 * q^91 - 88 * q^92 + 156 * q^93 - 24 * q^94 - 71 * q^95 - 168 * q^96 + 54 * q^97 - 160 * q^98 + 186 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1840))\)

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
1840.2.a	\(\chi_{1840}(1, \cdot)\)	1840.2.a.a	1	1
		1840.2.a.b	1
		1840.2.a.c	1
		1840.2.a.d	1
		1840.2.a.e	1
		1840.2.a.f	1
		1840.2.a.g	1
		1840.2.a.h	1
		1840.2.a.i	1
		1840.2.a.j	2
		1840.2.a.k	2
		1840.2.a.l	2
		1840.2.a.m	2
		1840.2.a.n	2
		1840.2.a.o	2
		1840.2.a.p	2
		1840.2.a.q	3
		1840.2.a.r	3
		1840.2.a.s	3
		1840.2.a.t	3
		1840.2.a.u	4
		1840.2.a.v	5
1840.2.b	\(\chi_{1840}(919, \cdot)\)	None	0	1
1840.2.e	\(\chi_{1840}(369, \cdot)\)	1840.2.e.a	2	1
		1840.2.e.b	2
		1840.2.e.c	4
		1840.2.e.d	8
		1840.2.e.e	8
		1840.2.e.f	12
		1840.2.e.g	14
		1840.2.e.h	16
1840.2.f	\(\chi_{1840}(921, \cdot)\)	None	0	1
1840.2.i	\(\chi_{1840}(1471, \cdot)\)	1840.2.i.a	16	1
		1840.2.i.b	16
		1840.2.i.c	16
1840.2.j	\(\chi_{1840}(1289, \cdot)\)	None	0	1
1840.2.m	\(\chi_{1840}(1839, \cdot)\)	1840.2.m.a	4	1
		1840.2.m.b	4
		1840.2.m.c	4
		1840.2.m.d	4
		1840.2.m.e	8
		1840.2.m.f	8
		1840.2.m.g	40
1840.2.n	\(\chi_{1840}(551, \cdot)\)	None	0	1
1840.2.r	\(\chi_{1840}(413, \cdot)\)	n/a	568	2
1840.2.t	\(\chi_{1840}(1243, \cdot)\)	n/a	528	2
1840.2.u	\(\chi_{1840}(91, \cdot)\)	n/a	384	2
1840.2.x	\(\chi_{1840}(461, \cdot)\)	n/a	352	2
1840.2.y	\(\chi_{1840}(1057, \cdot)\)	n/a	140	2
1840.2.ba	\(\chi_{1840}(47, \cdot)\)	n/a	132	2
1840.2.bd	\(\chi_{1840}(967, \cdot)\)	None	0	2
1840.2.bf	\(\chi_{1840}(137, \cdot)\)	None	0	2
1840.2.bg	\(\chi_{1840}(829, \cdot)\)	n/a	528	2
1840.2.bj	\(\chi_{1840}(459, \cdot)\)	n/a	568	2
1840.2.bk	\(\chi_{1840}(323, \cdot)\)	n/a	528	2
1840.2.bm	\(\chi_{1840}(1333, \cdot)\)	n/a	568	2
1840.2.bo	\(\chi_{1840}(81, \cdot)\)	n/a	480	10
1840.2.br	\(\chi_{1840}(471, \cdot)\)	None	0	10
1840.2.bs	\(\chi_{1840}(79, \cdot)\)	n/a	720	10
1840.2.bv	\(\chi_{1840}(9, \cdot)\)	None	0	10
1840.2.bw	\(\chi_{1840}(111, \cdot)\)	n/a	480	10
1840.2.bz	\(\chi_{1840}(41, \cdot)\)	None	0	10
1840.2.ca	\(\chi_{1840}(49, \cdot)\)	n/a	700	10
1840.2.cd	\(\chi_{1840}(199, \cdot)\)	None	0	10
1840.2.cf	\(\chi_{1840}(53, \cdot)\)	n/a	5680	20
1840.2.ch	\(\chi_{1840}(3, \cdot)\)	n/a	5680	20
1840.2.cj	\(\chi_{1840}(19, \cdot)\)	n/a	5680	20
1840.2.ck	\(\chi_{1840}(29, \cdot)\)	n/a	5680	20
1840.2.cm	\(\chi_{1840}(57, \cdot)\)	None	0	20
1840.2.co	\(\chi_{1840}(87, \cdot)\)	None	0	20
1840.2.cr	\(\chi_{1840}(127, \cdot)\)	n/a	1440	20
1840.2.ct	\(\chi_{1840}(17, \cdot)\)	n/a	1400	20
1840.2.cv	\(\chi_{1840}(101, \cdot)\)	n/a	3840	20
1840.2.cw	\(\chi_{1840}(11, \cdot)\)	n/a	3840	20
1840.2.cy	\(\chi_{1840}(123, \cdot)\)	n/a	5680	20
1840.2.da	\(\chi_{1840}(37, \cdot)\)	n/a	5680	20

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1840))\) into lower level spaces

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