Space of modular forms of level 1740 and weight 2

• Label: 1740.2
• Level: 1740
• Weight: 2
• Dimension: 31936
• Nonzero newspaces: 40
• Sturm bound: 322560
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 1740 = 2^{2} \cdot 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(322560\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1740))\).

	Total	New	Old
Modular forms	82880	32592	50288
Cusp forms	78401	31936	46465
Eisenstein series	4479	656	3823

Trace form

31936 * q - 4 * q^3 - 40 * q^4 - 4 * q^5 - 68 * q^6 + 8 * q^7 + 24 * q^8 - 36 * q^9 - 44 * q^10 + 16 * q^11 - 20 * q^12 - 64 * q^13 + 28 * q^15 - 168 * q^16 + 40 * q^17 - 60 * q^18 - 40 * q^20 - 200 * q^21 - 72 * q^22 - 56 * q^23 - 76 * q^24 - 196 * q^25 - 32 * q^26 - 112 * q^27 - 48 * q^28 - 124 * q^29 - 156 * q^30 - 160 * q^31 - 40 * q^32 - 164 * q^33 - 104 * q^34 - 88 * q^35 - 84 * q^36 - 168 * q^37 - 32 * q^38 - 56 * q^39 - 116 * q^40 + 8 * q^41 - 44 * q^42 + 24 * q^43 + 56 * q^44 - 66 * q^45 + 160 * q^46 + 112 * q^47 + 236 * q^48 + 148 * q^49 + 228 * q^50 + 136 * q^51 + 472 * q^52 + 244 * q^53 + 84 * q^54 + 240 * q^55 + 520 * q^56 + 72 * q^57 + 672 * q^58 + 128 * q^59 + 254 * q^60 - 40 * q^61 + 504 * q^62 + 40 * q^63 + 560 * q^64 + 86 * q^65 + 268 * q^66 + 232 * q^67 + 424 * q^68 - 8 * q^69 + 156 * q^70 + 112 * q^71 + 4 * q^72 - 68 * q^73 + 56 * q^74 + 66 * q^75 - 232 * q^76 - 96 * q^77 - 60 * q^78 - 48 * q^79 - 8 * q^80 + 4 * q^81 - 168 * q^82 - 224 * q^84 - 280 * q^85 - 128 * q^86 + 120 * q^87 - 320 * q^88 - 40 * q^89 - 162 * q^90 - 48 * q^91 - 112 * q^92 + 8 * q^93 - 264 * q^94 - 296 * q^96 + 260 * q^97 - 328 * q^98 + 236 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1740))\)

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
1740.2.a	\(\chi_{1740}(1, \cdot)\)	1740.2.a.a	1	1
		1740.2.a.b	1
		1740.2.a.c	1
		1740.2.a.d	1
		1740.2.a.e	1
		1740.2.a.f	1
		1740.2.a.g	1
		1740.2.a.h	1
		1740.2.a.i	2
		1740.2.a.j	2
		1740.2.a.k	2
		1740.2.a.l	2
		1740.2.a.m	2
		1740.2.a.n	2
1740.2.b	\(\chi_{1740}(289, \cdot)\)	1740.2.b.a	14	1
		1740.2.b.b	14
1740.2.e	\(\chi_{1740}(1391, \cdot)\)	n/a	240	1
1740.2.g	\(\chi_{1740}(349, \cdot)\)	1740.2.g.a	2	1
		1740.2.g.b	2
		1740.2.g.c	12
		1740.2.g.d	12
1740.2.h	\(\chi_{1740}(1451, \cdot)\)	n/a	224	1
1740.2.k	\(\chi_{1740}(1739, \cdot)\)	n/a	352	1
1740.2.l	\(\chi_{1740}(1681, \cdot)\)	1740.2.l.a	2	1
		1740.2.l.b	2
		1740.2.l.c	6
		1740.2.l.d	10
1740.2.n	\(\chi_{1740}(59, \cdot)\)	n/a	336	1
1740.2.q	\(\chi_{1740}(331, \cdot)\)	n/a	240	2
1740.2.t	\(\chi_{1740}(389, \cdot)\)	n/a	120	2
1740.2.u	\(\chi_{1740}(233, \cdot)\)	n/a	112	2
1740.2.x	\(\chi_{1740}(523, \cdot)\)	n/a	336	2
1740.2.z	\(\chi_{1740}(563, \cdot)\)	n/a	704	2
1740.2.bb	\(\chi_{1740}(133, \cdot)\)	1740.2.bb.a	2	2
		1740.2.bb.b	28
		1740.2.bb.c	30
1740.2.bc	\(\chi_{1740}(853, \cdot)\)	1740.2.bc.a	2	2
		1740.2.bc.b	28
		1740.2.bc.c	30
1740.2.be	\(\chi_{1740}(1583, \cdot)\)	n/a	704	2
1740.2.bg	\(\chi_{1740}(463, \cdot)\)	n/a	360	2
1740.2.bj	\(\chi_{1740}(173, \cdot)\)	n/a	120	2
1740.2.bk	\(\chi_{1740}(41, \cdot)\)	1740.2.bk.a	4	2
		1740.2.bk.b	4
		1740.2.bk.c	36
		1740.2.bk.d	36
1740.2.bn	\(\chi_{1740}(679, \cdot)\)	n/a	360	2
1740.2.bo	\(\chi_{1740}(181, \cdot)\)	n/a	120	6
1740.2.br	\(\chi_{1740}(239, \cdot)\)	n/a	2112	6
1740.2.bt	\(\chi_{1740}(121, \cdot)\)	n/a	120	6
1740.2.bu	\(\chi_{1740}(179, \cdot)\)	n/a	2112	6
1740.2.bx	\(\chi_{1740}(371, \cdot)\)	n/a	1440	6
1740.2.by	\(\chi_{1740}(49, \cdot)\)	n/a	192	6
1740.2.ca	\(\chi_{1740}(71, \cdot)\)	n/a	1440	6
1740.2.cd	\(\chi_{1740}(109, \cdot)\)	n/a	168	6
1740.2.ce	\(\chi_{1740}(19, \cdot)\)	n/a	2160	12
1740.2.ch	\(\chi_{1740}(101, \cdot)\)	n/a	480	12
1740.2.cj	\(\chi_{1740}(353, \cdot)\)	n/a	720	12
1740.2.ck	\(\chi_{1740}(67, \cdot)\)	n/a	2160	12
1740.2.cm	\(\chi_{1740}(37, \cdot)\)	n/a	360	12
1740.2.co	\(\chi_{1740}(143, \cdot)\)	n/a	4224	12
1740.2.cr	\(\chi_{1740}(47, \cdot)\)	n/a	4224	12
1740.2.ct	\(\chi_{1740}(73, \cdot)\)	n/a	360	12
1740.2.cv	\(\chi_{1740}(7, \cdot)\)	n/a	2160	12
1740.2.cw	\(\chi_{1740}(53, \cdot)\)	n/a	720	12
1740.2.cy	\(\chi_{1740}(89, \cdot)\)	n/a	720	12
1740.2.db	\(\chi_{1740}(31, \cdot)\)	n/a	1440	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1740))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1740)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(348))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(870))\)\(^{\oplus 2}\)