Space of modular forms of level 740 and weight 2

• Label: 740.2
• Level: 740
• Weight: 2
• Dimension: 8556
• Nonzero newspaces: 30
• Newform subspaces: 58
• Sturm bound: 65664
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 30 \)
Newform subspaces:			\( 58 \)
Sturm bound:			\(65664\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(740))\).

	Total	New	Old
Modular forms	17136	8972	8164
Cusp forms	15697	8556	7141
Eisenstein series	1439	416	1023

Trace form

8556 * q - 32 * q^2 + 4 * q^3 - 36 * q^4 - 98 * q^5 - 108 * q^6 - 4 * q^7 - 44 * q^8 - 74 * q^9 - 66 * q^10 - 36 * q^12 - 72 * q^13 - 36 * q^14 - 4 * q^15 - 92 * q^16 - 72 * q^17 - 24 * q^18 + 8 * q^19 - 46 * q^20 - 208 * q^21 - 36 * q^22 - 12 * q^23 - 36 * q^24 - 122 * q^25 - 116 * q^26 + 40 * q^27 - 36 * q^28 - 48 * q^29 - 54 * q^30 + 116 * q^31 - 52 * q^32 - 36 * q^34 + 58 * q^35 - 168 * q^36 + 24 * q^37 - 72 * q^38 + 92 * q^39 - 46 * q^40 - 88 * q^41 - 36 * q^42 + 92 * q^43 - 36 * q^44 - 64 * q^45 - 108 * q^46 + 48 * q^47 - 36 * q^48 - 18 * q^49 - 26 * q^50 - 24 * q^51 - 28 * q^52 - 96 * q^53 - 36 * q^54 - 108 * q^56 - 88 * q^57 - 88 * q^58 - 96 * q^59 - 180 * q^60 - 358 * q^61 - 216 * q^62 - 220 * q^63 - 288 * q^64 - 189 * q^65 - 612 * q^66 - 76 * q^67 - 228 * q^68 - 336 * q^69 - 252 * q^70 - 120 * q^71 - 516 * q^72 - 248 * q^73 - 324 * q^74 - 176 * q^75 - 396 * q^76 - 216 * q^77 - 540 * q^78 - 160 * q^79 - 284 * q^80 - 446 * q^81 - 284 * q^82 - 84 * q^83 - 540 * q^84 - 165 * q^85 - 360 * q^86 - 192 * q^87 - 216 * q^88 - 150 * q^89 - 192 * q^90 - 68 * q^91 - 72 * q^92 + 20 * q^93 - 36 * q^94 + 64 * q^95 - 108 * q^96 + 16 * q^97 - 64 * q^98 + 180 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(740))\)

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
740.2.a	\(\chi_{740}(1, \cdot)\)	740.2.a.a	1	1
		740.2.a.b	1
		740.2.a.c	1
		740.2.a.d	2
		740.2.a.e	3
		740.2.a.f	4
740.2.d	\(\chi_{740}(149, \cdot)\)	740.2.d.a	18	1
740.2.e	\(\chi_{740}(369, \cdot)\)	740.2.e.a	20	1
740.2.h	\(\chi_{740}(221, \cdot)\)	740.2.h.a	2	1
		740.2.h.b	12
740.2.i	\(\chi_{740}(121, \cdot)\)	740.2.i.a	14	2
		740.2.i.b	14
740.2.k	\(\chi_{740}(179, \cdot)\)	740.2.k.a	2	2
		740.2.k.b	2
		740.2.k.c	216
740.2.l	\(\chi_{740}(413, \cdot)\)	740.2.l.a	6	2
		740.2.l.b	32
740.2.m	\(\chi_{740}(147, \cdot)\)	740.2.m.a	2	2
		740.2.m.b	2
		740.2.m.c	216
740.2.n	\(\chi_{740}(223, \cdot)\)	740.2.n.a	216	2
740.2.o	\(\chi_{740}(117, \cdot)\)	740.2.o.a	6	2
		740.2.o.b	32
740.2.u	\(\chi_{740}(31, \cdot)\)	740.2.u.a	152	2
740.2.x	\(\chi_{740}(101, \cdot)\)	740.2.x.a	28	2
740.2.ba	\(\chi_{740}(249, \cdot)\)	740.2.ba.a	40	2
740.2.bb	\(\chi_{740}(269, \cdot)\)	740.2.bb.a	36	2
740.2.bc	\(\chi_{740}(81, \cdot)\)	740.2.bc.a	6	6
		740.2.bc.b	12
		740.2.bc.c	18
		740.2.bc.d	36
740.2.be	\(\chi_{740}(51, \cdot)\)	740.2.be.a	304	4
740.2.bf	\(\chi_{740}(97, \cdot)\)	740.2.bf.a	76	4
740.2.bg	\(\chi_{740}(47, \cdot)\)	740.2.bg.a	4	4
		740.2.bg.b	4
		740.2.bg.c	432
740.2.bh	\(\chi_{740}(27, \cdot)\)	740.2.bh.a	4	4
		740.2.bh.b	4
		740.2.bh.c	432
740.2.bi	\(\chi_{740}(177, \cdot)\)	740.2.bi.a	76	4
740.2.bo	\(\chi_{740}(119, \cdot)\)	740.2.bo.a	4	4
		740.2.bo.b	4
		740.2.bo.c	432
740.2.bp	\(\chi_{740}(169, \cdot)\)	740.2.bp.a	120	6
740.2.bq	\(\chi_{740}(21, \cdot)\)	740.2.bq.a	72	6
740.2.br	\(\chi_{740}(9, \cdot)\)	740.2.br.a	108	6
740.2.bx	\(\chi_{740}(91, \cdot)\)	740.2.bx.a	912	12
740.2.ca	\(\chi_{740}(19, \cdot)\)	740.2.ca.a	12	12
		740.2.ca.b	12
		740.2.ca.c	1296
740.2.cc	\(\chi_{740}(17, \cdot)\)	740.2.cc.a	228	12
740.2.ce	\(\chi_{740}(3, \cdot)\)	740.2.ce.a	12	12
		740.2.ce.b	12
		740.2.ce.c	1296
740.2.cf	\(\chi_{740}(7, \cdot)\)	740.2.cf.a	12	12
		740.2.cf.b	12
		740.2.cf.c	1296
740.2.ch	\(\chi_{740}(13, \cdot)\)	740.2.ch.a	228	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(740))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(740)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(37))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(74))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(148))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(185))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(370))\)\(^{\oplus 2}\)