Space of modular forms of level 742 and weight 2

• Label: 742.2
• Level: 742
• Weight: 2
• Dimension: 5381
• Nonzero newspaces: 12
• Newform subspaces: 40
• Sturm bound: 67392
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 742 = 2 \cdot 7 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 40 \)
Sturm bound:			\(67392\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(742))\).

	Total	New	Old
Modular forms	17472	5381	12091
Cusp forms	16225	5381	10844
Eisenstein series	1247	0	1247

Trace form

5381 * q + 3 * q^2 + 8 * q^3 - q^4 + 6 * q^5 - q^7 + 3 * q^8 + 11 * q^9 + 6 * q^10 + 12 * q^11 + 8 * q^12 + 22 * q^13 + 3 * q^14 + 24 * q^15 - q^16 + 6 * q^17 + 15 * q^18 + 16 * q^19 + 6 * q^20 + 8 * q^21 + 12 * q^22 + 24 * q^23 + 41 * q^25 + 6 * q^26 + 32 * q^27 - q^28 + 42 * q^29 + 24 * q^30 + 40 * q^31 + 3 * q^32 + 48 * q^33 + 30 * q^34 + 6 * q^35 + 11 * q^36 + 34 * q^37 + 24 * q^38 + 40 * q^39 - 20 * q^40 - 74 * q^41 - 104 * q^42 - 180 * q^43 + 12 * q^44 - 442 * q^45 - 80 * q^46 - 32 * q^47 - 96 * q^48 - 105 * q^49 - 213 * q^50 - 320 * q^51 - 82 * q^52 - 265 * q^53 - 264 * q^54 - 240 * q^55 - 49 * q^56 - 328 * q^57 - 216 * q^58 - 136 * q^59 - 80 * q^60 - 58 * q^61 - 80 * q^62 - 249 * q^63 - q^64 - 124 * q^65 - 160 * q^66 - 28 * q^67 - 20 * q^68 + 96 * q^69 + 6 * q^70 + 72 * q^71 + 15 * q^72 + 70 * q^73 + 42 * q^74 + 104 * q^75 + 16 * q^76 + 12 * q^77 + 72 * q^78 + 64 * q^79 + 6 * q^80 + 143 * q^81 + 54 * q^82 + 96 * q^83 + 8 * q^84 + 108 * q^85 + 60 * q^86 - 8 * q^87 + 12 * q^88 - 28 * q^89 + 78 * q^90 - 82 * q^91 + 24 * q^92 - 96 * q^93 + 24 * q^94 - 88 * q^95 - 324 * q^97 + 3 * q^98 - 364 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(742))\)

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
742.2.a	\(\chi_{742}(1, \cdot)\)	742.2.a.a	1	1
		742.2.a.b	1
		742.2.a.c	1
		742.2.a.d	1
		742.2.a.e	1
		742.2.a.f	1
		742.2.a.g	1
		742.2.a.h	2
		742.2.a.i	2
		742.2.a.j	2
		742.2.a.k	3
		742.2.a.l	3
		742.2.a.m	6
742.2.c	\(\chi_{742}(211, \cdot)\)	742.2.c.a	6	1
		742.2.c.b	8
		742.2.c.c	14
742.2.e	\(\chi_{742}(107, \cdot)\)	742.2.e.a	2	2
		742.2.e.b	2
		742.2.e.c	2
		742.2.e.d	4
		742.2.e.e	6
		742.2.e.f	8
		742.2.e.g	14
		742.2.e.h	16
		742.2.e.i	18
742.2.f	\(\chi_{742}(83, \cdot)\)	742.2.f.a	72	2
742.2.j	\(\chi_{742}(317, \cdot)\)	742.2.j.a	4	2
		742.2.j.b	68
742.2.k	\(\chi_{742}(129, \cdot)\)	742.2.k.a	144	4
742.2.m	\(\chi_{742}(15, \cdot)\)	742.2.m.a	72	12
		742.2.m.b	72
		742.2.m.c	84
		742.2.m.d	84
742.2.o	\(\chi_{742}(29, \cdot)\)	742.2.o.a	168	12
		742.2.o.b	168
742.2.q	\(\chi_{742}(81, \cdot)\)	742.2.q.a	432	24
		742.2.q.b	432
742.2.s	\(\chi_{742}(27, \cdot)\)	742.2.s.a	864	24
742.2.t	\(\chi_{742}(9, \cdot)\)	742.2.t.a	864	24
742.2.x	\(\chi_{742}(3, \cdot)\)	742.2.x.a	1728	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(742))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(742)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(371))\)\(^{\oplus 2}\)