Space of modular forms of level 722 and weight 2

• Label: 722.2
• Level: 722
• Weight: 2
• Dimension: 5386
• Nonzero newspaces: 6
• Newform subspaces: 53
• Sturm bound: 64980
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 53 \)
Sturm bound:			\(64980\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(722))\).

	Total	New	Old
Modular forms	16749	5386	11363
Cusp forms	15742	5386	10356
Eisenstein series	1007	0	1007

Trace form

5386 * q + q^2 + 4 * q^3 + q^4 + 6 * q^5 + 4 * q^6 + 8 * q^7 + q^8 + 13 * q^9 + 6 * q^10 + 12 * q^11 - 8 * q^12 - 34 * q^13 - 28 * q^14 - 48 * q^15 + q^16 - 18 * q^17 - 41 * q^18 - 42 * q^19 - 30 * q^20 - 52 * q^21 - 42 * q^22 - 12 * q^23 + 4 * q^24 - 41 * q^25 - 22 * q^26 - 26 * q^27 - 4 * q^28 - 6 * q^29 + 24 * q^30 - 4 * q^31 + q^32 - 60 * q^33 + 18 * q^34 - 24 * q^35 + 13 * q^36 + 2 * q^37 - 52 * q^39 + 6 * q^40 + 6 * q^41 + 32 * q^42 - 40 * q^43 - 6 * q^44 - 138 * q^45 - 48 * q^46 - 96 * q^47 - 14 * q^48 - 63 * q^49 - 113 * q^50 - 126 * q^51 + 2 * q^52 - 90 * q^53 - 68 * q^54 - 72 * q^55 - 64 * q^56 - 90 * q^57 - 42 * q^58 - 120 * q^59 - 48 * q^60 - 94 * q^61 - 76 * q^62 - 88 * q^63 - 11 * q^64 - 132 * q^65 - 96 * q^66 - 88 * q^67 - 12 * q^69 - 24 * q^70 - 72 * q^71 - 5 * q^72 + 8 * q^73 + 38 * q^74 + 40 * q^75 + 24 * q^77 - 16 * q^78 - 76 * q^79 + 6 * q^80 - 77 * q^81 - 30 * q^82 - 60 * q^83 - 76 * q^84 - 36 * q^85 - 28 * q^86 - 240 * q^87 + 12 * q^88 - 54 * q^89 - 102 * q^90 - 80 * q^91 - 48 * q^92 - 172 * q^93 - 96 * q^94 - 90 * q^95 + 4 * q^96 - 82 * q^97 - 87 * q^98 - 258 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(722))\)

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
722.2.a	\(\chi_{722}(1, \cdot)\)	722.2.a.a	1	1
		722.2.a.b	1
		722.2.a.c	1
		722.2.a.d	1
		722.2.a.e	1
		722.2.a.f	1
		722.2.a.g	2
		722.2.a.h	2
		722.2.a.i	2
		722.2.a.j	2
		722.2.a.k	3
		722.2.a.l	3
		722.2.a.m	4
		722.2.a.n	4
722.2.c	\(\chi_{722}(429, \cdot)\)	722.2.c.a	2	2
		722.2.c.b	2
		722.2.c.c	2
		722.2.c.d	2
		722.2.c.e	2
		722.2.c.f	2
		722.2.c.g	2
		722.2.c.h	4
		722.2.c.i	4
		722.2.c.j	4
		722.2.c.k	6
		722.2.c.l	6
		722.2.c.m	8
		722.2.c.n	8
722.2.e	\(\chi_{722}(99, \cdot)\)	722.2.e.a	6	6
		722.2.e.b	6
		722.2.e.c	6
		722.2.e.d	6
		722.2.e.e	6
		722.2.e.f	6
		722.2.e.g	6
		722.2.e.h	6
		722.2.e.i	6
		722.2.e.j	6
		722.2.e.k	6
		722.2.e.l	6
		722.2.e.m	6
		722.2.e.n	12
		722.2.e.o	12
		722.2.e.p	12
		722.2.e.q	12
		722.2.e.r	24
		722.2.e.s	24
722.2.g	\(\chi_{722}(39, \cdot)\)	722.2.g.a	288	18
		722.2.g.b	306
722.2.i	\(\chi_{722}(7, \cdot)\)	722.2.i.a	576	36
		722.2.i.b	612
722.2.k	\(\chi_{722}(5, \cdot)\)	722.2.k.a	1620	108
		722.2.k.b	1728

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(722))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(722)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 2}\)