Space of modular forms of level 726 and weight 2

• Label: 726.2
• Level: 726
• Weight: 2
• Dimension: 3569
• Nonzero newspaces: 8
• Newform subspaces: 61
• Sturm bound: 58080
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 726 = 2 \cdot 3 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 61 \)
Sturm bound:			\(58080\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(726))\).

	Total	New	Old
Modular forms	15160	3569	11591
Cusp forms	13881	3569	10312
Eisenstein series	1279	0	1279

Trace form

3569 * q - q^2 - q^3 - q^4 - 6 * q^5 + 9 * q^6 + 32 * q^7 - q^8 + 39 * q^9 + 34 * q^10 + 20 * q^11 + 19 * q^12 + 26 * q^13 + 32 * q^14 + 54 * q^15 - q^16 + 62 * q^17 + 9 * q^18 + 40 * q^19 - 6 * q^20 + 32 * q^21 + 16 * q^23 - 11 * q^24 + 49 * q^25 - 14 * q^26 - 61 * q^27 - 8 * q^28 + 10 * q^29 - 66 * q^30 + 8 * q^31 - q^32 - 45 * q^33 - 18 * q^34 - 8 * q^35 - 11 * q^36 - 38 * q^37 - 20 * q^38 - 34 * q^39 - 6 * q^40 - 2 * q^41 - 28 * q^42 + 76 * q^43 + 20 * q^44 - 6 * q^45 + 56 * q^46 + 112 * q^47 - q^48 + 183 * q^49 + 49 * q^50 + 92 * q^51 + 66 * q^52 + 66 * q^53 + 19 * q^54 + 100 * q^55 - 8 * q^56 - 10 * q^57 + 130 * q^58 + 60 * q^59 + 34 * q^60 + 138 * q^61 + 88 * q^62 + 12 * q^63 - q^64 + 156 * q^65 + 60 * q^66 + 132 * q^67 + 62 * q^68 + 36 * q^69 + 112 * q^70 + 88 * q^71 + 39 * q^72 + 86 * q^73 + 42 * q^74 + 59 * q^75 + 20 * q^76 + 80 * q^77 + 66 * q^78 + 40 * q^79 + 34 * q^80 + 79 * q^81 - 22 * q^82 + 36 * q^83 - 8 * q^84 + 12 * q^85 + 76 * q^86 - 30 * q^87 + 20 * q^88 + 30 * q^89 - 26 * q^90 - 192 * q^91 - 24 * q^92 + 28 * q^93 - 128 * q^94 - q^96 - 38 * q^97 - 57 * q^98 - 30 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)

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
726.2.a	\(\chi_{726}(1, \cdot)\)	726.2.a.a	1	1
		726.2.a.b	1
		726.2.a.c	1
		726.2.a.d	1
		726.2.a.e	1
		726.2.a.f	1
		726.2.a.g	1
		726.2.a.h	1
		726.2.a.i	1
		726.2.a.j	2
		726.2.a.k	2
		726.2.a.l	2
		726.2.a.m	2
726.2.b	\(\chi_{726}(725, \cdot)\)	726.2.b.a	2	1
		726.2.b.b	2
		726.2.b.c	8
		726.2.b.d	8
		726.2.b.e	8
		726.2.b.f	8
726.2.e	\(\chi_{726}(487, \cdot)\)	726.2.e.a	4	4
		726.2.e.b	4
		726.2.e.c	4
		726.2.e.d	4
		726.2.e.e	4
		726.2.e.f	4
		726.2.e.g	4
		726.2.e.h	4
		726.2.e.i	4
		726.2.e.j	4
		726.2.e.k	4
		726.2.e.l	4
		726.2.e.m	4
		726.2.e.n	4
		726.2.e.o	4
		726.2.e.p	4
		726.2.e.q	4
		726.2.e.r	4
726.2.h	\(\chi_{726}(161, \cdot)\)	726.2.h.a	8	4
		726.2.h.b	8
		726.2.h.c	8
		726.2.h.d	8
		726.2.h.e	8
		726.2.h.f	8
		726.2.h.g	8
		726.2.h.h	8
		726.2.h.i	8
		726.2.h.j	8
		726.2.h.k	32
		726.2.h.l	32
726.2.i	\(\chi_{726}(67, \cdot)\)	726.2.i.a	50	10
		726.2.i.b	50
		726.2.i.c	60
		726.2.i.d	60
726.2.l	\(\chi_{726}(65, \cdot)\)	726.2.l.a	220	10
		726.2.l.b	220
726.2.m	\(\chi_{726}(25, \cdot)\)	726.2.m.a	200	40
		726.2.m.b	200
		726.2.m.c	240
		726.2.m.d	240
726.2.n	\(\chi_{726}(17, \cdot)\)	726.2.n.a	880	40
		726.2.n.b	880

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(726))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(726)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 2}\)