Space of modular forms of level 736 and weight 5

• Label: 736.5
• Level: 736
• Weight: 5
• Dimension: 37662
• Nonzero newspaces: 12
• Sturm bound: 168960
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(168960\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(736))\).

	Total	New	Old
Modular forms	68288	38082	30206
Cusp forms	66880	37662	29218
Eisenstein series	1408	420	988

Trace form

37662 * q - 80 * q^2 - 62 * q^3 - 80 * q^4 - 32 * q^5 - 80 * q^6 - 58 * q^7 - 80 * q^8 - 182 * q^9 + 320 * q^10 - 254 * q^11 - 1520 * q^12 - 544 * q^13 - 944 * q^14 - 50 * q^15 + 1160 * q^16 + 824 * q^17 + 3160 * q^18 + 1346 * q^19 + 2320 * q^20 + 1712 * q^21 - 3864 * q^22 + 1090 * q^23 - 5200 * q^24 - 3514 * q^25 + 5320 * q^26 - 11330 * q^27 + 5560 * q^28 - 3872 * q^29 + 4768 * q^30 - 66 * q^31 - 2600 * q^32 + 7708 * q^33 - 7288 * q^34 + 17990 * q^35 - 5944 * q^36 + 6880 * q^37 - 5120 * q^38 + 5318 * q^39 - 13608 * q^40 - 12888 * q^41 - 7400 * q^42 - 25726 * q^43 - 12512 * q^44 - 15768 * q^45 - 2996 * q^46 - 116 * q^47 + 9800 * q^48 + 12934 * q^49 + 6784 * q^50 + 4662 * q^51 + 16224 * q^52 + 26464 * q^53 + 51816 * q^54 + 23494 * q^55 + 46936 * q^56 - 11540 * q^57 + 29160 * q^58 + 5506 * q^59 - 1736 * q^60 - 35616 * q^61 - 30664 * q^62 - 66 * q^63 + 22648 * q^64 + 23316 * q^65 - 4592 * q^66 - 16062 * q^67 - 38008 * q^68 + 21164 * q^69 - 99552 * q^70 - 39994 * q^71 - 120704 * q^72 - 39256 * q^73 - 70832 * q^74 - 25206 * q^75 - 13392 * q^76 - 47312 * q^77 - 28224 * q^78 + 100302 * q^79 + 2872 * q^80 + 27886 * q^81 + 31920 * q^82 - 7742 * q^83 + 166504 * q^84 + 40328 * q^85 + 140200 * q^86 - 98618 * q^87 + 146280 * q^88 + 9000 * q^89 + 199768 * q^90 - 71460 * q^91 + 60288 * q^92 + 30928 * q^93 + 69336 * q^94 - 66 * q^95 - 91992 * q^96 - 31976 * q^97 - 171400 * q^98 + 87874 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(736))\)

We only show spaces with odd 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
736.5.d	\(\chi_{736}(415, \cdot)\)	736.5.d.a	44	1
		736.5.d.b	44
736.5.e	\(\chi_{736}(689, \cdot)\)	736.5.e.a	1	1
		736.5.e.b	1
		736.5.e.c	2
		736.5.e.d	6
		736.5.e.e	84
736.5.f	\(\chi_{736}(321, \cdot)\)	736.5.f.a	48	1
		736.5.f.b	48
736.5.g	\(\chi_{736}(47, \cdot)\)	736.5.g.a	88	1
736.5.k	\(\chi_{736}(137, \cdot)\)	None	0	2
736.5.l	\(\chi_{736}(231, \cdot)\)	None	0	2
736.5.o	\(\chi_{736}(139, \cdot)\)	n/a	1408	4
736.5.p	\(\chi_{736}(45, \cdot)\)	n/a	1528	4
736.5.s	\(\chi_{736}(239, \cdot)\)	n/a	940	10
736.5.t	\(\chi_{736}(33, \cdot)\)	n/a	960	10
736.5.u	\(\chi_{736}(17, \cdot)\)	n/a	940	10
736.5.v	\(\chi_{736}(31, \cdot)\)	n/a	960	10
736.5.y	\(\chi_{736}(39, \cdot)\)	None	0	20
736.5.z	\(\chi_{736}(57, \cdot)\)	None	0	20
736.5.bc	\(\chi_{736}(5, \cdot)\)	n/a	15280	40
736.5.bd	\(\chi_{736}(3, \cdot)\)	n/a	15280	40

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

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(736))\) into lower level spaces

\( S_{5}^{\mathrm{old}}(\Gamma_1(736)) \cong \) \(S_{5}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 5}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(184))\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(\Gamma_1(368))\)\(^{\oplus 2}\)