Space of modular forms of level 736 and weight 4

• Label: 736.4
• Level: 736
• Weight: 4
• Dimension: 28194
• Nonzero newspaces: 12
• Sturm bound: 135168
• Trace bound: 9

Defining parameters

Level:	\( N \)	=	\( 736 = 2^{5} \cdot 23 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 12 \)
Sturm bound:			\(135168\)
Trace bound:			\(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(736))\).

	Total	New	Old
Modular forms	51392	28614	22778
Cusp forms	49984	28194	21790
Eisenstein series	1408	420	988

Trace form

28194 * q - 80 * q^2 - 58 * q^3 - 80 * q^4 - 84 * q^5 - 80 * q^6 - 90 * q^7 - 80 * q^8 - 214 * q^9 - 320 * q^10 - 58 * q^11 + 16 * q^12 + 156 * q^13 + 336 * q^14 + 158 * q^15 + 520 * q^16 + 320 * q^17 + 280 * q^18 - 58 * q^19 - 240 * q^20 - 592 * q^21 - 472 * q^22 - 694 * q^23 - 80 * q^24 - 794 * q^25 - 120 * q^26 + 470 * q^27 - 840 * q^28 + 316 * q^29 - 2464 * q^30 + 2334 * q^31 - 1320 * q^32 + 740 * q^33 - 1144 * q^34 + 854 * q^35 - 3000 * q^36 - 1748 * q^37 - 2048 * q^38 - 2378 * q^39 + 984 * q^40 - 1024 * q^41 + 4440 * q^42 - 1674 * q^43 + 4000 * q^44 + 2372 * q^45 + 1356 * q^46 + 1212 * q^47 + 4808 * q^48 + 2106 * q^49 + 7040 * q^50 + 2702 * q^51 + 4960 * q^52 - 980 * q^53 + 2088 * q^54 - 154 * q^55 - 2472 * q^56 - 2188 * q^57 - 6488 * q^58 - 2810 * q^59 - 11592 * q^60 + 1788 * q^61 - 6856 * q^62 - 5058 * q^63 - 9992 * q^64 - 3652 * q^65 - 12080 * q^66 - 4138 * q^67 - 5624 * q^68 + 204 * q^69 - 2976 * q^70 - 794 * q^71 + 3328 * q^72 + 1376 * q^73 + 6864 * q^74 + 3358 * q^75 + 10160 * q^76 - 1328 * q^77 + 23744 * q^78 - 1922 * q^79 + 20536 * q^80 + 2954 * q^81 + 12720 * q^82 - 4938 * q^83 + 13032 * q^84 + 1856 * q^85 + 1768 * q^86 + 5878 * q^87 - 2584 * q^88 + 3456 * q^89 - 14888 * q^90 + 7120 * q^91 - 10240 * q^92 - 10192 * q^93 - 25768 * q^94 + 10542 * q^95 - 35672 * q^96 - 4928 * q^97 - 22536 * q^98 + 10782 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(736))\)

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
736.4.a	\(\chi_{736}(1, \cdot)\)	736.4.a.a	3	1
		736.4.a.b	3
		736.4.a.c	4
		736.4.a.d	4
		736.4.a.e	8
		736.4.a.f	8
		736.4.a.g	9
		736.4.a.h	9
		736.4.a.i	9
		736.4.a.j	9
736.4.b	\(\chi_{736}(369, \cdot)\)	736.4.b.a	30	1
		736.4.b.b	36
736.4.c	\(\chi_{736}(735, \cdot)\)	736.4.c.a	72	1
736.4.h	\(\chi_{736}(367, \cdot)\)	736.4.h.a	2	1
		736.4.h.b	4
		736.4.h.c	64
736.4.i	\(\chi_{736}(183, \cdot)\)	None	0	2
736.4.j	\(\chi_{736}(185, \cdot)\)	None	0	2
736.4.m	\(\chi_{736}(93, \cdot)\)	n/a	1056	4
736.4.n	\(\chi_{736}(91, \cdot)\)	n/a	1144	4
736.4.q	\(\chi_{736}(193, \cdot)\)	n/a	720	10
736.4.r	\(\chi_{736}(15, \cdot)\)	n/a	700	10
736.4.w	\(\chi_{736}(63, \cdot)\)	n/a	720	10
736.4.x	\(\chi_{736}(49, \cdot)\)	n/a	700	10
736.4.ba	\(\chi_{736}(9, \cdot)\)	None	0	20
736.4.bb	\(\chi_{736}(7, \cdot)\)	None	0	20
736.4.be	\(\chi_{736}(11, \cdot)\)	n/a	11440	40
736.4.bf	\(\chi_{736}(13, \cdot)\)	n/a	11440	40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(736))\) into lower level spaces

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