Space of modular forms of level 1368 and weight 4

• Label: 1368.4
• Level: 1368
• Weight: 4
• Dimension: 68563
• Nonzero newspaces: 48
• Sturm bound: 414720
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(414720\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(1368))\).

	Total	New	Old
Modular forms	157248	69175	88073
Cusp forms	153792	68563	85229
Eisenstein series	3456	612	2844

Trace form

68563 * q - 46 * q^2 - 66 * q^3 - 26 * q^4 + 44 * q^5 - 32 * q^6 + 30 * q^7 - 106 * q^8 - 186 * q^9 - 322 * q^10 - 268 * q^11 - 284 * q^12 - 128 * q^13 - 346 * q^14 - 120 * q^15 - 322 * q^16 + 176 * q^17 + 168 * q^18 + 24 * q^19 + 800 * q^20 - 456 * q^21 + 1190 * q^22 - 546 * q^23 + 456 * q^24 - 126 * q^25 - 118 * q^26 - 648 * q^27 + 142 * q^28 - 246 * q^29 - 308 * q^30 - 80 * q^31 - 386 * q^32 + 794 * q^33 - 2818 * q^34 + 1950 * q^35 + 1460 * q^36 + 1002 * q^37 - 448 * q^38 + 408 * q^39 - 1674 * q^40 + 1736 * q^41 + 164 * q^42 + 3212 * q^43 + 2022 * q^44 - 892 * q^45 + 5230 * q^46 + 1644 * q^47 + 1520 * q^48 - 3224 * q^49 + 6182 * q^50 - 762 * q^51 + 3070 * q^52 - 3880 * q^53 - 1320 * q^54 - 3762 * q^55 - 5302 * q^56 - 1681 * q^57 - 9704 * q^58 - 8752 * q^59 - 1668 * q^60 + 3634 * q^61 + 976 * q^62 - 2440 * q^63 + 4246 * q^64 + 2074 * q^65 - 5072 * q^66 + 1248 * q^67 + 1272 * q^68 + 7420 * q^69 + 3030 * q^70 + 9040 * q^71 - 1980 * q^72 - 3093 * q^73 - 7570 * q^74 + 11686 * q^75 - 12312 * q^76 - 1422 * q^77 - 7964 * q^78 - 15584 * q^79 - 24294 * q^80 - 4018 * q^81 - 26880 * q^82 - 15824 * q^83 - 376 * q^84 - 2488 * q^85 + 4064 * q^86 - 14172 * q^87 + 2750 * q^88 - 3562 * q^89 - 3812 * q^90 + 15894 * q^91 + 19584 * q^92 - 7492 * q^93 + 19662 * q^94 + 29686 * q^95 + 7920 * q^96 + 18186 * q^97 + 20598 * q^98 + 27066 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(1368))\)

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
1368.4.a	\(\chi_{1368}(1, \cdot)\)	1368.4.a.a	2	1
		1368.4.a.b	2
		1368.4.a.c	2
		1368.4.a.d	3
		1368.4.a.e	3
		1368.4.a.f	3
		1368.4.a.g	4
		1368.4.a.h	4
		1368.4.a.i	4
		1368.4.a.j	4
		1368.4.a.k	5
		1368.4.a.l	5
		1368.4.a.m	5
		1368.4.a.n	5
		1368.4.a.o	8
		1368.4.a.p	8
1368.4.d	\(\chi_{1368}(647, \cdot)\)	None	0	1
1368.4.e	\(\chi_{1368}(379, \cdot)\)	n/a	298	1
1368.4.f	\(\chi_{1368}(1025, \cdot)\)	1368.4.f.a	30	1
		1368.4.f.b	30
1368.4.g	\(\chi_{1368}(685, \cdot)\)	n/a	270	1
1368.4.j	\(\chi_{1368}(1331, \cdot)\)	n/a	216	1
1368.4.k	\(\chi_{1368}(1063, \cdot)\)	None	0	1
1368.4.p	\(\chi_{1368}(341, \cdot)\)	n/a	240	1
1368.4.q	\(\chi_{1368}(457, \cdot)\)	n/a	324	2
1368.4.r	\(\chi_{1368}(49, \cdot)\)	n/a	360	2
1368.4.s	\(\chi_{1368}(505, \cdot)\)	n/a	150	2
1368.4.t	\(\chi_{1368}(121, \cdot)\)	n/a	360	2
1368.4.w	\(\chi_{1368}(277, \cdot)\)	n/a	1432	2
1368.4.x	\(\chi_{1368}(65, \cdot)\)	n/a	360	2
1368.4.y	\(\chi_{1368}(331, \cdot)\)	n/a	1432	2
1368.4.z	\(\chi_{1368}(311, \cdot)\)	None	0	2
1368.4.be	\(\chi_{1368}(487, \cdot)\)	None	0	2
1368.4.bf	\(\chi_{1368}(467, \cdot)\)	n/a	480	2
1368.4.bi	\(\chi_{1368}(797, \cdot)\)	n/a	1432	2
1368.4.bl	\(\chi_{1368}(293, \cdot)\)	n/a	1432	2
1368.4.bm	\(\chi_{1368}(103, \cdot)\)	None	0	2
1368.4.bn	\(\chi_{1368}(83, \cdot)\)	n/a	1432	2
1368.4.bq	\(\chi_{1368}(419, \cdot)\)	n/a	1296	2
1368.4.br	\(\chi_{1368}(151, \cdot)\)	None	0	2
1368.4.bu	\(\chi_{1368}(1133, \cdot)\)	n/a	480	2
1368.4.bx	\(\chi_{1368}(1171, \cdot)\)	n/a	596	2
1368.4.by	\(\chi_{1368}(1151, \cdot)\)	None	0	2
1368.4.cb	\(\chi_{1368}(349, \cdot)\)	n/a	1432	2
1368.4.cc	\(\chi_{1368}(977, \cdot)\)	n/a	360	2
1368.4.cf	\(\chi_{1368}(113, \cdot)\)	n/a	360	2
1368.4.cg	\(\chi_{1368}(229, \cdot)\)	n/a	1296	2
1368.4.cl	\(\chi_{1368}(191, \cdot)\)	None	0	2
1368.4.cm	\(\chi_{1368}(835, \cdot)\)	n/a	1432	2
1368.4.cp	\(\chi_{1368}(259, \cdot)\)	n/a	1432	2
1368.4.cq	\(\chi_{1368}(239, \cdot)\)	None	0	2
1368.4.ct	\(\chi_{1368}(1189, \cdot)\)	n/a	596	2
1368.4.cu	\(\chi_{1368}(449, \cdot)\)	n/a	120	2
1368.4.cv	\(\chi_{1368}(221, \cdot)\)	n/a	1432	2
1368.4.da	\(\chi_{1368}(31, \cdot)\)	None	0	2
1368.4.db	\(\chi_{1368}(11, \cdot)\)	n/a	1432	2
1368.4.dc	\(\chi_{1368}(73, \cdot)\)	n/a	450	6
1368.4.dd	\(\chi_{1368}(25, \cdot)\)	n/a	1080	6
1368.4.de	\(\chi_{1368}(169, \cdot)\)	n/a	1080	6
1368.4.dg	\(\chi_{1368}(67, \cdot)\)	n/a	4296	6
1368.4.di	\(\chi_{1368}(23, \cdot)\)	None	0	6
1368.4.dj	\(\chi_{1368}(79, \cdot)\)	None	0	6
1368.4.dl	\(\chi_{1368}(275, \cdot)\)	n/a	4296	6
1368.4.dn	\(\chi_{1368}(41, \cdot)\)	n/a	1080	6
1368.4.dp	\(\chi_{1368}(61, \cdot)\)	n/a	4296	6
1368.4.dt	\(\chi_{1368}(53, \cdot)\)	n/a	1440	6
1368.4.du	\(\chi_{1368}(253, \cdot)\)	n/a	1788	6
1368.4.dw	\(\chi_{1368}(89, \cdot)\)	n/a	360	6
1368.4.dz	\(\chi_{1368}(29, \cdot)\)	n/a	4296	6
1368.4.eb	\(\chi_{1368}(131, \cdot)\)	n/a	4296	6
1368.4.ed	\(\chi_{1368}(295, \cdot)\)	None	0	6
1368.4.eg	\(\chi_{1368}(91, \cdot)\)	n/a	1788	6
1368.4.ei	\(\chi_{1368}(215, \cdot)\)	None	0	6
1368.4.ej	\(\chi_{1368}(127, \cdot)\)	None	0	6
1368.4.el	\(\chi_{1368}(35, \cdot)\)	n/a	1440	6
1368.4.eo	\(\chi_{1368}(47, \cdot)\)	None	0	6
1368.4.eq	\(\chi_{1368}(211, \cdot)\)	n/a	4296	6
1368.4.et	\(\chi_{1368}(173, \cdot)\)	n/a	4296	6
1368.4.eu	\(\chi_{1368}(85, \cdot)\)	n/a	4296	6
1368.4.ew	\(\chi_{1368}(257, \cdot)\)	n/a	1080	6

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(1368))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(1368)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 2}\)