Space of modular forms of level 1368 and weight 2

• Label: 1368.2
• Level: 1368
• Weight: 2
• Dimension: 22651
• Nonzero newspaces: 48
• Sturm bound: 207360
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 48 \)
Sturm bound:			\(207360\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1368))\).

	Total	New	Old
Modular forms	53568	23263	30305
Cusp forms	50113	22651	27462
Eisenstein series	3455	612	2843

Trace form

22651 * q - 50 * q^2 - 66 * q^3 - 50 * q^4 - 8 * q^5 - 56 * q^6 - 50 * q^7 - 26 * q^8 - 126 * q^9 - 114 * q^10 - 20 * q^11 - 44 * q^12 + 4 * q^13 - 26 * q^14 - 24 * q^15 - 34 * q^16 - 68 * q^17 - 72 * q^18 - 140 * q^19 - 128 * q^20 + 24 * q^21 - 82 * q^22 - 18 * q^23 - 120 * q^24 - 92 * q^25 - 110 * q^26 - 72 * q^27 - 178 * q^28 - 30 * q^29 - 164 * q^30 - 40 * q^31 - 130 * q^32 - 130 * q^33 - 26 * q^34 - 162 * q^35 - 172 * q^36 - 30 * q^37 - 92 * q^38 - 216 * q^39 - 74 * q^40 - 116 * q^41 - 172 * q^42 - 140 * q^43 - 138 * q^44 - 4 * q^45 - 194 * q^46 - 156 * q^47 - 112 * q^48 - 22 * q^49 - 110 * q^50 - 90 * q^51 - 2 * q^52 + 28 * q^53 - 48 * q^54 - 130 * q^55 + 10 * q^56 - 115 * q^57 - 88 * q^58 - 56 * q^59 + 60 * q^60 + 34 * q^61 + 164 * q^62 - 136 * q^63 + 22 * q^64 + 14 * q^65 + 136 * q^66 + 104 * q^67 + 240 * q^68 - 44 * q^69 + 254 * q^70 - 16 * q^71 + 132 * q^72 - 195 * q^73 + 310 * q^74 - 170 * q^75 + 160 * q^76 + 30 * q^77 + 76 * q^78 + 80 * q^79 + 282 * q^80 - 166 * q^81 + 68 * q^82 - 64 * q^83 + 56 * q^84 - 16 * q^85 + 172 * q^86 - 108 * q^87 + 62 * q^88 - 98 * q^89 - 44 * q^90 - 138 * q^91 - 72 * q^92 + 20 * q^93 - 66 * q^94 - 10 * q^95 - 240 * q^96 - 102 * q^97 - 246 * q^98 - 6 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1368))\)

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
1368.2.a	\(\chi_{1368}(1, \cdot)\)	1368.2.a.a	1	1
		1368.2.a.b	1
		1368.2.a.c	1
		1368.2.a.d	1
		1368.2.a.e	1
		1368.2.a.f	1
		1368.2.a.g	1
		1368.2.a.h	1
		1368.2.a.i	1
		1368.2.a.j	1
		1368.2.a.k	2
		1368.2.a.l	2
		1368.2.a.m	3
		1368.2.a.n	3
		1368.2.a.o	3
1368.2.d	\(\chi_{1368}(647, \cdot)\)	None	0	1
1368.2.e	\(\chi_{1368}(379, \cdot)\)	1368.2.e.a	2	1
		1368.2.e.b	4
		1368.2.e.c	8
		1368.2.e.d	8
		1368.2.e.e	12
		1368.2.e.f	24
		1368.2.e.g	40
1368.2.f	\(\chi_{1368}(1025, \cdot)\)	1368.2.f.a	2	1
		1368.2.f.b	2
		1368.2.f.c	8
		1368.2.f.d	8
1368.2.g	\(\chi_{1368}(685, \cdot)\)	1368.2.g.a	2	1
		1368.2.g.b	16
		1368.2.g.c	18
		1368.2.g.d	18
		1368.2.g.e	36
1368.2.j	\(\chi_{1368}(1331, \cdot)\)	1368.2.j.a	4	1
		1368.2.j.b	4
		1368.2.j.c	28
		1368.2.j.d	36
1368.2.k	\(\chi_{1368}(1063, \cdot)\)	None	0	1
1368.2.p	\(\chi_{1368}(341, \cdot)\)	1368.2.p.a	80	1
1368.2.q	\(\chi_{1368}(457, \cdot)\)	n/a	108	2
1368.2.r	\(\chi_{1368}(49, \cdot)\)	n/a	120	2
1368.2.s	\(\chi_{1368}(505, \cdot)\)	1368.2.s.a	2	2
		1368.2.s.b	2
		1368.2.s.c	2
		1368.2.s.d	2
		1368.2.s.e	2
		1368.2.s.f	2
		1368.2.s.g	2
		1368.2.s.h	4
		1368.2.s.i	4
		1368.2.s.j	6
		1368.2.s.k	6
		1368.2.s.l	8
		1368.2.s.m	8
1368.2.t	\(\chi_{1368}(121, \cdot)\)	n/a	120	2
1368.2.w	\(\chi_{1368}(277, \cdot)\)	n/a	472	2
1368.2.x	\(\chi_{1368}(65, \cdot)\)	n/a	120	2
1368.2.y	\(\chi_{1368}(331, \cdot)\)	n/a	472	2
1368.2.z	\(\chi_{1368}(311, \cdot)\)	None	0	2
1368.2.be	\(\chi_{1368}(487, \cdot)\)	None	0	2
1368.2.bf	\(\chi_{1368}(467, \cdot)\)	n/a	160	2
1368.2.bi	\(\chi_{1368}(797, \cdot)\)	n/a	472	2
1368.2.bl	\(\chi_{1368}(293, \cdot)\)	n/a	472	2
1368.2.bm	\(\chi_{1368}(103, \cdot)\)	None	0	2
1368.2.bn	\(\chi_{1368}(83, \cdot)\)	n/a	472	2
1368.2.bq	\(\chi_{1368}(419, \cdot)\)	n/a	432	2
1368.2.br	\(\chi_{1368}(151, \cdot)\)	None	0	2
1368.2.bu	\(\chi_{1368}(1133, \cdot)\)	n/a	160	2
1368.2.bx	\(\chi_{1368}(1171, \cdot)\)	n/a	196	2
1368.2.by	\(\chi_{1368}(1151, \cdot)\)	None	0	2
1368.2.cb	\(\chi_{1368}(349, \cdot)\)	n/a	472	2
1368.2.cc	\(\chi_{1368}(977, \cdot)\)	n/a	120	2
1368.2.cf	\(\chi_{1368}(113, \cdot)\)	n/a	120	2
1368.2.cg	\(\chi_{1368}(229, \cdot)\)	n/a	432	2
1368.2.cl	\(\chi_{1368}(191, \cdot)\)	None	0	2
1368.2.cm	\(\chi_{1368}(835, \cdot)\)	n/a	472	2
1368.2.cp	\(\chi_{1368}(259, \cdot)\)	n/a	472	2
1368.2.cq	\(\chi_{1368}(239, \cdot)\)	None	0	2
1368.2.ct	\(\chi_{1368}(1189, \cdot)\)	n/a	196	2
1368.2.cu	\(\chi_{1368}(449, \cdot)\)	1368.2.cu.a	20	2
		1368.2.cu.b	20
1368.2.cv	\(\chi_{1368}(221, \cdot)\)	n/a	472	2
1368.2.da	\(\chi_{1368}(31, \cdot)\)	None	0	2
1368.2.db	\(\chi_{1368}(11, \cdot)\)	n/a	472	2
1368.2.dc	\(\chi_{1368}(73, \cdot)\)	n/a	150	6
1368.2.dd	\(\chi_{1368}(25, \cdot)\)	n/a	360	6
1368.2.de	\(\chi_{1368}(169, \cdot)\)	n/a	360	6
1368.2.dg	\(\chi_{1368}(67, \cdot)\)	n/a	1416	6
1368.2.di	\(\chi_{1368}(23, \cdot)\)	None	0	6
1368.2.dj	\(\chi_{1368}(79, \cdot)\)	None	0	6
1368.2.dl	\(\chi_{1368}(275, \cdot)\)	n/a	1416	6
1368.2.dn	\(\chi_{1368}(41, \cdot)\)	n/a	360	6
1368.2.dp	\(\chi_{1368}(61, \cdot)\)	n/a	1416	6
1368.2.dt	\(\chi_{1368}(53, \cdot)\)	n/a	480	6
1368.2.du	\(\chi_{1368}(253, \cdot)\)	n/a	588	6
1368.2.dw	\(\chi_{1368}(89, \cdot)\)	n/a	120	6
1368.2.dz	\(\chi_{1368}(29, \cdot)\)	n/a	1416	6
1368.2.eb	\(\chi_{1368}(131, \cdot)\)	n/a	1416	6
1368.2.ed	\(\chi_{1368}(295, \cdot)\)	None	0	6
1368.2.eg	\(\chi_{1368}(91, \cdot)\)	n/a	588	6
1368.2.ei	\(\chi_{1368}(215, \cdot)\)	None	0	6
1368.2.ej	\(\chi_{1368}(127, \cdot)\)	None	0	6
1368.2.el	\(\chi_{1368}(35, \cdot)\)	n/a	480	6
1368.2.eo	\(\chi_{1368}(47, \cdot)\)	None	0	6
1368.2.eq	\(\chi_{1368}(211, \cdot)\)	n/a	1416	6
1368.2.et	\(\chi_{1368}(173, \cdot)\)	n/a	1416	6
1368.2.eu	\(\chi_{1368}(85, \cdot)\)	n/a	1416	6
1368.2.ew	\(\chi_{1368}(257, \cdot)\)	n/a	360	6

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1368))\) into lower level spaces

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