Space of modular forms of level 2376 and weight 2

• Label: 2376.2
• Level: 2376
• Weight: 2
• Dimension: 67392
• Nonzero newspaces: 36
• Sturm bound: 622080
• Trace bound: 17

Defining parameters

Level:	\( N \)	=	\( 2376 = 2^{3} \cdot 3^{3} \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(622080\)
Trace bound:			\(17\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2376))\).

	Total	New	Old
Modular forms	159120	68544	90576
Cusp forms	151921	67392	84529
Eisenstein series	7199	1152	6047

Trace form

67392 * q - 64 * q^2 - 96 * q^3 - 112 * q^4 + 4 * q^5 - 96 * q^6 - 112 * q^7 - 76 * q^8 - 192 * q^9 - 128 * q^10 - 84 * q^11 - 216 * q^12 - 20 * q^13 - 76 * q^14 - 120 * q^15 - 120 * q^16 - 180 * q^17 - 96 * q^18 - 144 * q^19 - 52 * q^20 - 24 * q^21 - 106 * q^22 - 196 * q^23 - 60 * q^24 - 246 * q^25 + 20 * q^26 - 66 * q^27 - 168 * q^28 + 60 * q^29 - 72 * q^31 + 156 * q^32 - 207 * q^33 - 156 * q^34 + 100 * q^35 + 24 * q^36 + 60 * q^37 + 156 * q^38 - 24 * q^39 + 8 * q^40 - 84 * q^41 + 24 * q^42 - 40 * q^43 + 22 * q^44 + 108 * q^45 - 40 * q^46 + 88 * q^47 - 60 * q^48 - 290 * q^49 + 56 * q^50 + 24 * q^51 - 88 * q^52 - 96 * q^54 - 302 * q^55 - 300 * q^56 - 102 * q^57 - 192 * q^58 + 40 * q^59 - 216 * q^60 - 12 * q^61 - 324 * q^62 + 96 * q^63 - 232 * q^64 - 76 * q^65 - 198 * q^66 - 220 * q^67 - 380 * q^68 + 96 * q^69 - 360 * q^70 + 100 * q^71 - 264 * q^72 - 236 * q^73 - 388 * q^74 + 36 * q^75 - 360 * q^76 - 56 * q^77 - 444 * q^78 - 64 * q^79 - 428 * q^80 - 168 * q^81 - 336 * q^82 + 50 * q^83 - 228 * q^84 + 8 * q^85 - 252 * q^86 - 84 * q^87 - 130 * q^88 - 370 * q^89 - 372 * q^90 - 68 * q^91 - 188 * q^92 - 144 * q^93 - 56 * q^94 - 160 * q^95 - 408 * q^96 - 196 * q^97 - 308 * q^98 - 246 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2376))\)

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
2376.2.a	\(\chi_{2376}(1, \cdot)\)	2376.2.a.a	1	1
		2376.2.a.b	1
		2376.2.a.c	1
		2376.2.a.d	1
		2376.2.a.e	2
		2376.2.a.f	2
		2376.2.a.g	2
		2376.2.a.h	2
		2376.2.a.i	2
		2376.2.a.j	2
		2376.2.a.k	3
		2376.2.a.l	3
		2376.2.a.m	3
		2376.2.a.n	3
		2376.2.a.o	3
		2376.2.a.p	3
		2376.2.a.q	3
		2376.2.a.r	3
2376.2.b	\(\chi_{2376}(593, \cdot)\)	2376.2.b.a	12	1
		2376.2.b.b	12
		2376.2.b.c	12
		2376.2.b.d	12
2376.2.d	\(\chi_{2376}(1079, \cdot)\)	None	0	1
2376.2.f	\(\chi_{2376}(1189, \cdot)\)	n/a	160	1
2376.2.h	\(\chi_{2376}(1891, \cdot)\)	n/a	192	1
2376.2.k	\(\chi_{2376}(2267, \cdot)\)	n/a	160	1
2376.2.m	\(\chi_{2376}(1781, \cdot)\)	n/a	192	1
2376.2.o	\(\chi_{2376}(703, \cdot)\)	None	0	1
2376.2.q	\(\chi_{2376}(793, \cdot)\)	2376.2.q.a	2	2
		2376.2.q.b	2
		2376.2.q.c	2
		2376.2.q.d	4
		2376.2.q.e	6
		2376.2.q.f	12
		2376.2.q.g	16
		2376.2.q.h	16
2376.2.r	\(\chi_{2376}(433, \cdot)\)	n/a	192	4
2376.2.u	\(\chi_{2376}(1495, \cdot)\)	None	0	2
2376.2.w	\(\chi_{2376}(197, \cdot)\)	n/a	280	2
2376.2.y	\(\chi_{2376}(683, \cdot)\)	n/a	240	2
2376.2.z	\(\chi_{2376}(307, \cdot)\)	n/a	280	2
2376.2.bb	\(\chi_{2376}(397, \cdot)\)	n/a	240	2
2376.2.bd	\(\chi_{2376}(287, \cdot)\)	None	0	2
2376.2.bf	\(\chi_{2376}(1385, \cdot)\)	2376.2.bf.a	36	2
		2376.2.bf.b	36
2376.2.bh	\(\chi_{2376}(265, \cdot)\)	n/a	540	6
2376.2.bj	\(\chi_{2376}(271, \cdot)\)	None	0	4
2376.2.bl	\(\chi_{2376}(701, \cdot)\)	n/a	768	4
2376.2.bn	\(\chi_{2376}(323, \cdot)\)	n/a	768	4
2376.2.bq	\(\chi_{2376}(811, \cdot)\)	n/a	768	4
2376.2.bs	\(\chi_{2376}(757, \cdot)\)	n/a	768	4
2376.2.bu	\(\chi_{2376}(647, \cdot)\)	None	0	4
2376.2.bw	\(\chi_{2376}(161, \cdot)\)	n/a	192	4
2376.2.bx	\(\chi_{2376}(289, \cdot)\)	n/a	288	8
2376.2.ca	\(\chi_{2376}(461, \cdot)\)	n/a	2568	6
2376.2.cb	\(\chi_{2376}(65, \cdot)\)	n/a	648	6
2376.2.ce	\(\chi_{2376}(133, \cdot)\)	n/a	2160	6
2376.2.cf	\(\chi_{2376}(175, \cdot)\)	None	0	6
2376.2.ci	\(\chi_{2376}(155, \cdot)\)	n/a	2160	6
2376.2.cj	\(\chi_{2376}(23, \cdot)\)	None	0	6
2376.2.cm	\(\chi_{2376}(43, \cdot)\)	n/a	2568	6
2376.2.co	\(\chi_{2376}(17, \cdot)\)	n/a	288	8
2376.2.cq	\(\chi_{2376}(71, \cdot)\)	None	0	8
2376.2.cs	\(\chi_{2376}(37, \cdot)\)	n/a	1120	8
2376.2.cu	\(\chi_{2376}(19, \cdot)\)	n/a	1120	8
2376.2.cv	\(\chi_{2376}(179, \cdot)\)	n/a	1120	8
2376.2.cx	\(\chi_{2376}(413, \cdot)\)	n/a	1120	8
2376.2.cz	\(\chi_{2376}(127, \cdot)\)	None	0	8
2376.2.dc	\(\chi_{2376}(25, \cdot)\)	n/a	2592	24
2376.2.dd	\(\chi_{2376}(139, \cdot)\)	n/a	10272	24
2376.2.dg	\(\chi_{2376}(47, \cdot)\)	None	0	24
2376.2.dh	\(\chi_{2376}(59, \cdot)\)	n/a	10272	24
2376.2.dk	\(\chi_{2376}(7, \cdot)\)	None	0	24
2376.2.dl	\(\chi_{2376}(157, \cdot)\)	n/a	10272	24
2376.2.do	\(\chi_{2376}(41, \cdot)\)	n/a	2592	24
2376.2.dp	\(\chi_{2376}(29, \cdot)\)	n/a	10272	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2376))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2376)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(297))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(594))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(792))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1188))\)\(^{\oplus 2}\)