Space of modular forms of level 2112 and weight 4

• Label: 2112.4
• Level: 2112
• Weight: 4
• Dimension: 152532
• Nonzero newspaces: 32
• Sturm bound: 983040
• Trace bound: 33

Defining parameters

Level:	\( N \)	=	\( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(983040\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(2112))\).

	Total	New	Old
Modular forms	371520	153324	218196
Cusp forms	365760	152532	213228
Eisenstein series	5760	792	4968

Trace form

152532 * q - 48 * q^3 - 128 * q^4 - 64 * q^6 - 104 * q^7 - 80 * q^9 - 128 * q^10 - 40 * q^11 - 144 * q^12 + 160 * q^13 + 196 * q^15 - 128 * q^16 + 416 * q^17 - 64 * q^18 - 88 * q^21 + 800 * q^22 + 1936 * q^24 + 44 * q^25 - 160 * q^26 - 312 * q^27 - 3168 * q^28 - 1600 * q^29 - 4704 * q^30 - 1544 * q^31 - 4960 * q^32 - 928 * q^33 - 4288 * q^34 - 912 * q^35 - 1824 * q^36 - 192 * q^37 + 1760 * q^38 + 1148 * q^39 + 6432 * q^40 + 3776 * q^41 + 6256 * q^42 + 1520 * q^43 + 2000 * q^44 - 1112 * q^45 - 128 * q^46 - 64 * q^48 + 1148 * q^49 - 11424 * q^50 + 6100 * q^51 - 13376 * q^52 - 928 * q^54 + 1328 * q^55 + 1568 * q^56 + 516 * q^57 + 9376 * q^58 - 13760 * q^59 + 9728 * q^60 - 128 * q^61 + 11712 * q^62 - 5100 * q^63 + 24064 * q^64 - 8096 * q^65 + 5464 * q^66 - 24312 * q^67 + 8256 * q^68 - 1768 * q^69 + 7936 * q^70 - 1792 * q^71 - 64 * q^72 + 3936 * q^73 - 10528 * q^74 + 13904 * q^75 - 23936 * q^76 + 3504 * q^77 - 24384 * q^78 + 34552 * q^79 - 20064 * q^80 - 2544 * q^81 - 128 * q^82 + 5360 * q^83 - 8352 * q^84 + 4576 * q^85 + 2544 * q^87 - 144 * q^88 - 704 * q^89 + 18656 * q^90 - 6232 * q^91 + 272 * q^93 - 128 * q^94 - 15456 * q^95 + 25776 * q^96 - 13696 * q^97 + 784 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(2112))\)

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
2112.4.a	\(\chi_{2112}(1, \cdot)\)	2112.4.a.a	1	1
		2112.4.a.b	1
		2112.4.a.c	1
		2112.4.a.d	1
		2112.4.a.e	1
		2112.4.a.f	1
		2112.4.a.g	1
		2112.4.a.h	1
		2112.4.a.i	1
		2112.4.a.j	1
		2112.4.a.k	1
		2112.4.a.l	1
		2112.4.a.m	1
		2112.4.a.n	1
		2112.4.a.o	1
		2112.4.a.p	1
		2112.4.a.q	1
		2112.4.a.r	1
		2112.4.a.s	1
		2112.4.a.t	1
		2112.4.a.u	1
		2112.4.a.v	1
		2112.4.a.w	1
		2112.4.a.x	1
		2112.4.a.y	1
		2112.4.a.z	1
		2112.4.a.ba	2
		2112.4.a.bb	2
		2112.4.a.bc	2
		2112.4.a.bd	2
		2112.4.a.be	2
		2112.4.a.bf	2
		2112.4.a.bg	2
		2112.4.a.bh	2
		2112.4.a.bi	2
		2112.4.a.bj	2
		2112.4.a.bk	2
		2112.4.a.bl	2
		2112.4.a.bm	2
		2112.4.a.bn	2
		2112.4.a.bo	3
		2112.4.a.bp	3
		2112.4.a.bq	3
		2112.4.a.br	3
		2112.4.a.bs	3
		2112.4.a.bt	3
		2112.4.a.bu	3
		2112.4.a.bv	3
		2112.4.a.bw	3
		2112.4.a.bx	3
		2112.4.a.by	4
		2112.4.a.bz	4
		2112.4.a.ca	4
		2112.4.a.cb	4
		2112.4.a.cc	5
		2112.4.a.cd	5
		2112.4.a.ce	5
		2112.4.a.cf	5
2112.4.b	\(\chi_{2112}(65, \cdot)\)	n/a	284	1
2112.4.d	\(\chi_{2112}(1343, \cdot)\)	n/a	240	1
2112.4.f	\(\chi_{2112}(1057, \cdot)\)	n/a	120	1
2112.4.h	\(\chi_{2112}(1759, \cdot)\)	n/a	144	1
2112.4.k	\(\chi_{2112}(287, \cdot)\)	n/a	240	1
2112.4.m	\(\chi_{2112}(1121, \cdot)\)	n/a	288	1
2112.4.o	\(\chi_{2112}(703, \cdot)\)	n/a	144	1
2112.4.q	\(\chi_{2112}(175, \cdot)\)	n/a	288	2
2112.4.t	\(\chi_{2112}(529, \cdot)\)	n/a	240	2
2112.4.u	\(\chi_{2112}(815, \cdot)\)	n/a	480	2
2112.4.x	\(\chi_{2112}(593, \cdot)\)	n/a	568	2
2112.4.y	\(\chi_{2112}(577, \cdot)\)	n/a	576	4
2112.4.bb	\(\chi_{2112}(265, \cdot)\)	None	0	4
2112.4.bc	\(\chi_{2112}(329, \cdot)\)	None	0	4
2112.4.bd	\(\chi_{2112}(23, \cdot)\)	None	0	4
2112.4.be	\(\chi_{2112}(439, \cdot)\)	None	0	4
2112.4.bi	\(\chi_{2112}(127, \cdot)\)	n/a	576	4
2112.4.bk	\(\chi_{2112}(161, \cdot)\)	n/a	1152	4
2112.4.bm	\(\chi_{2112}(863, \cdot)\)	n/a	1152	4
2112.4.bp	\(\chi_{2112}(415, \cdot)\)	n/a	576	4
2112.4.br	\(\chi_{2112}(97, \cdot)\)	n/a	576	4
2112.4.bt	\(\chi_{2112}(191, \cdot)\)	n/a	1136	4
2112.4.bv	\(\chi_{2112}(833, \cdot)\)	n/a	1136	4
2112.4.by	\(\chi_{2112}(197, \cdot)\)	n/a	9184	8
2112.4.bz	\(\chi_{2112}(133, \cdot)\)	n/a	3840	8
2112.4.ca	\(\chi_{2112}(155, \cdot)\)	n/a	7680	8
2112.4.cb	\(\chi_{2112}(43, \cdot)\)	n/a	4608	8
2112.4.ce	\(\chi_{2112}(17, \cdot)\)	n/a	2272	8
2112.4.ch	\(\chi_{2112}(47, \cdot)\)	n/a	2272	8
2112.4.ci	\(\chi_{2112}(49, \cdot)\)	n/a	1152	8
2112.4.cl	\(\chi_{2112}(79, \cdot)\)	n/a	1152	8
2112.4.co	\(\chi_{2112}(7, \cdot)\)	None	0	16
2112.4.cp	\(\chi_{2112}(71, \cdot)\)	None	0	16
2112.4.cq	\(\chi_{2112}(41, \cdot)\)	None	0	16
2112.4.cr	\(\chi_{2112}(25, \cdot)\)	None	0	16
2112.4.cu	\(\chi_{2112}(19, \cdot)\)	n/a	18432	32
2112.4.cv	\(\chi_{2112}(59, \cdot)\)	n/a	36736	32
2112.4.da	\(\chi_{2112}(37, \cdot)\)	n/a	18432	32
2112.4.db	\(\chi_{2112}(29, \cdot)\)	n/a	36736	32

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(2112))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(2112)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 7}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(264))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(528))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(1056))\)\(^{\oplus 2}\)