Space of modular forms of level 3888 and weight 2

• Label: 3888.2
• Level: 3888
• Weight: 2
• Dimension: 185760
• Nonzero newspaces: 20
• Sturm bound: 1679616
• Trace bound: 46

Defining parameters

Level:	\( N \)	=	\( 3888 = 2^{4} \cdot 3^{5} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Sturm bound:			\(1679616\)
Trace bound:			\(46\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3888))\).

	Total	New	Old
Modular forms	425196	187488	237708
Cusp forms	414613	185760	228853
Eisenstein series	10583	1728	8855

Trace form

185760 * q - 144 * q^2 - 162 * q^3 - 240 * q^4 - 180 * q^5 - 216 * q^6 - 180 * q^7 - 144 * q^8 - 54 * q^9 - 336 * q^10 - 108 * q^11 - 216 * q^12 - 300 * q^13 - 144 * q^14 - 162 * q^15 - 240 * q^16 - 324 * q^17 - 216 * q^18 - 252 * q^19 - 144 * q^20 - 270 * q^21 - 240 * q^22 - 108 * q^23 - 216 * q^24 - 60 * q^25 - 144 * q^26 - 162 * q^27 - 444 * q^28 - 180 * q^29 - 216 * q^30 - 180 * q^31 - 144 * q^32 - 486 * q^33 - 240 * q^34 - 108 * q^35 - 216 * q^36 - 420 * q^37 - 144 * q^38 - 162 * q^39 - 240 * q^40 - 36 * q^41 - 216 * q^42 - 180 * q^43 - 144 * q^44 - 270 * q^45 - 336 * q^46 - 108 * q^47 - 216 * q^48 - 540 * q^49 - 144 * q^50 - 162 * q^51 - 240 * q^52 - 189 * q^53 - 216 * q^54 - 333 * q^55 - 144 * q^56 - 54 * q^57 - 240 * q^58 - 108 * q^59 - 216 * q^60 - 300 * q^61 - 144 * q^62 - 162 * q^63 - 336 * q^64 - 324 * q^65 - 216 * q^66 - 180 * q^67 - 144 * q^68 - 270 * q^69 - 240 * q^70 - 108 * q^71 - 216 * q^72 - 84 * q^73 - 144 * q^74 - 162 * q^75 - 240 * q^76 - 180 * q^77 - 216 * q^78 - 180 * q^79 - 144 * q^80 - 486 * q^81 - 444 * q^82 - 108 * q^83 - 216 * q^84 - 330 * q^85 - 144 * q^86 - 162 * q^87 - 240 * q^88 - 72 * q^89 - 216 * q^90 - 306 * q^91 - 144 * q^92 - 270 * q^93 - 240 * q^94 - 270 * q^95 - 216 * q^96 - 612 * q^97 - 144 * q^98 - 162 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3888))\)

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
3888.2.a	\(\chi_{3888}(1, \cdot)\)	3888.2.a.a	1	1
		3888.2.a.b	1
		3888.2.a.c	1
		3888.2.a.d	1
		3888.2.a.e	1
		3888.2.a.f	1
		3888.2.a.g	1
		3888.2.a.h	1
		3888.2.a.i	1
		3888.2.a.j	1
		3888.2.a.k	1
		3888.2.a.l	1
		3888.2.a.m	1
		3888.2.a.n	1
		3888.2.a.o	1
		3888.2.a.p	1
		3888.2.a.q	1
		3888.2.a.r	1
		3888.2.a.s	1
		3888.2.a.t	1
		3888.2.a.u	1
		3888.2.a.v	1
		3888.2.a.w	2
		3888.2.a.x	2
		3888.2.a.y	2
		3888.2.a.z	2
		3888.2.a.ba	2
		3888.2.a.bb	2
		3888.2.a.bc	2
		3888.2.a.bd	3
		3888.2.a.be	3
		3888.2.a.bf	3
		3888.2.a.bg	3
		3888.2.a.bh	3
		3888.2.a.bi	3
		3888.2.a.bj	3
		3888.2.a.bk	3
		3888.2.a.bl	6
		3888.2.a.bm	6
3888.2.c	\(\chi_{3888}(3887, \cdot)\)	3888.2.c.a	2	1
		3888.2.c.b	2
		3888.2.c.c	2
		3888.2.c.d	2
		3888.2.c.e	2
		3888.2.c.f	2
		3888.2.c.g	2
		3888.2.c.h	2
		3888.2.c.i	2
		3888.2.c.j	2
		3888.2.c.k	2
		3888.2.c.l	2
		3888.2.c.m	4
		3888.2.c.n	4
		3888.2.c.o	4
		3888.2.c.p	12
		3888.2.c.q	24
3888.2.d	\(\chi_{3888}(1945, \cdot)\)	None	0	1
3888.2.f	\(\chi_{3888}(1943, \cdot)\)	None	0	1
3888.2.i	\(\chi_{3888}(1297, \cdot)\)	n/a	144	2
3888.2.k	\(\chi_{3888}(973, \cdot)\)	n/a	576	2
3888.2.l	\(\chi_{3888}(971, \cdot)\)	n/a	576	2
3888.2.p	\(\chi_{3888}(647, \cdot)\)	None	0	2
3888.2.r	\(\chi_{3888}(649, \cdot)\)	None	0	2
3888.2.s	\(\chi_{3888}(1295, \cdot)\)	n/a	144	2
3888.2.u	\(\chi_{3888}(433, \cdot)\)	n/a	408	6
3888.2.v	\(\chi_{3888}(323, \cdot)\)	n/a	1152	4
3888.2.y	\(\chi_{3888}(325, \cdot)\)	n/a	1152	4
3888.2.bb	\(\chi_{3888}(217, \cdot)\)	None	0	6
3888.2.bd	\(\chi_{3888}(215, \cdot)\)	None	0	6
3888.2.be	\(\chi_{3888}(431, \cdot)\)	n/a	432	6
3888.2.bg	\(\chi_{3888}(145, \cdot)\)	n/a	954	18
3888.2.bh	\(\chi_{3888}(109, \cdot)\)	n/a	3360	12
3888.2.bk	\(\chi_{3888}(107, \cdot)\)	n/a	3360	12
3888.2.bn	\(\chi_{3888}(71, \cdot)\)	None	0	18
3888.2.bp	\(\chi_{3888}(73, \cdot)\)	None	0	18
3888.2.bq	\(\chi_{3888}(143, \cdot)\)	n/a	972	18
3888.2.bs	\(\chi_{3888}(49, \cdot)\)	n/a	8694	54
3888.2.bt	\(\chi_{3888}(35, \cdot)\)	n/a	7704	36
3888.2.bw	\(\chi_{3888}(37, \cdot)\)	n/a	7704	36
3888.2.bz	\(\chi_{3888}(25, \cdot)\)	None	0	54
3888.2.cb	\(\chi_{3888}(23, \cdot)\)	None	0	54
3888.2.cc	\(\chi_{3888}(47, \cdot)\)	n/a	8748	54
3888.2.ce	\(\chi_{3888}(13, \cdot)\)	n/a	69768	108
3888.2.ch	\(\chi_{3888}(11, \cdot)\)	n/a	69768	108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3888))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3888)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 25}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(54))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(108))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(162))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(216))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(243))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(324))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(432))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(486))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(648))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(972))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1296))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1944))\)\(^{\oplus 2}\)