Space of modular forms of level 3936 and weight 2

• Label: 3936.2
• Level: 3936
• Weight: 2
• Dimension: 180444
• Nonzero newspaces: 64
• Sturm bound: 1720320
• Trace bound: 25

Defining parameters

Level:	\( N \)	=	\( 3936 = 2^{5} \cdot 3 \cdot 41 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 64 \)
Sturm bound:			\(1720320\)
Trace bound:			\(25\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3936))\).

	Total	New	Old
Modular forms	435200	182004	253196
Cusp forms	424961	180444	244517
Eisenstein series	10239	1560	8679

Trace form

180444 * q - 116 * q^3 - 304 * q^4 - 8 * q^5 - 152 * q^6 - 232 * q^7 - 236 * q^9 - 272 * q^10 - 120 * q^12 - 280 * q^13 + 64 * q^14 - 96 * q^15 - 224 * q^16 + 32 * q^17 - 136 * q^18 - 216 * q^19 + 64 * q^20 - 120 * q^21 - 256 * q^22 + 48 * q^23 - 176 * q^24 - 420 * q^25 - 80 * q^26 - 44 * q^27 - 384 * q^28 - 8 * q^29 - 248 * q^30 - 136 * q^31 - 80 * q^32 - 384 * q^33 - 352 * q^34 + 96 * q^35 - 256 * q^36 - 344 * q^37 - 80 * q^38 - 80 * q^39 - 384 * q^40 - 8 * q^41 - 432 * q^42 - 232 * q^43 - 16 * q^44 - 224 * q^45 - 304 * q^46 - 48 * q^47 - 256 * q^48 - 236 * q^49 - 48 * q^50 - 152 * q^51 - 400 * q^52 + 24 * q^53 - 256 * q^54 - 352 * q^55 - 112 * q^56 - 272 * q^57 - 448 * q^58 - 128 * q^59 - 272 * q^60 - 184 * q^61 - 96 * q^62 - 144 * q^63 - 448 * q^64 - 16 * q^65 - 200 * q^66 - 328 * q^67 + 16 * q^68 - 24 * q^69 - 352 * q^70 - 80 * q^71 - 32 * q^72 - 376 * q^73 + 64 * q^74 - 196 * q^75 - 304 * q^76 + 128 * q^77 - 24 * q^78 - 232 * q^79 + 112 * q^80 - 4 * q^81 - 232 * q^82 + 112 * q^84 - 176 * q^85 + 128 * q^86 - 248 * q^87 - 128 * q^88 + 112 * q^90 - 224 * q^91 + 160 * q^92 - 176 * q^93 - 128 * q^94 - 32 * q^95 + 128 * q^96 - 744 * q^97 + 160 * q^98 - 272 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3936))\)

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
3936.2.a	\(\chi_{3936}(1, \cdot)\)	3936.2.a.a	1	1
		3936.2.a.b	1
		3936.2.a.c	1
		3936.2.a.d	1
		3936.2.a.e	1
		3936.2.a.f	1
		3936.2.a.g	3
		3936.2.a.h	3
		3936.2.a.i	4
		3936.2.a.j	4
		3936.2.a.k	4
		3936.2.a.l	4
		3936.2.a.m	4
		3936.2.a.n	4
		3936.2.a.o	4
		3936.2.a.p	4
		3936.2.a.q	5
		3936.2.a.r	5
		3936.2.a.s	6
		3936.2.a.t	6
		3936.2.a.u	7
		3936.2.a.v	7
3936.2.d	\(\chi_{3936}(575, \cdot)\)	n/a	160	1
3936.2.e	\(\chi_{3936}(1393, \cdot)\)	3936.2.e.a	42	1
		3936.2.e.b	42
3936.2.f	\(\chi_{3936}(1969, \cdot)\)	3936.2.f.a	40	1
		3936.2.f.b	40
3936.2.g	\(\chi_{3936}(3935, \cdot)\)	n/a	168	1
3936.2.j	\(\chi_{3936}(3361, \cdot)\)	3936.2.j.a	2	1
		3936.2.j.b	2
		3936.2.j.c	2
		3936.2.j.d	2
		3936.2.j.e	4
		3936.2.j.f	8
		3936.2.j.g	20
		3936.2.j.h	22
		3936.2.j.i	22
3936.2.k	\(\chi_{3936}(2543, \cdot)\)	n/a	160	1
3936.2.p	\(\chi_{3936}(1967, \cdot)\)	n/a	164	1
3936.2.s	\(\chi_{3936}(911, \cdot)\)	n/a	328	2
3936.2.t	\(\chi_{3936}(1057, \cdot)\)	n/a	168	2
3936.2.w	\(\chi_{3936}(983, \cdot)\)	None	0	2
3936.2.x	\(\chi_{3936}(985, \cdot)\)	None	0	2
3936.2.ba	\(\chi_{3936}(73, \cdot)\)	None	0	2
3936.2.bb	\(\chi_{3936}(1895, \cdot)\)	None	0	2
3936.2.bc	\(\chi_{3936}(647, \cdot)\)	None	0	2
3936.2.bd	\(\chi_{3936}(1321, \cdot)\)	None	0	2
3936.2.bg	\(\chi_{3936}(1559, \cdot)\)	None	0	2
3936.2.bh	\(\chi_{3936}(409, \cdot)\)	None	0	2
3936.2.bm	\(\chi_{3936}(1631, \cdot)\)	n/a	336	2
3936.2.bn	\(\chi_{3936}(337, \cdot)\)	n/a	168	2
3936.2.bo	\(\chi_{3936}(385, \cdot)\)	n/a	336	4
3936.2.bp	\(\chi_{3936}(905, \cdot)\)	None	0	4
3936.2.bq	\(\chi_{3936}(55, \cdot)\)	None	0	4
3936.2.bu	\(\chi_{3936}(155, \cdot)\)	n/a	2672	4
3936.2.bv	\(\chi_{3936}(1549, \cdot)\)	n/a	1344	4
3936.2.by	\(\chi_{3936}(1315, \cdot)\)	n/a	1344	4
3936.2.bz	\(\chi_{3936}(413, \cdot)\)	n/a	2672	4
3936.2.cb	\(\chi_{3936}(1613, \cdot)\)	n/a	2672	4
3936.2.ce	\(\chi_{3936}(355, \cdot)\)	n/a	1344	4
3936.2.cf	\(\chi_{3936}(491, \cdot)\)	n/a	2672	4
3936.2.ch	\(\chi_{3936}(493, \cdot)\)	n/a	1280	4
3936.2.cn	\(\chi_{3936}(2129, \cdot)\)	n/a	656	4
3936.2.co	\(\chi_{3936}(161, \cdot)\)	n/a	672	4
3936.2.cp	\(\chi_{3936}(79, \cdot)\)	n/a	336	4
3936.2.cq	\(\chi_{3936}(2047, \cdot)\)	n/a	336	4
3936.2.cs	\(\chi_{3936}(83, \cdot)\)	n/a	2560	4
3936.2.cu	\(\chi_{3936}(901, \cdot)\)	n/a	1344	4
3936.2.cw	\(\chi_{3936}(331, \cdot)\)	n/a	1344	4
3936.2.cx	\(\chi_{3936}(1397, \cdot)\)	n/a	2672	4
3936.2.cz	\(\chi_{3936}(437, \cdot)\)	n/a	2672	4
3936.2.dc	\(\chi_{3936}(1531, \cdot)\)	n/a	1344	4
3936.2.dd	\(\chi_{3936}(1139, \cdot)\)	n/a	2672	4
3936.2.dg	\(\chi_{3936}(565, \cdot)\)	n/a	1344	4
3936.2.dh	\(\chi_{3936}(137, \cdot)\)	None	0	4
3936.2.di	\(\chi_{3936}(823, \cdot)\)	None	0	4
3936.2.dl	\(\chi_{3936}(1007, \cdot)\)	n/a	656	4
3936.2.dq	\(\chi_{3936}(1103, \cdot)\)	n/a	656	4
3936.2.dr	\(\chi_{3936}(769, \cdot)\)	n/a	336	4
3936.2.du	\(\chi_{3936}(1343, \cdot)\)	n/a	672	4
3936.2.dv	\(\chi_{3936}(529, \cdot)\)	n/a	336	4
3936.2.dw	\(\chi_{3936}(433, \cdot)\)	n/a	336	4
3936.2.dx	\(\chi_{3936}(959, \cdot)\)	n/a	672	4
3936.2.ea	\(\chi_{3936}(49, \cdot)\)	n/a	672	8
3936.2.eb	\(\chi_{3936}(863, \cdot)\)	n/a	1344	8
3936.2.eg	\(\chi_{3936}(25, \cdot)\)	None	0	8
3936.2.eh	\(\chi_{3936}(119, \cdot)\)	None	0	8
3936.2.ek	\(\chi_{3936}(169, \cdot)\)	None	0	8
3936.2.el	\(\chi_{3936}(695, \cdot)\)	None	0	8
3936.2.em	\(\chi_{3936}(743, \cdot)\)	None	0	8
3936.2.en	\(\chi_{3936}(121, \cdot)\)	None	0	8
3936.2.eq	\(\chi_{3936}(1369, \cdot)\)	None	0	8
3936.2.er	\(\chi_{3936}(23, \cdot)\)	None	0	8
3936.2.eu	\(\chi_{3936}(289, \cdot)\)	n/a	672	8
3936.2.ev	\(\chi_{3936}(143, \cdot)\)	n/a	1312	8
3936.2.fa	\(\chi_{3936}(151, \cdot)\)	None	0	16
3936.2.fb	\(\chi_{3936}(89, \cdot)\)	None	0	16
3936.2.fc	\(\chi_{3936}(349, \cdot)\)	n/a	5376	16
3936.2.ff	\(\chi_{3936}(203, \cdot)\)	n/a	10688	16
3936.2.fg	\(\chi_{3936}(499, \cdot)\)	n/a	5376	16
3936.2.fj	\(\chi_{3936}(101, \cdot)\)	n/a	10688	16
3936.2.fl	\(\chi_{3936}(341, \cdot)\)	n/a	10688	16
3936.2.fm	\(\chi_{3936}(67, \cdot)\)	n/a	5376	16
3936.2.fp	\(\chi_{3936}(277, \cdot)\)	n/a	5376	16
3936.2.fr	\(\chi_{3936}(59, \cdot)\)	n/a	10688	16
3936.2.fs	\(\chi_{3936}(511, \cdot)\)	n/a	1344	16
3936.2.ft	\(\chi_{3936}(175, \cdot)\)	n/a	1344	16
3936.2.fu	\(\chi_{3936}(65, \cdot)\)	n/a	2688	16
3936.2.fv	\(\chi_{3936}(17, \cdot)\)	n/a	2624	16
3936.2.ga	\(\chi_{3936}(37, \cdot)\)	n/a	5376	16
3936.2.gc	\(\chi_{3936}(107, \cdot)\)	n/a	10688	16
3936.2.ge	\(\chi_{3936}(19, \cdot)\)	n/a	5376	16
3936.2.gh	\(\chi_{3936}(53, \cdot)\)	n/a	10688	16
3936.2.gj	\(\chi_{3936}(29, \cdot)\)	n/a	10688	16
3936.2.gk	\(\chi_{3936}(259, \cdot)\)	n/a	5376	16
3936.2.gn	\(\chi_{3936}(61, \cdot)\)	n/a	5376	16
3936.2.go	\(\chi_{3936}(131, \cdot)\)	n/a	10688	16
3936.2.gs	\(\chi_{3936}(7, \cdot)\)	None	0	16
3936.2.gt	\(\chi_{3936}(233, \cdot)\)	None	0	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3936))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3936)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(41))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(82))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(123))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(164))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(246))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(328))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(492))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(656))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(984))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1312))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1968))\)\(^{\oplus 2}\)