Space of modular forms of level 3808 and weight 2

• Label: 3808.2
• Level: 3808
• Weight: 2
• Dimension: 235308
• Nonzero newspaces: 88
• Sturm bound: 1769472
• Trace bound: 61

Defining parameters

Level:	\( N \)	=	\( 3808 = 2^{5} \cdot 7 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 88 \)
Sturm bound:			\(1769472\)
Trace bound:			\(61\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3808))\).

	Total	New	Old
Modular forms	448512	238308	210204
Cusp forms	436225	235308	200917
Eisenstein series	12287	3000	9287

Trace form

235308 * q - 224 * q^2 - 172 * q^3 - 224 * q^4 - 232 * q^5 - 224 * q^6 - 212 * q^7 - 560 * q^8 - 340 * q^9 - 192 * q^10 - 172 * q^11 - 160 * q^12 - 200 * q^13 - 248 * q^14 - 408 * q^15 - 144 * q^16 - 112 * q^17 - 400 * q^18 - 172 * q^19 - 160 * q^20 - 280 * q^21 - 512 * q^22 - 140 * q^23 - 272 * q^24 - 332 * q^25 - 304 * q^26 - 64 * q^27 - 320 * q^28 - 600 * q^29 - 352 * q^30 - 92 * q^31 - 304 * q^32 - 552 * q^33 - 264 * q^34 - 404 * q^35 - 672 * q^36 - 232 * q^37 - 192 * q^38 - 40 * q^39 - 176 * q^40 - 288 * q^41 - 240 * q^42 - 368 * q^43 - 64 * q^44 - 56 * q^45 - 96 * q^46 - 84 * q^47 - 16 * q^48 - 68 * q^49 - 400 * q^50 - 130 * q^51 - 448 * q^52 - 8 * q^53 - 176 * q^54 - 216 * q^55 - 256 * q^56 - 640 * q^57 - 240 * q^58 - 204 * q^59 - 240 * q^60 - 40 * q^61 - 304 * q^62 - 180 * q^63 - 704 * q^64 - 504 * q^65 - 320 * q^66 - 228 * q^67 - 200 * q^68 - 256 * q^69 - 304 * q^70 - 528 * q^71 - 128 * q^72 - 352 * q^73 - 160 * q^74 - 160 * q^75 - 224 * q^76 - 248 * q^77 - 400 * q^78 - 156 * q^79 - 240 * q^80 - 140 * q^81 - 224 * q^82 - 240 * q^84 - 568 * q^85 - 560 * q^86 + 88 * q^87 - 208 * q^88 - 288 * q^89 - 464 * q^90 - 200 * q^91 - 752 * q^92 - 368 * q^93 - 464 * q^94 - 4 * q^95 - 688 * q^96 - 672 * q^97 - 656 * q^98 - 240 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3808))\)

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
3808.2.a	\(\chi_{3808}(1, \cdot)\)	3808.2.a.a	1	1
		3808.2.a.b	1
		3808.2.a.c	4
		3808.2.a.d	4
		3808.2.a.e	5
		3808.2.a.f	5
		3808.2.a.g	6
		3808.2.a.h	6
		3808.2.a.i	6
		3808.2.a.j	6
		3808.2.a.k	6
		3808.2.a.l	6
		3808.2.a.m	6
		3808.2.a.n	6
		3808.2.a.o	6
		3808.2.a.p	6
		3808.2.a.q	8
		3808.2.a.r	8
3808.2.b	\(\chi_{3808}(1905, \cdot)\)	3808.2.b.a	2	1
		3808.2.b.b	2
		3808.2.b.c	2
		3808.2.b.d	16
		3808.2.b.e	16
		3808.2.b.f	28
		3808.2.b.g	30
3808.2.c	\(\chi_{3808}(1121, \cdot)\)	n/a	108	1
3808.2.h	\(\chi_{3808}(3807, \cdot)\)	n/a	144	1
3808.2.i	\(\chi_{3808}(783, \cdot)\)	n/a	128	1
3808.2.j	\(\chi_{3808}(2687, \cdot)\)	n/a	128	1
3808.2.k	\(\chi_{3808}(1903, \cdot)\)	n/a	140	1
3808.2.p	\(\chi_{3808}(3025, \cdot)\)	n/a	108	1
3808.2.q	\(\chi_{3808}(1089, \cdot)\)	n/a	256	2
3808.2.s	\(\chi_{3808}(727, \cdot)\)	None	0	2
3808.2.t	\(\chi_{3808}(1177, \cdot)\)	None	0	2
3808.2.w	\(\chi_{3808}(2129, \cdot)\)	n/a	216	2
3808.2.x	\(\chi_{3808}(2911, \cdot)\)	n/a	288	2
3808.2.z	\(\chi_{3808}(951, \cdot)\)	None	0	2
3808.2.bc	\(\chi_{3808}(1735, \cdot)\)	None	0	2
3808.2.be	\(\chi_{3808}(953, \cdot)\)	None	0	2
3808.2.bf	\(\chi_{3808}(169, \cdot)\)	None	0	2
3808.2.bi	\(\chi_{3808}(225, \cdot)\)	n/a	216	2
3808.2.bj	\(\chi_{3808}(1007, \cdot)\)	n/a	280	2
3808.2.bm	\(\chi_{3808}(1849, \cdot)\)	None	0	2
3808.2.bn	\(\chi_{3808}(55, \cdot)\)	None	0	2
3808.2.bp	\(\chi_{3808}(305, \cdot)\)	n/a	280	2
3808.2.bu	\(\chi_{3808}(1055, \cdot)\)	n/a	256	2
3808.2.bv	\(\chi_{3808}(271, \cdot)\)	n/a	280	2
3808.2.bw	\(\chi_{3808}(2175, \cdot)\)	n/a	288	2
3808.2.bx	\(\chi_{3808}(2959, \cdot)\)	n/a	256	2
3808.2.cc	\(\chi_{3808}(2993, \cdot)\)	n/a	256	2
3808.2.cd	\(\chi_{3808}(2209, \cdot)\)	n/a	288	2
3808.2.cf	\(\chi_{3808}(253, \cdot)\)	n/a	1728	4
3808.2.ch	\(\chi_{3808}(1651, \cdot)\)	n/a	2288	4
3808.2.cj	\(\chi_{3808}(1539, \cdot)\)	n/a	2288	4
3808.2.cl	\(\chi_{3808}(869, \cdot)\)	n/a	1728	4
3808.2.cm	\(\chi_{3808}(111, \cdot)\)	n/a	560	4
3808.2.co	\(\chi_{3808}(1345, \cdot)\)	n/a	432	4
3808.2.cq	\(\chi_{3808}(1203, \cdot)\)	n/a	2288	4
3808.2.ct	\(\chi_{3808}(645, \cdot)\)	n/a	1728	4
3808.2.cv	\(\chi_{3808}(477, \cdot)\)	n/a	1536	4
3808.2.cw	\(\chi_{3808}(251, \cdot)\)	n/a	2288	4
3808.2.cy	\(\chi_{3808}(1063, \cdot)\)	None	0	4
3808.2.da	\(\chi_{3808}(281, \cdot)\)	None	0	4
3808.2.dc	\(\chi_{3808}(1511, \cdot)\)	None	0	4
3808.2.de	\(\chi_{3808}(729, \cdot)\)	None	0	4
3808.2.dh	\(\chi_{3808}(421, \cdot)\)	n/a	1728	4
3808.2.di	\(\chi_{3808}(475, \cdot)\)	n/a	2288	4
3808.2.dk	\(\chi_{3808}(307, \cdot)\)	n/a	2048	4
3808.2.dn	\(\chi_{3808}(1373, \cdot)\)	n/a	1728	4
3808.2.do	\(\chi_{3808}(223, \cdot)\)	n/a	576	4
3808.2.dq	\(\chi_{3808}(1233, \cdot)\)	n/a	432	4
3808.2.dt	\(\chi_{3808}(195, \cdot)\)	n/a	2288	4
3808.2.dv	\(\chi_{3808}(365, \cdot)\)	n/a	1728	4
3808.2.dw	\(\chi_{3808}(83, \cdot)\)	n/a	2288	4
3808.2.dy	\(\chi_{3808}(757, \cdot)\)	n/a	1728	4
3808.2.eb	\(\chi_{3808}(999, \cdot)\)	None	0	4
3808.2.ec	\(\chi_{3808}(361, \cdot)\)	None	0	4
3808.2.ee	\(\chi_{3808}(81, \cdot)\)	n/a	560	4
3808.2.eh	\(\chi_{3808}(1279, \cdot)\)	n/a	576	4
3808.2.ei	\(\chi_{3808}(103, \cdot)\)	None	0	4
3808.2.el	\(\chi_{3808}(1223, \cdot)\)	None	0	4
3808.2.en	\(\chi_{3808}(1257, \cdot)\)	None	0	4
3808.2.eo	\(\chi_{3808}(137, \cdot)\)	None	0	4
3808.2.eq	\(\chi_{3808}(1313, \cdot)\)	n/a	576	4
3808.2.et	\(\chi_{3808}(47, \cdot)\)	n/a	560	4
3808.2.ev	\(\chi_{3808}(1033, \cdot)\)	None	0	4
3808.2.ew	\(\chi_{3808}(327, \cdot)\)	None	0	4
3808.2.ez	\(\chi_{3808}(295, \cdot)\)	None	0	8
3808.2.fb	\(\chi_{3808}(41, \cdot)\)	None	0	8
3808.2.fc	\(\chi_{3808}(827, \cdot)\)	n/a	3456	8
3808.2.fe	\(\chi_{3808}(573, \cdot)\)	n/a	4576	8
3808.2.fh	\(\chi_{3808}(267, \cdot)\)	n/a	3456	8
3808.2.fi	\(\chi_{3808}(687, \cdot)\)	n/a	864	8
3808.2.fl	\(\chi_{3808}(351, \cdot)\)	n/a	864	8
3808.2.fn	\(\chi_{3808}(211, \cdot)\)	n/a	3456	8
3808.2.fp	\(\chi_{3808}(1133, \cdot)\)	n/a	4576	8
3808.2.fq	\(\chi_{3808}(97, \cdot)\)	n/a	1152	8
3808.2.ft	\(\chi_{3808}(209, \cdot)\)	n/a	1120	8
3808.2.fv	\(\chi_{3808}(125, \cdot)\)	n/a	4576	8
3808.2.fw	\(\chi_{3808}(99, \cdot)\)	n/a	3456	8
3808.2.fy	\(\chi_{3808}(181, \cdot)\)	n/a	4576	8
3808.2.gb	\(\chi_{3808}(71, \cdot)\)	None	0	8
3808.2.gd	\(\chi_{3808}(601, \cdot)\)	None	0	8
3808.2.ge	\(\chi_{3808}(1845, \cdot)\)	n/a	4576	8
3808.2.gg	\(\chi_{3808}(59, \cdot)\)	n/a	4576	8
3808.2.gi	\(\chi_{3808}(53, \cdot)\)	n/a	4576	8
3808.2.gk	\(\chi_{3808}(1811, \cdot)\)	n/a	4576	8
3808.2.gn	\(\chi_{3808}(417, \cdot)\)	n/a	1152	8
3808.2.gp	\(\chi_{3808}(495, \cdot)\)	n/a	1120	8
3808.2.gr	\(\chi_{3808}(523, \cdot)\)	n/a	4576	8
3808.2.gs	\(\chi_{3808}(205, \cdot)\)	n/a	4096	8
3808.2.gu	\(\chi_{3808}(373, \cdot)\)	n/a	4576	8
3808.2.gx	\(\chi_{3808}(115, \cdot)\)	n/a	4576	8
3808.2.gz	\(\chi_{3808}(9, \cdot)\)	None	0	8
3808.2.hb	\(\chi_{3808}(423, \cdot)\)	None	0	8
3808.2.hd	\(\chi_{3808}(25, \cdot)\)	None	0	8
3808.2.hf	\(\chi_{3808}(87, \cdot)\)	None	0	8
3808.2.hg	\(\chi_{3808}(557, \cdot)\)	n/a	4576	8
3808.2.hj	\(\chi_{3808}(171, \cdot)\)	n/a	4096	8
3808.2.hl	\(\chi_{3808}(339, \cdot)\)	n/a	4576	8
3808.2.hm	\(\chi_{3808}(149, \cdot)\)	n/a	4576	8
3808.2.hp	\(\chi_{3808}(529, \cdot)\)	n/a	1120	8
3808.2.hr	\(\chi_{3808}(383, \cdot)\)	n/a	1152	8
3808.2.hs	\(\chi_{3808}(93, \cdot)\)	n/a	4576	8
3808.2.hu	\(\chi_{3808}(451, \cdot)\)	n/a	4576	8
3808.2.hx	\(\chi_{3808}(19, \cdot)\)	n/a	4576	8
3808.2.hz	\(\chi_{3808}(485, \cdot)\)	n/a	4576	8
3808.2.ia	\(\chi_{3808}(521, \cdot)\)	None	0	16
3808.2.ic	\(\chi_{3808}(471, \cdot)\)	None	0	16
3808.2.ie	\(\chi_{3808}(845, \cdot)\)	n/a	9152	16
3808.2.ig	\(\chi_{3808}(11, \cdot)\)	n/a	9152	16
3808.2.ij	\(\chi_{3808}(5, \cdot)\)	n/a	9152	16
3808.2.il	\(\chi_{3808}(241, \cdot)\)	n/a	2240	16
3808.2.im	\(\chi_{3808}(129, \cdot)\)	n/a	2304	16
3808.2.ip	\(\chi_{3808}(45, \cdot)\)	n/a	9152	16
3808.2.ir	\(\chi_{3808}(235, \cdot)\)	n/a	9152	16
3808.2.it	\(\chi_{3808}(95, \cdot)\)	n/a	2304	16
3808.2.iu	\(\chi_{3808}(79, \cdot)\)	n/a	2240	16
3808.2.ix	\(\chi_{3808}(107, \cdot)\)	n/a	9152	16
3808.2.iy	\(\chi_{3808}(173, \cdot)\)	n/a	9152	16
3808.2.ja	\(\chi_{3808}(275, \cdot)\)	n/a	9152	16
3808.2.jc	\(\chi_{3808}(73, \cdot)\)	None	0	16
3808.2.je	\(\chi_{3808}(23, \cdot)\)	None	0	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3808))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3808)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(136))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(544))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(952))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1904))\)\(^{\oplus 2}\)