Space of modular forms of level 3420 and weight 2

• Label: 3420.2
• Level: 3420
• Weight: 2
• Dimension: 130024
• Nonzero newspaces: 96
• Sturm bound: 1244160
• Trace bound: 26

Defining parameters

Level:	\( N \)	=	\( 3420 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 96 \)
Sturm bound:			\(1244160\)
Trace bound:			\(26\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3420))\).

	Total	New	Old
Modular forms	316800	131856	184944
Cusp forms	305281	130024	175257
Eisenstein series	11519	1832	9687

Trace form

130024 * q - 54 * q^2 - 66 * q^4 - 154 * q^5 - 196 * q^6 - 16 * q^7 - 54 * q^8 - 168 * q^9 - 231 * q^10 - 44 * q^11 - 32 * q^12 - 128 * q^13 + 18 * q^14 - 6 * q^15 - 102 * q^16 - 74 * q^17 + 32 * q^18 + 30 * q^19 - 46 * q^20 - 380 * q^21 + 30 * q^22 + 66 * q^23 + 12 * q^24 - 116 * q^25 - 26 * q^26 + 48 * q^27 - 104 * q^28 - 48 * q^30 - 124 * q^32 + 12 * q^33 - 60 * q^34 + 76 * q^35 - 252 * q^36 - 332 * q^37 - 190 * q^38 + 100 * q^39 - 60 * q^40 - 160 * q^41 - 104 * q^42 - 66 * q^43 - 144 * q^44 - 48 * q^45 - 496 * q^46 - 78 * q^47 - 4 * q^48 - 108 * q^49 - 160 * q^50 - 84 * q^51 - 70 * q^52 - 116 * q^53 - 4 * q^54 - 56 * q^55 - 244 * q^56 - 224 * q^57 - 148 * q^58 - 194 * q^59 - 200 * q^60 - 432 * q^61 - 164 * q^62 - 148 * q^63 - 138 * q^64 - 277 * q^65 - 392 * q^66 - 238 * q^67 - 196 * q^68 - 320 * q^69 - 57 * q^70 - 366 * q^71 - 348 * q^72 - 584 * q^73 - 66 * q^74 - 138 * q^75 + 44 * q^76 - 546 * q^77 - 376 * q^78 - 180 * q^79 - 233 * q^80 - 624 * q^81 + 260 * q^82 - 258 * q^83 - 272 * q^84 - 306 * q^85 - 80 * q^86 - 260 * q^87 + 174 * q^88 - 466 * q^89 - 294 * q^90 - 216 * q^91 - 76 * q^92 - 140 * q^93 + 204 * q^94 - 69 * q^95 - 352 * q^96 + 122 * q^97 + 288 * q^98 + 64 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3420))\)

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
3420.2.a	\(\chi_{3420}(1, \cdot)\)	3420.2.a.a	1	1
		3420.2.a.b	1
		3420.2.a.c	1
		3420.2.a.d	1
		3420.2.a.e	1
		3420.2.a.f	1
		3420.2.a.g	2
		3420.2.a.h	2
		3420.2.a.i	2
		3420.2.a.j	3
		3420.2.a.k	3
		3420.2.a.l	3
		3420.2.a.m	3
		3420.2.a.n	3
		3420.2.a.o	3
3420.2.b	\(\chi_{3420}(2431, \cdot)\)	n/a	200	1
3420.2.e	\(\chi_{3420}(1709, \cdot)\)	3420.2.e.a	16	1
		3420.2.e.b	24
3420.2.f	\(\chi_{3420}(1369, \cdot)\)	3420.2.f.a	4	1
		3420.2.f.b	6
		3420.2.f.c	6
		3420.2.f.d	8
		3420.2.f.e	10
		3420.2.f.f	12
3420.2.i	\(\chi_{3420}(1331, \cdot)\)	n/a	144	1
3420.2.j	\(\chi_{3420}(341, \cdot)\)	3420.2.j.a	24	1
3420.2.m	\(\chi_{3420}(379, \cdot)\)	n/a	296	1
3420.2.n	\(\chi_{3420}(2699, \cdot)\)	n/a	216	1
3420.2.q	\(\chi_{3420}(121, \cdot)\)	n/a	160	2
3420.2.r	\(\chi_{3420}(1141, \cdot)\)	n/a	144	2
3420.2.s	\(\chi_{3420}(2101, \cdot)\)	n/a	160	2
3420.2.t	\(\chi_{3420}(1261, \cdot)\)	3420.2.t.a	2	2
		3420.2.t.b	2
		3420.2.t.c	2
		3420.2.t.d	2
		3420.2.t.e	2
		3420.2.t.f	2
		3420.2.t.g	2
		3420.2.t.h	2
		3420.2.t.i	2
		3420.2.t.j	2
		3420.2.t.k	2
		3420.2.t.l	2
		3420.2.t.m	2
		3420.2.t.n	2
		3420.2.t.o	2
		3420.2.t.p	2
		3420.2.t.q	2
		3420.2.t.r	4
		3420.2.t.s	4
		3420.2.t.t	4
		3420.2.t.u	4
		3420.2.t.v	6
		3420.2.t.w	8
3420.2.v	\(\chi_{3420}(343, \cdot)\)	n/a	540	2
3420.2.x	\(\chi_{3420}(1673, \cdot)\)	3420.2.x.a	4	2
		3420.2.x.b	8
		3420.2.x.c	24
		3420.2.x.d	36
3420.2.z	\(\chi_{3420}(683, \cdot)\)	n/a	480	2
3420.2.bb	\(\chi_{3420}(37, \cdot)\)	3420.2.bb.a	8	2
		3420.2.bb.b	8
		3420.2.bb.c	8
		3420.2.bb.d	12
		3420.2.bb.e	24
		3420.2.bb.f	40
3420.2.bc	\(\chi_{3420}(449, \cdot)\)	3420.2.bc.a	8	2
		3420.2.bc.b	8
		3420.2.bc.c	16
		3420.2.bc.d	48
3420.2.bf	\(\chi_{3420}(1171, \cdot)\)	n/a	400	2
3420.2.bg	\(\chi_{3420}(1151, \cdot)\)	n/a	320	2
3420.2.bj	\(\chi_{3420}(1189, \cdot)\)	3420.2.bj.a	4	2
		3420.2.bj.b	4
		3420.2.bj.c	20
		3420.2.bj.d	32
		3420.2.bj.e	40
3420.2.bk	\(\chi_{3420}(239, \cdot)\)	n/a	1424	2
3420.2.bp	\(\chi_{3420}(1379, \cdot)\)	n/a	1424	2
3420.2.br	\(\chi_{3420}(419, \cdot)\)	n/a	1296	2
3420.2.bt	\(\chi_{3420}(1361, \cdot)\)	n/a	160	2
3420.2.bv	\(\chi_{3420}(1519, \cdot)\)	n/a	1424	2
3420.2.bx	\(\chi_{3420}(1399, \cdot)\)	n/a	1424	2
3420.2.ca	\(\chi_{3420}(1481, \cdot)\)	n/a	160	2
3420.2.cc	\(\chi_{3420}(221, \cdot)\)	n/a	160	2
3420.2.ce	\(\chi_{3420}(259, \cdot)\)	n/a	1424	2
3420.2.cf	\(\chi_{3420}(49, \cdot)\)	n/a	240	2
3420.2.ch	\(\chi_{3420}(191, \cdot)\)	n/a	864	2
3420.2.cj	\(\chi_{3420}(11, \cdot)\)	n/a	960	2
3420.2.cm	\(\chi_{3420}(229, \cdot)\)	n/a	216	2
3420.2.co	\(\chi_{3420}(1489, \cdot)\)	n/a	240	2
3420.2.cq	\(\chi_{3420}(1451, \cdot)\)	n/a	960	2
3420.2.cr	\(\chi_{3420}(1471, \cdot)\)	n/a	960	2
3420.2.ct	\(\chi_{3420}(749, \cdot)\)	n/a	240	2
3420.2.cv	\(\chi_{3420}(569, \cdot)\)	n/a	240	2
3420.2.cy	\(\chi_{3420}(31, \cdot)\)	n/a	960	2
3420.2.da	\(\chi_{3420}(151, \cdot)\)	n/a	960	2
3420.2.dc	\(\chi_{3420}(2729, \cdot)\)	n/a	240	2
3420.2.dd	\(\chi_{3420}(559, \cdot)\)	n/a	592	2
3420.2.dg	\(\chi_{3420}(521, \cdot)\)	3420.2.dg.a	8	2
		3420.2.dg.b	8
		3420.2.dg.c	32
3420.2.dj	\(\chi_{3420}(539, \cdot)\)	n/a	480	2
3420.2.dk	\(\chi_{3420}(541, \cdot)\)	n/a	204	6
3420.2.dl	\(\chi_{3420}(61, \cdot)\)	n/a	480	6
3420.2.dm	\(\chi_{3420}(481, \cdot)\)	n/a	480	6
3420.2.dn	\(\chi_{3420}(197, \cdot)\)	n/a	160	4
3420.2.dp	\(\chi_{3420}(163, \cdot)\)	n/a	1184	4
3420.2.ds	\(\chi_{3420}(407, \cdot)\)	n/a	2848	4
3420.2.dt	\(\chi_{3420}(493, \cdot)\)	n/a	480	4
3420.2.du	\(\chi_{3420}(1813, \cdot)\)	n/a	480	4
3420.2.dx	\(\chi_{3420}(227, \cdot)\)	n/a	2848	4
3420.2.dy	\(\chi_{3420}(1703, \cdot)\)	n/a	2848	4
3420.2.ec	\(\chi_{3420}(373, \cdot)\)	n/a	480	4
3420.2.ee	\(\chi_{3420}(463, \cdot)\)	n/a	2848	4
3420.2.ef	\(\chi_{3420}(77, \cdot)\)	n/a	432	4
3420.2.eg	\(\chi_{3420}(1793, \cdot)\)	n/a	480	4
3420.2.ej	\(\chi_{3420}(1483, \cdot)\)	n/a	2592	4
3420.2.ek	\(\chi_{3420}(7, \cdot)\)	n/a	2848	4
3420.2.eo	\(\chi_{3420}(353, \cdot)\)	n/a	480	4
3420.2.ep	\(\chi_{3420}(217, \cdot)\)	n/a	200	4
3420.2.er	\(\chi_{3420}(107, \cdot)\)	n/a	960	4
3420.2.et	\(\chi_{3420}(169, \cdot)\)	n/a	720	6
3420.2.ew	\(\chi_{3420}(671, \cdot)\)	n/a	2880	6
3420.2.ex	\(\chi_{3420}(751, \cdot)\)	n/a	2880	6
3420.2.fa	\(\chi_{3420}(509, \cdot)\)	n/a	720	6
3420.2.fc	\(\chi_{3420}(41, \cdot)\)	n/a	480	6
3420.2.fd	\(\chi_{3420}(679, \cdot)\)	n/a	4272	6
3420.2.fh	\(\chi_{3420}(359, \cdot)\)	n/a	1440	6
3420.2.fi	\(\chi_{3420}(1459, \cdot)\)	n/a	1776	6
3420.2.fl	\(\chi_{3420}(1421, \cdot)\)	n/a	168	6
3420.2.fn	\(\chi_{3420}(479, \cdot)\)	n/a	4272	6
3420.2.fp	\(\chi_{3420}(29, \cdot)\)	n/a	720	6
3420.2.fs	\(\chi_{3420}(211, \cdot)\)	n/a	2880	6
3420.2.fu	\(\chi_{3420}(289, \cdot)\)	n/a	300	6
3420.2.fv	\(\chi_{3420}(251, \cdot)\)	n/a	960	6
3420.2.fy	\(\chi_{3420}(91, \cdot)\)	n/a	1200	6
3420.2.fz	\(\chi_{3420}(89, \cdot)\)	n/a	240	6
3420.2.gb	\(\chi_{3420}(131, \cdot)\)	n/a	2880	6
3420.2.ge	\(\chi_{3420}(709, \cdot)\)	n/a	720	6
3420.2.gg	\(\chi_{3420}(119, \cdot)\)	n/a	4272	6
3420.2.gj	\(\chi_{3420}(79, \cdot)\)	n/a	4272	6
3420.2.gk	\(\chi_{3420}(641, \cdot)\)	n/a	480	6
3420.2.gm	\(\chi_{3420}(283, \cdot)\)	n/a	8544	12
3420.2.go	\(\chi_{3420}(137, \cdot)\)	n/a	1440	12
3420.2.gq	\(\chi_{3420}(167, \cdot)\)	n/a	8544	12
3420.2.gs	\(\chi_{3420}(143, \cdot)\)	n/a	2880	12
3420.2.gu	\(\chi_{3420}(13, \cdot)\)	n/a	1440	12
3420.2.gw	\(\chi_{3420}(433, \cdot)\)	n/a	600	12
3420.2.gy	\(\chi_{3420}(617, \cdot)\)	n/a	1440	12
3420.2.ha	\(\chi_{3420}(17, \cdot)\)	n/a	480	12
3420.2.hc	\(\chi_{3420}(43, \cdot)\)	n/a	8544	12
3420.2.he	\(\chi_{3420}(883, \cdot)\)	n/a	3552	12
3420.2.hg	\(\chi_{3420}(193, \cdot)\)	n/a	1440	12
3420.2.hi	\(\chi_{3420}(383, \cdot)\)	n/a	8544	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3420))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3420)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(285))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(570))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(855))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1710))\)\(^{\oplus 2}\)