Space of modular forms of level 3380 and weight 2

• Label: 3380.2
• Level: 3380
• Weight: 2
• Dimension: 178805
• Nonzero newspaces: 40
• Sturm bound: 1362816
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(1362816\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3380))\).

	Total	New	Old
Modular forms	345264	181261	164003
Cusp forms	336145	178805	157340
Eisenstein series	9119	2456	6663

Trace form

178805 * q - 134 * q^2 - 2 * q^3 - 132 * q^4 - 401 * q^5 - 396 * q^6 - 6 * q^7 - 128 * q^8 - 295 * q^9 - 192 * q^10 - 24 * q^11 - 108 * q^12 - 312 * q^13 - 252 * q^14 - 22 * q^15 - 404 * q^16 - 276 * q^17 - 66 * q^18 + 12 * q^19 - 154 * q^20 - 708 * q^21 - 12 * q^22 + 54 * q^23 + 60 * q^24 - 365 * q^25 - 372 * q^26 + 148 * q^27 - 12 * q^28 - 246 * q^29 - 102 * q^30 - 12 * q^31 - 4 * q^32 - 240 * q^33 - 36 * q^34 - 38 * q^35 - 384 * q^36 - 320 * q^37 - 108 * q^38 - 40 * q^39 - 430 * q^40 - 766 * q^41 - 204 * q^42 - 2 * q^43 - 252 * q^44 - 361 * q^45 - 636 * q^46 - 30 * q^47 - 324 * q^48 - 19 * q^49 - 296 * q^50 + 108 * q^51 - 252 * q^52 - 300 * q^53 - 300 * q^54 + 156 * q^55 - 612 * q^56 + 168 * q^57 - 316 * q^58 + 132 * q^59 - 258 * q^60 - 538 * q^61 - 180 * q^62 + 330 * q^63 - 156 * q^64 - 291 * q^65 - 612 * q^66 + 210 * q^67 + 168 * q^68 + 36 * q^69 - 114 * q^70 + 228 * q^71 + 168 * q^72 - 28 * q^73 + 204 * q^74 + 290 * q^75 - 156 * q^76 - 24 * q^77 + 84 * q^78 + 56 * q^79 + 46 * q^80 - 541 * q^81 + 124 * q^82 + 174 * q^83 + 36 * q^84 - 390 * q^85 - 180 * q^86 + 36 * q^87 + 36 * q^88 - 270 * q^89 - 180 * q^90 - 4 * q^91 - 156 * q^92 - 312 * q^93 - 180 * q^94 + 4 * q^95 - 756 * q^96 - 460 * q^97 - 166 * q^98 - 216 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3380))\)

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
3380.2.a	\(\chi_{3380}(1, \cdot)\)	3380.2.a.a	1	1
		3380.2.a.b	1
		3380.2.a.c	1
		3380.2.a.d	1
		3380.2.a.e	1
		3380.2.a.f	1
		3380.2.a.g	1
		3380.2.a.h	1
		3380.2.a.i	1
		3380.2.a.j	1
		3380.2.a.k	3
		3380.2.a.l	3
		3380.2.a.m	3
		3380.2.a.n	3
		3380.2.a.o	3
		3380.2.a.p	4
		3380.2.a.q	4
		3380.2.a.r	9
		3380.2.a.s	9
3380.2.c	\(\chi_{3380}(2029, \cdot)\)	3380.2.c.a	6	1
		3380.2.c.b	6
		3380.2.c.c	6
		3380.2.c.d	8
		3380.2.c.e	16
		3380.2.c.f	18
		3380.2.c.g	18
3380.2.d	\(\chi_{3380}(1689, \cdot)\)	3380.2.d.a	6	1
		3380.2.d.b	6
		3380.2.d.c	12
		3380.2.d.d	16
		3380.2.d.e	36
3380.2.f	\(\chi_{3380}(3041, \cdot)\)	3380.2.f.a	2	1
		3380.2.f.b	2
		3380.2.f.c	2
		3380.2.f.d	2
		3380.2.f.e	2
		3380.2.f.f	2
		3380.2.f.g	6
		3380.2.f.h	6
		3380.2.f.i	8
		3380.2.f.j	18
3380.2.i	\(\chi_{3380}(1881, \cdot)\)	n/a	104	2
3380.2.j	\(\chi_{3380}(1451, \cdot)\)	n/a	616	2
3380.2.m	\(\chi_{3380}(577, \cdot)\)	n/a	154	2
3380.2.o	\(\chi_{3380}(2367, \cdot)\)	n/a	886	2
3380.2.p	\(\chi_{3380}(2027, \cdot)\)	n/a	884	2
3380.2.r	\(\chi_{3380}(437, \cdot)\)	n/a	154	2
3380.2.u	\(\chi_{3380}(99, \cdot)\)	n/a	884	2
3380.2.x	\(\chi_{3380}(361, \cdot)\)	n/a	104	2
3380.2.z	\(\chi_{3380}(2389, \cdot)\)	n/a	152	2
3380.2.ba	\(\chi_{3380}(529, \cdot)\)	n/a	156	2
3380.2.bc	\(\chi_{3380}(19, \cdot)\)	n/a	1768	4
3380.2.bf	\(\chi_{3380}(657, \cdot)\)	n/a	308	4
3380.2.bg	\(\chi_{3380}(23, \cdot)\)	n/a	1768	4
3380.2.bj	\(\chi_{3380}(867, \cdot)\)	n/a	1768	4
3380.2.bk	\(\chi_{3380}(357, \cdot)\)	n/a	308	4
3380.2.bn	\(\chi_{3380}(1371, \cdot)\)	n/a	1232	4
3380.2.bo	\(\chi_{3380}(261, \cdot)\)	n/a	744	12
3380.2.br	\(\chi_{3380}(181, \cdot)\)	n/a	744	12
3380.2.bt	\(\chi_{3380}(129, \cdot)\)	n/a	1104	12
3380.2.bu	\(\chi_{3380}(209, \cdot)\)	n/a	1080	12
3380.2.bw	\(\chi_{3380}(61, \cdot)\)	n/a	1440	24
3380.2.bx	\(\chi_{3380}(359, \cdot)\)	n/a	13008	24
3380.2.ca	\(\chi_{3380}(177, \cdot)\)	n/a	2184	24
3380.2.cc	\(\chi_{3380}(103, \cdot)\)	n/a	13008	24
3380.2.cd	\(\chi_{3380}(27, \cdot)\)	n/a	13008	24
3380.2.cf	\(\chi_{3380}(57, \cdot)\)	n/a	2184	24
3380.2.ci	\(\chi_{3380}(31, \cdot)\)	n/a	8736	24
3380.2.ck	\(\chi_{3380}(9, \cdot)\)	n/a	2160	24
3380.2.cl	\(\chi_{3380}(49, \cdot)\)	n/a	2208	24
3380.2.cn	\(\chi_{3380}(101, \cdot)\)	n/a	1440	24
3380.2.cq	\(\chi_{3380}(11, \cdot)\)	n/a	17472	48
3380.2.ct	\(\chi_{3380}(33, \cdot)\)	n/a	4368	48
3380.2.cu	\(\chi_{3380}(3, \cdot)\)	n/a	26016	48
3380.2.cx	\(\chi_{3380}(43, \cdot)\)	n/a	26016	48
3380.2.cy	\(\chi_{3380}(37, \cdot)\)	n/a	4368	48
3380.2.db	\(\chi_{3380}(59, \cdot)\)	n/a	26016	48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3380))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3380)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(676))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(845))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1690))\)\(^{\oplus 2}\)