Space of modular forms of level 3332 and weight 2

• Label: 3332.2
• Level: 3332
• Weight: 2
• Dimension: 186816
• Nonzero newspaces: 40
• Sturm bound: 1354752
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(1354752\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3332))\).

	Total	New	Old
Modular forms	343488	189728	153760
Cusp forms	333889	186816	147073
Eisenstein series	9599	2912	6687

Trace form

186816 * q - 218 * q^2 - 4 * q^3 - 218 * q^4 - 448 * q^5 - 206 * q^6 - 8 * q^7 - 374 * q^8 - 428 * q^9 - 182 * q^10 + 4 * q^11 - 158 * q^12 - 404 * q^13 - 228 * q^14 - 162 * q^16 - 480 * q^17 - 442 * q^18 - 4 * q^19 - 206 * q^20 - 482 * q^21 - 434 * q^22 - 20 * q^23 - 238 * q^24 - 392 * q^25 - 222 * q^26 - 16 * q^27 - 300 * q^28 - 704 * q^29 - 166 * q^30 + 60 * q^31 - 178 * q^32 - 328 * q^33 - 163 * q^34 + 30 * q^35 - 262 * q^36 - 296 * q^37 - 94 * q^38 + 106 * q^39 - 94 * q^40 - 284 * q^41 - 222 * q^42 + 60 * q^43 - 102 * q^44 - 190 * q^45 - 142 * q^46 + 80 * q^47 - 272 * q^48 - 356 * q^49 - 636 * q^50 + 46 * q^51 - 454 * q^52 - 432 * q^53 - 294 * q^54 + 122 * q^55 - 228 * q^56 - 744 * q^57 - 286 * q^58 + 32 * q^59 - 358 * q^60 - 350 * q^61 - 262 * q^62 + 36 * q^63 - 374 * q^64 - 296 * q^65 - 318 * q^66 + 44 * q^67 - 315 * q^68 - 804 * q^69 - 234 * q^70 - 370 * q^72 - 220 * q^73 - 302 * q^74 - 262 * q^76 - 450 * q^77 - 586 * q^78 + 36 * q^79 - 444 * q^80 - 400 * q^81 - 408 * q^82 - 72 * q^83 - 708 * q^84 - 830 * q^85 - 740 * q^86 - 312 * q^87 - 532 * q^88 - 400 * q^89 - 924 * q^90 - 184 * q^91 - 568 * q^92 - 832 * q^93 - 608 * q^94 - 276 * q^95 - 864 * q^96 - 744 * q^97 - 864 * q^98 - 80 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3332))\)

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
3332.2.a	\(\chi_{3332}(1, \cdot)\)	3332.2.a.a	1	1
		3332.2.a.b	1
		3332.2.a.c	1
		3332.2.a.d	1
		3332.2.a.e	1
		3332.2.a.f	1
		3332.2.a.g	2
		3332.2.a.h	2
		3332.2.a.i	2
		3332.2.a.j	2
		3332.2.a.k	2
		3332.2.a.l	2
		3332.2.a.m	2
		3332.2.a.n	2
		3332.2.a.o	2
		3332.2.a.p	3
		3332.2.a.q	3
		3332.2.a.r	4
		3332.2.a.s	4
		3332.2.a.t	8
		3332.2.a.u	8
3332.2.b	\(\chi_{3332}(2549, \cdot)\)	3332.2.b.a	2	1
		3332.2.b.b	8
		3332.2.b.c	8
		3332.2.b.d	12
		3332.2.b.e	12
		3332.2.b.f	20
3332.2.e	\(\chi_{3332}(3331, \cdot)\)	n/a	352	1
3332.2.f	\(\chi_{3332}(783, \cdot)\)	n/a	320	1
3332.2.i	\(\chi_{3332}(1157, \cdot)\)	n/a	108	2
3332.2.k	\(\chi_{3332}(1959, \cdot)\)	n/a	704	2
3332.2.l	\(\chi_{3332}(1177, \cdot)\)	n/a	124	2
3332.2.p	\(\chi_{3332}(1599, \cdot)\)	n/a	640	2
3332.2.q	\(\chi_{3332}(815, \cdot)\)	n/a	704	2
3332.2.t	\(\chi_{3332}(373, \cdot)\)	n/a	120	2
3332.2.u	\(\chi_{3332}(477, \cdot)\)	n/a	456	6
3332.2.v	\(\chi_{3332}(393, \cdot)\)	n/a	244	4
3332.2.x	\(\chi_{3332}(195, \cdot)\)	n/a	1408	4
3332.2.ba	\(\chi_{3332}(803, \cdot)\)	n/a	1408	4
3332.2.bb	\(\chi_{3332}(361, \cdot)\)	n/a	240	4
3332.2.bf	\(\chi_{3332}(307, \cdot)\)	n/a	2688	6
3332.2.bg	\(\chi_{3332}(475, \cdot)\)	n/a	3000	6
3332.2.bj	\(\chi_{3332}(169, \cdot)\)	n/a	504	6
3332.2.bl	\(\chi_{3332}(99, \cdot)\)	n/a	2872	8
3332.2.bm	\(\chi_{3332}(97, \cdot)\)	n/a	480	8
3332.2.bo	\(\chi_{3332}(137, \cdot)\)	n/a	888	12
3332.2.bq	\(\chi_{3332}(569, \cdot)\)	n/a	480	8
3332.2.bs	\(\chi_{3332}(19, \cdot)\)	n/a	2816	8
3332.2.bu	\(\chi_{3332}(225, \cdot)\)	n/a	1008	12
3332.2.bv	\(\chi_{3332}(55, \cdot)\)	n/a	6000	12
3332.2.bx	\(\chi_{3332}(305, \cdot)\)	n/a	1008	12
3332.2.ca	\(\chi_{3332}(271, \cdot)\)	n/a	6000	12
3332.2.cb	\(\chi_{3332}(103, \cdot)\)	n/a	5376	12
3332.2.cf	\(\chi_{3332}(129, \cdot)\)	n/a	960	16
3332.2.cg	\(\chi_{3332}(79, \cdot)\)	n/a	5632	16
3332.2.cj	\(\chi_{3332}(83, \cdot)\)	n/a	12000	24
3332.2.cl	\(\chi_{3332}(253, \cdot)\)	n/a	2016	24
3332.2.cn	\(\chi_{3332}(81, \cdot)\)	n/a	2016	24
3332.2.co	\(\chi_{3332}(47, \cdot)\)	n/a	12000	24
3332.2.cq	\(\chi_{3332}(41, \cdot)\)	n/a	4032	48
3332.2.ct	\(\chi_{3332}(71, \cdot)\)	n/a	24000	48
3332.2.cu	\(\chi_{3332}(59, \cdot)\)	n/a	24000	48
3332.2.cw	\(\chi_{3332}(9, \cdot)\)	n/a	4032	48
3332.2.cy	\(\chi_{3332}(11, \cdot)\)	n/a	48000	96
3332.2.db	\(\chi_{3332}(5, \cdot)\)	n/a	8064	96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3332))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3332)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(833))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1666))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3332))\)\(^{\oplus 1}\)