Space of modular forms of level 3392 and weight 2

• Label: 3392.2
• Level: 3392
• Weight: 2
• Dimension: 200910
• Nonzero newspaces: 28
• Sturm bound: 1437696
• Trace bound: 18

Defining parameters

Level:	\( N \)	=	\( 3392 = 2^{6} \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 28 \)
Sturm bound:			\(1437696\)
Trace bound:			\(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3392))\).

	Total	New	Old
Modular forms	363168	203154	160014
Cusp forms	355681	200910	154771
Eisenstein series	7487	2244	5243

Trace form

200910 * q - 400 * q^2 - 300 * q^3 - 400 * q^4 - 400 * q^5 - 400 * q^6 - 296 * q^7 - 400 * q^8 - 494 * q^9 - 400 * q^10 - 292 * q^11 - 400 * q^12 - 384 * q^13 - 400 * q^14 - 288 * q^15 - 400 * q^16 - 684 * q^17 - 400 * q^18 - 284 * q^19 - 400 * q^20 - 408 * q^21 - 416 * q^22 - 296 * q^23 - 480 * q^24 - 522 * q^25 - 480 * q^26 - 312 * q^27 - 480 * q^28 - 432 * q^29 - 560 * q^30 - 344 * q^31 - 480 * q^32 - 352 * q^33 - 480 * q^34 - 304 * q^35 - 560 * q^36 - 416 * q^37 - 480 * q^38 - 296 * q^39 - 480 * q^40 - 500 * q^41 - 480 * q^42 - 276 * q^43 - 416 * q^44 - 392 * q^45 - 400 * q^46 - 264 * q^47 - 400 * q^48 - 682 * q^49 - 352 * q^50 - 352 * q^51 - 304 * q^52 - 384 * q^53 - 688 * q^54 - 424 * q^55 - 288 * q^56 - 488 * q^57 - 256 * q^58 - 436 * q^59 - 208 * q^60 - 384 * q^61 - 336 * q^62 - 432 * q^63 - 208 * q^64 - 1096 * q^65 - 240 * q^66 - 476 * q^67 - 304 * q^68 - 376 * q^69 - 208 * q^70 - 424 * q^71 - 256 * q^72 - 500 * q^73 - 288 * q^74 - 412 * q^75 - 272 * q^76 - 408 * q^77 - 352 * q^78 - 360 * q^79 - 480 * q^80 - 706 * q^81 - 560 * q^82 - 300 * q^83 - 624 * q^84 - 416 * q^85 - 608 * q^86 - 296 * q^87 - 560 * q^88 - 596 * q^89 - 688 * q^90 - 288 * q^91 - 704 * q^92 - 480 * q^93 - 592 * q^94 - 336 * q^95 - 672 * q^96 - 380 * q^97 - 672 * q^98 - 348 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3392))\)

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
3392.2.a	\(\chi_{3392}(1, \cdot)\)	3392.2.a.a	1	1
		3392.2.a.b	1
		3392.2.a.c	1
		3392.2.a.d	1
		3392.2.a.e	1
		3392.2.a.f	1
		3392.2.a.g	1
		3392.2.a.h	1
		3392.2.a.i	1
		3392.2.a.j	1
		3392.2.a.k	1
		3392.2.a.l	1
		3392.2.a.m	1
		3392.2.a.n	1
		3392.2.a.o	1
		3392.2.a.p	1
		3392.2.a.q	1
		3392.2.a.r	1
		3392.2.a.s	1
		3392.2.a.t	1
		3392.2.a.u	2
		3392.2.a.v	2
		3392.2.a.w	2
		3392.2.a.x	3
		3392.2.a.y	3
		3392.2.a.z	3
		3392.2.a.ba	3
		3392.2.a.bb	3
		3392.2.a.bc	3
		3392.2.a.bd	3
		3392.2.a.be	3
		3392.2.a.bf	4
		3392.2.a.bg	4
		3392.2.a.bh	4
		3392.2.a.bi	4
		3392.2.a.bj	5
		3392.2.a.bk	5
		3392.2.a.bl	6
		3392.2.a.bm	7
		3392.2.a.bn	7
		3392.2.a.bo	8
3392.2.b	\(\chi_{3392}(1697, \cdot)\)	n/a	104	1
3392.2.c	\(\chi_{3392}(3073, \cdot)\)	n/a	106	1
3392.2.h	\(\chi_{3392}(1377, \cdot)\)	n/a	108	1
3392.2.j	\(\chi_{3392}(719, \cdot)\)	n/a	212	2
3392.2.l	\(\chi_{3392}(849, \cdot)\)	n/a	208	2
3392.2.m	\(\chi_{3392}(529, \cdot)\)	n/a	212	2
3392.2.o	\(\chi_{3392}(1567, \cdot)\)	n/a	216	2
3392.2.r	\(\chi_{3392}(447, \cdot)\)	n/a	212	2
3392.2.s	\(\chi_{3392}(1295, \cdot)\)	n/a	212	2
3392.2.u	\(\chi_{3392}(105, \cdot)\)	None	0	4
3392.2.v	\(\chi_{3392}(425, \cdot)\)	None	0	4
3392.2.ba	\(\chi_{3392}(871, \cdot)\)	None	0	4
3392.2.bb	\(\chi_{3392}(23, \cdot)\)	None	0	4
3392.2.bc	\(\chi_{3392}(513, \cdot)\)	n/a	1272	12
3392.2.bd	\(\chi_{3392}(213, \cdot)\)	n/a	3328	8
3392.2.bf	\(\chi_{3392}(83, \cdot)\)	n/a	3440	8
3392.2.bg	\(\chi_{3392}(507, \cdot)\)	n/a	3440	8
3392.2.bk	\(\chi_{3392}(317, \cdot)\)	n/a	3440	8
3392.2.bl	\(\chi_{3392}(481, \cdot)\)	n/a	1296	12
3392.2.bq	\(\chi_{3392}(449, \cdot)\)	n/a	1272	12
3392.2.br	\(\chi_{3392}(97, \cdot)\)	n/a	1296	12
3392.2.bt	\(\chi_{3392}(527, \cdot)\)	n/a	2544	24
3392.2.bu	\(\chi_{3392}(127, \cdot)\)	n/a	2544	24
3392.2.bx	\(\chi_{3392}(31, \cdot)\)	n/a	2592	24
3392.2.bz	\(\chi_{3392}(49, \cdot)\)	n/a	2544	24
3392.2.ca	\(\chi_{3392}(17, \cdot)\)	n/a	2544	24
3392.2.cc	\(\chi_{3392}(79, \cdot)\)	n/a	2544	24
3392.2.ce	\(\chi_{3392}(55, \cdot)\)	None	0	48
3392.2.cf	\(\chi_{3392}(39, \cdot)\)	None	0	48
3392.2.ck	\(\chi_{3392}(89, \cdot)\)	None	0	48
3392.2.cl	\(\chi_{3392}(9, \cdot)\)	None	0	48
3392.2.cm	\(\chi_{3392}(29, \cdot)\)	n/a	41280	96
3392.2.cq	\(\chi_{3392}(51, \cdot)\)	n/a	41280	96
3392.2.cr	\(\chi_{3392}(3, \cdot)\)	n/a	41280	96
3392.2.ct	\(\chi_{3392}(13, \cdot)\)	n/a	41280	96

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3392))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3392)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(106))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(212))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(424))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(848))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1696))\)\(^{\oplus 2}\)