Space of modular forms of level 3969 and weight 2

• Label: 3969.2
• Level: 3969
• Weight: 2
• Dimension: 430628
• Nonzero newspaces: 44
• Sturm bound: 2286144
• Trace bound: 23

Defining parameters

Level:	\( N \)	=	\( 3969 = 3^{4} \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 44 \)
Sturm bound:			\(2286144\)
Trace bound:			\(23\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3969))\).

	Total	New	Old
Modular forms	578016	436060	141956
Cusp forms	565057	430628	134429
Eisenstein series	12959	5432	7527

Trace form

430628 * q - 372 * q^2 - 558 * q^3 - 622 * q^4 - 375 * q^5 - 558 * q^6 - 720 * q^7 - 672 * q^8 - 558 * q^9 - 909 * q^10 - 381 * q^11 - 558 * q^12 - 629 * q^13 - 432 * q^14 - 990 * q^15 - 622 * q^16 - 387 * q^17 - 549 * q^18 - 893 * q^19 - 339 * q^20 - 648 * q^21 - 1095 * q^22 - 339 * q^23 - 504 * q^24 - 610 * q^25 - 285 * q^26 - 531 * q^27 - 1044 * q^28 - 633 * q^29 - 504 * q^30 - 611 * q^31 - 324 * q^32 - 531 * q^33 - 609 * q^34 - 432 * q^35 - 954 * q^36 - 911 * q^37 - 411 * q^38 - 558 * q^39 - 549 * q^40 - 375 * q^41 - 648 * q^42 - 1103 * q^43 - 309 * q^44 - 504 * q^45 - 855 * q^46 - 309 * q^47 - 459 * q^48 - 702 * q^49 - 876 * q^50 - 495 * q^51 - 437 * q^52 - 117 * q^53 - 432 * q^54 - 711 * q^55 - 252 * q^56 - 936 * q^57 - 381 * q^58 - 123 * q^59 - 441 * q^60 - 497 * q^61 + 57 * q^62 - 648 * q^63 - 1294 * q^64 - 111 * q^65 - 558 * q^66 - 503 * q^67 - 36 * q^68 - 612 * q^69 - 612 * q^70 - 621 * q^71 - 774 * q^72 - 794 * q^73 - 339 * q^74 - 648 * q^75 - 455 * q^76 - 378 * q^77 - 1107 * q^78 - 587 * q^79 - 402 * q^80 - 630 * q^81 - 1752 * q^82 - 489 * q^83 - 648 * q^84 - 1071 * q^85 - 573 * q^86 - 702 * q^87 - 471 * q^88 - 450 * q^89 - 639 * q^90 - 1044 * q^91 - 753 * q^92 - 540 * q^93 - 579 * q^94 - 309 * q^95 - 567 * q^96 - 569 * q^97 - 432 * q^98 - 1674 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3969))\)

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
3969.2.a	\(\chi_{3969}(1, \cdot)\)	3969.2.a.a	1	1
		3969.2.a.b	1
		3969.2.a.c	1
		3969.2.a.d	1
		3969.2.a.e	1
		3969.2.a.f	1
		3969.2.a.g	2
		3969.2.a.h	2
		3969.2.a.i	2
		3969.2.a.j	2
		3969.2.a.k	2
		3969.2.a.l	3
		3969.2.a.m	3
		3969.2.a.n	3
		3969.2.a.o	3
		3969.2.a.p	3
		3969.2.a.q	3
		3969.2.a.r	4
		3969.2.a.s	4
		3969.2.a.t	4
		3969.2.a.u	4
		3969.2.a.v	4
		3969.2.a.w	4
		3969.2.a.x	4
		3969.2.a.y	4
		3969.2.a.z	5
		3969.2.a.ba	5
		3969.2.a.bb	5
		3969.2.a.bc	5
		3969.2.a.bd	6
		3969.2.a.be	6
		3969.2.a.bf	8
		3969.2.a.bg	8
		3969.2.a.bh	12
		3969.2.a.bi	12
		3969.2.a.bj	16
3969.2.c	\(\chi_{3969}(3968, \cdot)\)	n/a	152	1
3969.2.e	\(\chi_{3969}(2431, \cdot)\)	n/a	304	2
3969.2.f	\(\chi_{3969}(1324, \cdot)\)	n/a	318	2
3969.2.g	\(\chi_{3969}(1108, \cdot)\)	n/a	312	2
3969.2.h	\(\chi_{3969}(2566, \cdot)\)	n/a	312	2
3969.2.i	\(\chi_{3969}(215, \cdot)\)	n/a	312	2
3969.2.o	\(\chi_{3969}(1322, \cdot)\)	n/a	312	2
3969.2.p	\(\chi_{3969}(80, \cdot)\)	n/a	304	2
3969.2.s	\(\chi_{3969}(2726, \cdot)\)	n/a	312	2
3969.2.u	\(\chi_{3969}(568, \cdot)\)	n/a	1320	6
3969.2.v	\(\chi_{3969}(361, \cdot)\)	n/a	696	6
3969.2.w	\(\chi_{3969}(442, \cdot)\)	n/a	708	6
3969.2.x	\(\chi_{3969}(226, \cdot)\)	n/a	696	6
3969.2.z	\(\chi_{3969}(566, \cdot)\)	n/a	1320	6
3969.2.be	\(\chi_{3969}(521, \cdot)\)	n/a	696	6
3969.2.bh	\(\chi_{3969}(656, \cdot)\)	n/a	696	6
3969.2.bi	\(\chi_{3969}(440, \cdot)\)	n/a	696	6
3969.2.bk	\(\chi_{3969}(298, \cdot)\)	n/a	2664	12
3969.2.bl	\(\chi_{3969}(109, \cdot)\)	n/a	2664	12
3969.2.bm	\(\chi_{3969}(190, \cdot)\)	n/a	2664	12
3969.2.bn	\(\chi_{3969}(163, \cdot)\)	n/a	2640	12
3969.2.bo	\(\chi_{3969}(67, \cdot)\)	n/a	6408	18
3969.2.bp	\(\chi_{3969}(148, \cdot)\)	n/a	6552	18
3969.2.bq	\(\chi_{3969}(214, \cdot)\)	n/a	6408	18
3969.2.bs	\(\chi_{3969}(26, \cdot)\)	n/a	2664	12
3969.2.bv	\(\chi_{3969}(404, \cdot)\)	n/a	2640	12
3969.2.bw	\(\chi_{3969}(188, \cdot)\)	n/a	2664	12
3969.2.cc	\(\chi_{3969}(269, \cdot)\)	n/a	2664	12
3969.2.cf	\(\chi_{3969}(362, \cdot)\)	n/a	6408	18
3969.2.cg	\(\chi_{3969}(146, \cdot)\)	n/a	6408	18
3969.2.cl	\(\chi_{3969}(68, \cdot)\)	n/a	6408	18
3969.2.cm	\(\chi_{3969}(37, \cdot)\)	n/a	5976	36
3969.2.cn	\(\chi_{3969}(64, \cdot)\)	n/a	5976	36
3969.2.co	\(\chi_{3969}(100, \cdot)\)	n/a	5976	36
3969.2.cq	\(\chi_{3969}(62, \cdot)\)	n/a	5976	36
3969.2.cr	\(\chi_{3969}(17, \cdot)\)	n/a	5976	36
3969.2.cu	\(\chi_{3969}(143, \cdot)\)	n/a	5976	36
3969.2.cy	\(\chi_{3969}(25, \cdot)\)	n/a	54216	108
3969.2.cz	\(\chi_{3969}(4, \cdot)\)	n/a	54216	108
3969.2.da	\(\chi_{3969}(22, \cdot)\)	n/a	54216	108
3969.2.db	\(\chi_{3969}(5, \cdot)\)	n/a	54216	108
3969.2.dg	\(\chi_{3969}(47, \cdot)\)	n/a	54216	108
3969.2.dh	\(\chi_{3969}(20, \cdot)\)	n/a	54216	108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3969))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3969)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(81))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(189))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(441))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(567))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1323))\)\(^{\oplus 2}\)