Space of modular forms of level 3249 and weight 2

• Label: 3249.2
• Level: 3249
• Weight: 2
• Dimension: 304839
• Nonzero newspaces: 32
• Sturm bound: 1559520
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 3249 = 3^{2} \cdot 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 32 \)
Sturm bound:			\(1559520\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3249))\).

	Total	New	Old
Modular forms	393912	309056	84856
Cusp forms	385849	304839	81010
Eisenstein series	8063	4217	3846

Trace form

304839 * q - 459 * q^2 - 612 * q^3 - 459 * q^4 - 459 * q^5 - 612 * q^6 - 459 * q^7 - 459 * q^8 - 612 * q^9 - 1377 * q^10 - 459 * q^11 - 612 * q^12 - 435 * q^13 - 423 * q^14 - 612 * q^15 - 387 * q^16 - 441 * q^17 - 612 * q^18 - 1437 * q^19 - 819 * q^20 - 612 * q^21 - 405 * q^22 - 441 * q^23 - 612 * q^24 - 423 * q^25 - 423 * q^26 - 612 * q^27 - 1299 * q^28 - 423 * q^29 - 612 * q^30 - 423 * q^31 - 369 * q^32 - 612 * q^33 - 369 * q^34 - 387 * q^35 - 684 * q^36 - 1323 * q^37 - 423 * q^38 - 1188 * q^39 - 297 * q^40 - 423 * q^41 - 612 * q^42 - 405 * q^43 - 531 * q^44 - 720 * q^45 - 1503 * q^46 - 585 * q^47 - 864 * q^48 - 549 * q^49 - 837 * q^50 - 792 * q^51 - 855 * q^52 - 675 * q^53 - 828 * q^54 - 1593 * q^55 - 1161 * q^56 - 738 * q^57 - 1107 * q^58 - 729 * q^59 - 1044 * q^60 - 615 * q^61 - 693 * q^62 - 756 * q^63 - 1629 * q^64 - 621 * q^65 - 900 * q^66 - 441 * q^67 - 711 * q^68 - 720 * q^69 - 459 * q^70 - 549 * q^71 - 720 * q^72 - 1233 * q^73 - 423 * q^74 - 612 * q^75 - 396 * q^76 - 693 * q^77 - 612 * q^78 - 255 * q^79 - 423 * q^80 - 612 * q^81 - 1035 * q^82 - 333 * q^83 - 612 * q^84 - 243 * q^85 - 261 * q^86 - 612 * q^87 - 135 * q^88 - 297 * q^89 - 792 * q^90 - 1209 * q^91 - 225 * q^92 - 612 * q^93 - 369 * q^94 - 567 * q^95 - 1476 * q^96 - 621 * q^97 - 909 * q^98 - 864 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3249))\)

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
3249.2.a	\(\chi_{3249}(1, \cdot)\)	3249.2.a.a	1	1
		3249.2.a.b	1
		3249.2.a.c	1
		3249.2.a.d	1
		3249.2.a.e	1
		3249.2.a.f	1
		3249.2.a.g	1
		3249.2.a.h	2
		3249.2.a.i	2
		3249.2.a.j	2
		3249.2.a.k	2
		3249.2.a.l	2
		3249.2.a.m	2
		3249.2.a.n	2
		3249.2.a.o	2
		3249.2.a.p	2
		3249.2.a.q	2
		3249.2.a.r	2
		3249.2.a.s	3
		3249.2.a.t	3
		3249.2.a.u	3
		3249.2.a.v	3
		3249.2.a.w	3
		3249.2.a.x	3
		3249.2.a.y	3
		3249.2.a.z	3
		3249.2.a.ba	4
		3249.2.a.bb	4
		3249.2.a.bc	4
		3249.2.a.bd	4
		3249.2.a.be	4
		3249.2.a.bf	4
		3249.2.a.bg	6
		3249.2.a.bh	6
		3249.2.a.bi	6
		3249.2.a.bj	6
		3249.2.a.bk	8
		3249.2.a.bl	8
		3249.2.a.bm	8
		3249.2.a.bn	8
3249.2.d	\(\chi_{3249}(3248, \cdot)\)	n/a	112	1
3249.2.e	\(\chi_{3249}(1084, \cdot)\)	n/a	648	2
3249.2.f	\(\chi_{3249}(1873, \cdot)\)	n/a	266	2
3249.2.g	\(\chi_{3249}(292, \cdot)\)	n/a	648	2
3249.2.h	\(\chi_{3249}(1375, \cdot)\)	n/a	648	2
3249.2.k	\(\chi_{3249}(2459, \cdot)\)	n/a	648	2
3249.2.l	\(\chi_{3249}(1082, \cdot)\)	n/a	648	2
3249.2.m	\(\chi_{3249}(791, \cdot)\)	n/a	224	2
3249.2.t	\(\chi_{3249}(293, \cdot)\)	n/a	648	2
3249.2.u	\(\chi_{3249}(28, \cdot)\)	n/a	804	6
3249.2.v	\(\chi_{3249}(967, \cdot)\)	n/a	1944	6
3249.2.w	\(\chi_{3249}(1111, \cdot)\)	n/a	1944	6
3249.2.x	\(\chi_{3249}(488, \cdot)\)	n/a	1944	6
3249.2.y	\(\chi_{3249}(116, \cdot)\)	n/a	684	6
3249.2.bd	\(\chi_{3249}(299, \cdot)\)	n/a	1944	6
3249.2.bg	\(\chi_{3249}(172, \cdot)\)	n/a	2844	18
3249.2.bh	\(\chi_{3249}(170, \cdot)\)	n/a	2304	18
3249.2.bk	\(\chi_{3249}(7, \cdot)\)	n/a	13608	36
3249.2.bl	\(\chi_{3249}(106, \cdot)\)	n/a	13608	36
3249.2.bm	\(\chi_{3249}(64, \cdot)\)	n/a	5688	36
3249.2.bn	\(\chi_{3249}(58, \cdot)\)	n/a	13608	36
3249.2.bo	\(\chi_{3249}(122, \cdot)\)	n/a	13608	36
3249.2.bv	\(\chi_{3249}(8, \cdot)\)	n/a	4608	36
3249.2.bw	\(\chi_{3249}(56, \cdot)\)	n/a	13608	36
3249.2.bx	\(\chi_{3249}(50, \cdot)\)	n/a	13608	36
3249.2.ca	\(\chi_{3249}(4, \cdot)\)	n/a	40824	108
3249.2.cb	\(\chi_{3249}(25, \cdot)\)	n/a	40824	108
3249.2.cc	\(\chi_{3249}(55, \cdot)\)	n/a	16956	108
3249.2.cf	\(\chi_{3249}(2, \cdot)\)	n/a	40824	108
3249.2.ck	\(\chi_{3249}(53, \cdot)\)	n/a	13608	108
3249.2.cl	\(\chi_{3249}(14, \cdot)\)	n/a	40824	108

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3249))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3249)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1083))\)\(^{\oplus 2}\)