Space of modular forms of level 3549 and weight 1

• Label: 3549.1
• Level: 3549
• Weight: 1
• Dimension: 380
• Nonzero newspaces: 18
• Newform subspaces: 48
• Sturm bound: 908544
• Trace bound: 144

Defining parameters

Level:	\( N \)	=	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 48 \)
Sturm bound:			\(908544\)
Trace bound:			\(144\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(3549))\).

	Total	New	Old
Modular forms	6090	2424	3666
Cusp forms	618	380	238
Eisenstein series	5472	2044	3428

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	340	40	0	0

Trace form

380 * q + 4 * q^6 + 2 * q^7 + 10 * q^9 + 2 * q^10 + 8 * q^12 + 4 * q^15 + 10 * q^16 + 8 * q^19 + 4 * q^21 - 2 * q^24 + 4 * q^28 + 4 * q^31 - 8 * q^34 + 6 * q^37 + 4 * q^39 + 20 * q^40 - 2 * q^42 + 20 * q^43 - 2 * q^46 + 6 * q^49 - 4 * q^51 + 4 * q^52 + 2 * q^54 + 8 * q^57 - 2 * q^58 + 6 * q^63 + 8 * q^64 + 8 * q^67 - 4 * q^69 + 8 * q^70 - 12 * q^73 - 16 * q^75 - 16 * q^76 - 20 * q^79 - 18 * q^81 + 2 * q^82 - 20 * q^84 + 4 * q^85 + 2 * q^87 - 8 * q^90 - 10 * q^91 - 16 * q^93 + 2 * q^94 + 4 * q^97

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(3549))\)

We only show spaces with odd 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
3549.1.b	\(\chi_{3549}(1184, \cdot)\)	None	0	1
3549.1.d	\(\chi_{3549}(2365, \cdot)\)	None	0	1
3549.1.f	\(\chi_{3549}(2029, \cdot)\)	None	0	1
3549.1.h	\(\chi_{3549}(1520, \cdot)\)	None	0	1
3549.1.m	\(\chi_{3549}(1282, \cdot)\)	None	0	2
3549.1.o	\(\chi_{3549}(944, \cdot)\)	3549.1.o.a	2	2
		3549.1.o.b	2
3549.1.q	\(\chi_{3549}(1837, \cdot)\)	None	0	2
3549.1.s	\(\chi_{3549}(653, \cdot)\)	3549.1.s.a	2	2
		3549.1.s.b	4
		3549.1.s.c	4
3549.1.v	\(\chi_{3549}(2050, \cdot)\)	None	0	2
3549.1.w	\(\chi_{3549}(506, \cdot)\)	3549.1.w.a	2	2
		3549.1.w.b	2
		3549.1.w.c	4
		3549.1.w.d	4
		3549.1.w.e	4
3549.1.x	\(\chi_{3549}(485, \cdot)\)	3549.1.x.a	2	2
		3549.1.x.b	4
		3549.1.x.c	4
		3549.1.x.d	4
3549.1.z	\(\chi_{3549}(2005, \cdot)\)	None	0	2
3549.1.bb	\(\chi_{3549}(1522, \cdot)\)	None	0	2
3549.1.bc	\(\chi_{3549}(1037, \cdot)\)	None	0	2
3549.1.be	\(\chi_{3549}(1205, \cdot)\)	None	0	2
3549.1.bg	\(\chi_{3549}(1375, \cdot)\)	None	0	2
3549.1.bi	\(\chi_{3549}(1858, \cdot)\)	None	0	2
3549.1.bk	\(\chi_{3549}(170, \cdot)\)	3549.1.bk.a	2	2
		3549.1.bk.b	2
		3549.1.bk.c	4
		3549.1.bk.d	4
		3549.1.bk.e	4
3549.1.bm	\(\chi_{3549}(191, \cdot)\)	3549.1.bm.a	2	2
		3549.1.bm.b	4
		3549.1.bm.c	4
3549.1.bo	\(\chi_{3549}(1882, \cdot)\)	None	0	2
3549.1.bp	\(\chi_{3549}(23, \cdot)\)	3549.1.bp.a	2	2
		3549.1.bp.b	4
		3549.1.bp.c	4
		3549.1.bp.d	4
3549.1.bq	\(\chi_{3549}(1543, \cdot)\)	None	0	2
3549.1.bs	\(\chi_{3549}(89, \cdot)\)	3549.1.bs.a	4	4
		3549.1.bs.b	4
		3549.1.bs.c	4
3549.1.bu	\(\chi_{3549}(319, \cdot)\)	None	0	4
3549.1.bx	\(\chi_{3549}(1432, \cdot)\)	None	0	4
3549.1.ca	\(\chi_{3549}(188, \cdot)\)	3549.1.ca.a	4	4
		3549.1.ca.b	4
		3549.1.ca.c	4
		3549.1.ca.d	4
3549.1.cb	\(\chi_{3549}(437, \cdot)\)	3549.1.cb.a	4	4
		3549.1.cb.b	4
		3549.1.cb.c	4
		3549.1.cb.d	4
3549.1.ce	\(\chi_{3549}(526, \cdot)\)	None	0	4
3549.1.cf	\(\chi_{3549}(268, \cdot)\)	None	0	4
3549.1.ch	\(\chi_{3549}(80, \cdot)\)	3549.1.ch.a	4	4
		3549.1.ch.b	4
		3549.1.ch.c	4
3549.1.cj	\(\chi_{3549}(155, \cdot)\)	None	0	12
3549.1.cl	\(\chi_{3549}(118, \cdot)\)	None	0	12
3549.1.cn	\(\chi_{3549}(181, \cdot)\)	None	0	12
3549.1.cp	\(\chi_{3549}(92, \cdot)\)	None	0	12
3549.1.cv	\(\chi_{3549}(83, \cdot)\)	3549.1.cv.a	24	24
		3549.1.cv.b	24
3549.1.cx	\(\chi_{3549}(148, \cdot)\)	None	0	24
3549.1.cz	\(\chi_{3549}(178, \cdot)\)	None	0	24
3549.1.da	\(\chi_{3549}(95, \cdot)\)	3549.1.da.a	24	24
3549.1.db	\(\chi_{3549}(160, \cdot)\)	None	0	24
3549.1.dd	\(\chi_{3549}(263, \cdot)\)	3549.1.dd.a	24	24
3549.1.df	\(\chi_{3549}(53, \cdot)\)	None	0	24
3549.1.dh	\(\chi_{3549}(103, \cdot)\)	None	0	24
3549.1.dj	\(\chi_{3549}(10, \cdot)\)	None	0	24
3549.1.dl	\(\chi_{3549}(29, \cdot)\)	None	0	24
3549.1.dn	\(\chi_{3549}(134, \cdot)\)	None	0	24
3549.1.do	\(\chi_{3549}(40, \cdot)\)	None	0	24
3549.1.dq	\(\chi_{3549}(61, \cdot)\)	None	0	24
3549.1.ds	\(\chi_{3549}(179, \cdot)\)	3549.1.ds.a	24	24
3549.1.dt	\(\chi_{3549}(116, \cdot)\)	None	0	24
3549.1.du	\(\chi_{3549}(55, \cdot)\)	None	0	24
3549.1.dx	\(\chi_{3549}(74, \cdot)\)	3549.1.dx.a	24	24
3549.1.dz	\(\chi_{3549}(166, \cdot)\)	None	0	24
3549.1.ea	\(\chi_{3549}(110, \cdot)\)	3549.1.ea.a	48	48
3549.1.ec	\(\chi_{3549}(85, \cdot)\)	None	0	48
3549.1.ed	\(\chi_{3549}(109, \cdot)\)	None	0	48
3549.1.eg	\(\chi_{3549}(20, \cdot)\)	None	0	48
3549.1.eh	\(\chi_{3549}(5, \cdot)\)	None	0	48
3549.1.ek	\(\chi_{3549}(58, \cdot)\)	None	0	48
3549.1.en	\(\chi_{3549}(37, \cdot)\)	None	0	48
3549.1.ep	\(\chi_{3549}(59, \cdot)\)	3549.1.ep.a	48	48

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(3549))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(3549)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(1183))\)\(^{\oplus 2}\)