Space of modular forms of level 546 and weight 4

• Label: 546.4
• Level: 546
• Weight: 4
• Dimension: 5728
• Nonzero newspaces: 30
• Sturm bound: 64512
• Trace bound: 7

Defining parameters

Level:	\( N \)	=	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 30 \)
Sturm bound:			\(64512\)
Trace bound:			\(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(546))\).

	Total	New	Old
Modular forms	24768	5728	19040
Cusp forms	23616	5728	17888
Eisenstein series	1152	0	1152

Trace form

5728 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 - 72 * q^5 - 48 * q^6 - 80 * q^7 + 64 * q^8 + 120 * q^9 - 264 * q^10 - 264 * q^11 - 48 * q^12 - 1088 * q^13 - 176 * q^14 - 864 * q^15 + 64 * q^16 + 420 * q^17 + 480 * q^18 + 3584 * q^19 + 624 * q^20 + 1512 * q^21 - 96 * q^22 - 408 * q^23 + 192 * q^24 - 1016 * q^25 + 304 * q^26 - 1872 * q^27 + 64 * q^28 - 852 * q^29 - 2832 * q^30 - 1648 * q^31 - 128 * q^32 - 708 * q^33 - 624 * q^34 - 384 * q^35 + 48 * q^36 + 3476 * q^37 + 272 * q^38 + 5268 * q^39 + 384 * q^40 + 1644 * q^41 + 1392 * q^42 + 944 * q^43 + 864 * q^44 + 3552 * q^45 - 2016 * q^46 - 1152 * q^47 - 384 * q^48 - 9020 * q^49 - 1952 * q^50 - 7236 * q^51 + 688 * q^52 + 2448 * q^53 + 3168 * q^54 + 3384 * q^55 + 640 * q^56 + 2328 * q^57 + 2424 * q^58 - 2352 * q^59 + 624 * q^60 + 10556 * q^61 - 1216 * q^62 + 984 * q^63 + 1024 * q^64 - 9588 * q^65 - 1632 * q^66 - 5920 * q^67 - 2736 * q^68 - 12360 * q^69 - 4080 * q^70 - 6576 * q^71 - 2016 * q^72 - 16696 * q^73 - 15688 * q^74 - 11712 * q^75 - 12640 * q^76 - 26664 * q^77 - 504 * q^78 - 8224 * q^79 + 960 * q^80 + 16296 * q^81 + 5544 * q^82 + 13776 * q^83 + 5280 * q^84 + 39252 * q^85 + 11504 * q^86 + 16032 * q^87 + 960 * q^88 + 36360 * q^89 + 6048 * q^90 + 45016 * q^91 + 15360 * q^92 + 2676 * q^93 + 34368 * q^94 + 18288 * q^95 + 768 * q^96 + 5888 * q^97 + 8248 * q^98 - 12744 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(546))\)

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
546.4.a	\(\chi_{546}(1, \cdot)\)	546.4.a.a	1	1
		546.4.a.b	1
		546.4.a.c	1
		546.4.a.d	1
		546.4.a.e	1
		546.4.a.f	2
		546.4.a.g	2
		546.4.a.h	2
		546.4.a.i	2
		546.4.a.j	2
		546.4.a.k	2
		546.4.a.l	3
		546.4.a.m	3
		546.4.a.n	3
		546.4.a.o	3
		546.4.a.p	3
		546.4.a.q	4
546.4.c	\(\chi_{546}(337, \cdot)\)	546.4.c.a	10	1
		546.4.c.b	10
		546.4.c.c	12
		546.4.c.d	12
546.4.e	\(\chi_{546}(545, \cdot)\)	n/a	112	1
546.4.g	\(\chi_{546}(209, \cdot)\)	546.4.g.a	48	1
		546.4.g.b	48
546.4.i	\(\chi_{546}(79, \cdot)\)	546.4.i.a	4	2
		546.4.i.b	8
		546.4.i.c	10
		546.4.i.d	10
		546.4.i.e	12
		546.4.i.f	12
		546.4.i.g	12
		546.4.i.h	14
		546.4.i.i	14
546.4.j	\(\chi_{546}(289, \cdot)\)	n/a	112	2
546.4.k	\(\chi_{546}(373, \cdot)\)	n/a	112	2
546.4.l	\(\chi_{546}(211, \cdot)\)	546.4.l.a	2	2
		546.4.l.b	2
		546.4.l.c	8
		546.4.l.d	8
		546.4.l.e	10
		546.4.l.f	10
		546.4.l.g	10
		546.4.l.h	10
		546.4.l.i	10
		546.4.l.j	10
546.4.o	\(\chi_{546}(265, \cdot)\)	n/a	112	2
546.4.p	\(\chi_{546}(239, \cdot)\)	n/a	168	2
546.4.q	\(\chi_{546}(251, \cdot)\)	n/a	224	2
546.4.s	\(\chi_{546}(43, \cdot)\)	546.4.s.a	20	2
		546.4.s.b	20
		546.4.s.c	24
		546.4.s.d	24
546.4.u	\(\chi_{546}(185, \cdot)\)	n/a	224	2
546.4.z	\(\chi_{546}(131, \cdot)\)	n/a	192	2
546.4.bb	\(\chi_{546}(269, \cdot)\)	n/a	224	2
546.4.bd	\(\chi_{546}(121, \cdot)\)	n/a	112	2
546.4.bg	\(\chi_{546}(311, \cdot)\)	n/a	224	2
546.4.bi	\(\chi_{546}(17, \cdot)\)	n/a	224	2
546.4.bk	\(\chi_{546}(25, \cdot)\)	n/a	112	2
546.4.bm	\(\chi_{546}(205, \cdot)\)	n/a	112	2
546.4.bn	\(\chi_{546}(101, \cdot)\)	n/a	224	2
546.4.bq	\(\chi_{546}(419, \cdot)\)	n/a	224	2
546.4.bu	\(\chi_{546}(71, \cdot)\)	n/a	336	4
546.4.bv	\(\chi_{546}(317, \cdot)\)	n/a	448	4
546.4.bw	\(\chi_{546}(11, \cdot)\)	n/a	448	4
546.4.bx	\(\chi_{546}(97, \cdot)\)	n/a	224	4
546.4.by	\(\chi_{546}(19, \cdot)\)	n/a	224	4
546.4.bz	\(\chi_{546}(31, \cdot)\)	n/a	224	4
546.4.cg	\(\chi_{546}(145, \cdot)\)	n/a	224	4
546.4.ch	\(\chi_{546}(137, \cdot)\)	n/a	448	4

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(546))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(546)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 16}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(91))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(182))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(273))\)\(^{\oplus 2}\)