Space of modular forms of level 363 and weight 3

• Label: 363.3
• Level: 363
• Weight: 3
• Dimension: 7000
• Nonzero newspaces: 8
• Newform subspaces: 49
• Sturm bound: 29040
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 49 \)
Sturm bound:			\(29040\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(363))\).

	Total	New	Old
Modular forms	10000	7282	2718
Cusp forms	9360	7000	2360
Eisenstein series	640	282	358

Trace form

7000 * q - 45 * q^3 - 90 * q^4 - 5 * q^6 - 30 * q^7 + 80 * q^8 - 25 * q^9 - 70 * q^10 - 10 * q^11 - 165 * q^12 - 150 * q^13 - 20 * q^14 - 25 * q^15 + 70 * q^16 + 20 * q^17 - 65 * q^18 + 30 * q^19 + 100 * q^20 - 35 * q^21 - 160 * q^22 - 80 * q^23 - 505 * q^24 - 410 * q^25 - 500 * q^26 - 195 * q^27 - 790 * q^28 - 320 * q^29 - 435 * q^30 - 490 * q^31 + 125 * q^33 + 550 * q^34 + 640 * q^35 + 795 * q^36 + 390 * q^37 + 500 * q^38 + 485 * q^39 + 650 * q^40 + 240 * q^41 + 665 * q^42 + 370 * q^43 + 330 * q^44 - 155 * q^45 + 50 * q^46 + 100 * q^47 + 45 * q^48 - 310 * q^49 - 660 * q^50 - 705 * q^51 - 670 * q^52 - 740 * q^53 - 1795 * q^54 - 620 * q^55 - 1360 * q^56 - 1225 * q^57 - 1030 * q^58 - 300 * q^59 - 1115 * q^60 - 350 * q^61 - 80 * q^62 + 5 * q^63 - 810 * q^64 + 175 * q^66 - 590 * q^67 - 160 * q^68 + 235 * q^69 + 970 * q^70 + 1040 * q^71 + 1785 * q^72 + 1770 * q^73 + 1460 * q^74 + 1695 * q^75 + 1690 * q^76 + 570 * q^77 + 2135 * q^78 + 1330 * q^79 + 740 * q^80 - 145 * q^81 - 530 * q^82 + 380 * q^83 - 1115 * q^84 - 1110 * q^85 - 1040 * q^86 - 1135 * q^87 - 1580 * q^88 - 760 * q^89 - 1315 * q^90 - 2070 * q^91 - 380 * q^92 - 565 * q^93 - 870 * q^94 - 860 * q^95 - 175 * q^96 - 510 * q^97 + 250 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(363))\)

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
363.3.b	\(\chi_{363}(122, \cdot)\)	363.3.b.a	1	1
		363.3.b.b	1
		363.3.b.c	2
		363.3.b.d	2
		363.3.b.e	2
		363.3.b.f	4
		363.3.b.g	4
		363.3.b.h	4
		363.3.b.i	4
		363.3.b.j	6
		363.3.b.k	6
		363.3.b.l	8
		363.3.b.m	8
		363.3.b.n	12
363.3.c	\(\chi_{363}(241, \cdot)\)	363.3.c.a	4	1
		363.3.c.b	4
		363.3.c.c	4
		363.3.c.d	8
		363.3.c.e	16
363.3.g	\(\chi_{363}(40, \cdot)\)	363.3.g.a	16	4
		363.3.g.b	16
		363.3.g.c	16
		363.3.g.d	16
		363.3.g.e	16
		363.3.g.f	16
		363.3.g.g	16
		363.3.g.h	32
363.3.h	\(\chi_{363}(245, \cdot)\)	363.3.h.a	4	4
		363.3.h.b	4
		363.3.h.c	8
		363.3.h.d	8
		363.3.h.e	8
		363.3.h.f	8
		363.3.h.g	8
		363.3.h.h	8
		363.3.h.i	8
		363.3.h.j	16
		363.3.h.k	16
		363.3.h.l	16
		363.3.h.m	16
		363.3.h.n	16
		363.3.h.o	16
		363.3.h.p	24
		363.3.h.q	24
		363.3.h.r	48
363.3.k	\(\chi_{363}(10, \cdot)\)	363.3.k.a	440	10
363.3.l	\(\chi_{363}(23, \cdot)\)	363.3.l.a	860	10
363.3.n	\(\chi_{363}(5, \cdot)\)	363.3.n.a	3440	40
363.3.o	\(\chi_{363}(7, \cdot)\)	363.3.o.a	1760	40

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(363))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(363)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 2}\)