Space of modular forms of level 363 and weight 4

• Label: 363.4
• Level: 363
• Weight: 4
• Dimension: 10570
• Nonzero newspaces: 8
• Sturm bound: 38720
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 8 \)
Sturm bound:			\(38720\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(363))\).

	Total	New	Old
Modular forms	14840	10850	3990
Cusp forms	14200	10570	3630
Eisenstein series	640	280	360

Trace form

10570 * q - 45 * q^3 - 90 * q^4 - 145 * q^6 - 130 * q^7 + 160 * q^8 + 115 * q^9 + 290 * q^10 + 100 * q^11 + 235 * q^12 - 10 * q^13 - 780 * q^14 - 665 * q^15 - 1610 * q^16 - 600 * q^17 - 325 * q^18 + 810 * q^19 + 1900 * q^20 + 785 * q^21 + 1160 * q^22 + 760 * q^23 + 1975 * q^24 + 630 * q^25 + 100 * q^26 - 105 * q^27 - 2190 * q^28 - 1400 * q^29 - 3915 * q^30 - 2850 * q^31 - 3560 * q^32 - 1855 * q^33 - 3930 * q^34 - 2320 * q^35 - 2485 * q^36 - 10 * q^37 + 1300 * q^38 + 2095 * q^39 + 2970 * q^40 + 4440 * q^41 + 4825 * q^42 + 210 * q^43 + 770 * q^44 + 5255 * q^45 + 3490 * q^46 + 2360 * q^47 + 4085 * q^48 + 3870 * q^49 + 2860 * q^50 + 2045 * q^51 + 4690 * q^52 - 640 * q^53 + 1025 * q^54 - 1500 * q^55 - 720 * q^56 - 1735 * q^57 + 3290 * q^58 + 2040 * q^59 - 6435 * q^60 - 2410 * q^61 - 5520 * q^62 - 8305 * q^63 - 12090 * q^64 - 6720 * q^65 - 7195 * q^66 - 6850 * q^67 - 9760 * q^68 - 6675 * q^69 - 10310 * q^70 - 3720 * q^71 + 165 * q^72 - 11010 * q^73 - 3900 * q^74 + 2105 * q^75 + 7890 * q^76 + 900 * q^77 + 14575 * q^78 + 7110 * q^79 + 19620 * q^80 + 15595 * q^81 + 25430 * q^82 + 15440 * q^83 + 23105 * q^84 + 24710 * q^85 + 11920 * q^86 + 10385 * q^87 + 11180 * q^88 + 7000 * q^89 - 15255 * q^90 - 4490 * q^91 - 22100 * q^92 - 12265 * q^93 - 26190 * q^94 - 7200 * q^95 - 28335 * q^96 - 12030 * q^97 - 10120 * q^98 - 4920 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(363))\)

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
363.4.a	\(\chi_{363}(1, \cdot)\)	363.4.a.a	1	1
		363.4.a.b	1
		363.4.a.c	1
		363.4.a.d	1
		363.4.a.e	1
		363.4.a.f	1
		363.4.a.g	1
		363.4.a.h	1
		363.4.a.i	2
		363.4.a.j	2
		363.4.a.k	2
		363.4.a.l	2
		363.4.a.m	2
		363.4.a.n	2
		363.4.a.o	2
		363.4.a.p	4
		363.4.a.q	4
		363.4.a.r	4
		363.4.a.s	4
		363.4.a.t	4
		363.4.a.u	6
		363.4.a.v	6
363.4.d	\(\chi_{363}(362, \cdot)\)	363.4.d.a	4	1
		363.4.d.b	4
		363.4.d.c	12
		363.4.d.d	40
		363.4.d.e	40
363.4.e	\(\chi_{363}(124, \cdot)\)	n/a	216	4
363.4.f	\(\chi_{363}(161, \cdot)\)	n/a	400	4
363.4.i	\(\chi_{363}(34, \cdot)\)	n/a	660	10
363.4.j	\(\chi_{363}(32, \cdot)\)	n/a	1300	10
363.4.m	\(\chi_{363}(4, \cdot)\)	n/a	2640	40
363.4.p	\(\chi_{363}(2, \cdot)\)	n/a	5200	40

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

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(363))\) into lower level spaces

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