Space of modular forms of level 363 and weight 2

• Label: 363.2
• Level: 363
• Weight: 2
• Dimension: 3431
• Nonzero newspaces: 8
• Newform subspaces: 45
• Sturm bound: 19360
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 8 \)
Newform subspaces:			\( 45 \)
Sturm bound:			\(19360\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(363))\).

	Total	New	Old
Modular forms	5160	3711	1449
Cusp forms	4521	3431	1090
Eisenstein series	639	280	359

Trace form

3431 * q + 3 * q^2 - 44 * q^3 - 83 * q^4 + 6 * q^5 - 52 * q^6 - 102 * q^7 - 25 * q^8 - 64 * q^9 - 132 * q^10 - 10 * q^11 - 118 * q^12 - 96 * q^13 - 36 * q^14 - 79 * q^15 - 179 * q^16 - 42 * q^17 - 72 * q^18 - 130 * q^19 - 58 * q^20 - 87 * q^21 - 160 * q^22 - 16 * q^23 - 80 * q^24 - 139 * q^25 - 58 * q^26 - 14 * q^27 - 134 * q^28 - 10 * q^29 - 37 * q^30 - 98 * q^31 + 23 * q^32 - 40 * q^33 - 196 * q^34 - 32 * q^35 - 48 * q^36 - 132 * q^37 - 40 * q^38 - 81 * q^39 - 220 * q^40 - 78 * q^41 - 91 * q^42 - 186 * q^43 - 110 * q^44 - 169 * q^45 - 278 * q^46 - 92 * q^47 - 164 * q^48 - 253 * q^49 - 127 * q^50 - 137 * q^51 - 252 * q^52 - 86 * q^53 - 72 * q^54 - 180 * q^55 - 120 * q^56 - 15 * q^57 - 180 * q^58 - 53 * q^60 - 128 * q^61 - 24 * q^62 - 7 * q^63 - 163 * q^64 - 36 * q^65 - 45 * q^66 - 202 * q^67 - 74 * q^68 - 41 * q^69 - 246 * q^70 - 48 * q^71 - 20 * q^72 - 196 * q^73 - 66 * q^74 - 104 * q^75 - 330 * q^76 - 90 * q^77 - 143 * q^78 - 270 * q^79 - 234 * q^80 - 64 * q^81 - 184 * q^82 - 176 * q^83 - 119 * q^84 - 242 * q^85 - 148 * q^86 - 145 * q^87 - 260 * q^88 - 70 * q^89 - 157 * q^90 - 198 * q^91 - 172 * q^92 - 173 * q^93 - 246 * q^94 - 180 * q^95 - 112 * q^96 - 232 * q^97 - 269 * q^98 - 80 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)

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
363.2.a	\(\chi_{363}(1, \cdot)\)	363.2.a.a	1	1
		363.2.a.b	1
		363.2.a.c	1
		363.2.a.d	2
		363.2.a.e	2
		363.2.a.f	2
		363.2.a.g	2
		363.2.a.h	2
		363.2.a.i	2
		363.2.a.j	4
363.2.d	\(\chi_{363}(362, \cdot)\)	363.2.d.a	2	1
		363.2.d.b	2
		363.2.d.c	4
		363.2.d.d	4
		363.2.d.e	8
		363.2.d.f	8
363.2.e	\(\chi_{363}(124, \cdot)\)	363.2.e.a	4	4
		363.2.e.b	4
		363.2.e.c	4
		363.2.e.d	4
		363.2.e.e	4
		363.2.e.f	4
		363.2.e.g	4
		363.2.e.h	4
		363.2.e.i	4
		363.2.e.j	4
		363.2.e.k	4
		363.2.e.l	4
		363.2.e.m	8
		363.2.e.n	16
363.2.f	\(\chi_{363}(161, \cdot)\)	363.2.f.a	8	4
		363.2.f.b	8
		363.2.f.c	8
		363.2.f.d	8
		363.2.f.e	8
		363.2.f.f	8
		363.2.f.g	16
		363.2.f.h	16
		363.2.f.i	32
363.2.i	\(\chi_{363}(34, \cdot)\)	363.2.i.a	110	10
		363.2.i.b	110
363.2.j	\(\chi_{363}(32, \cdot)\)	363.2.j.a	420	10
363.2.m	\(\chi_{363}(4, \cdot)\)	363.2.m.a	440	40
		363.2.m.b	440
363.2.p	\(\chi_{363}(2, \cdot)\)	363.2.p.a	1680	40

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(363))\) into lower level spaces

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