Space of modular forms of level 361 and weight 2

• Label: 361.2
• Level: 361
• Weight: 2
• Dimension: 5150
• Nonzero newspaces: 6
• Newform subspaces: 35
• Sturm bound: 21660
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 361 = 19^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 35 \)
Sturm bound:			\(21660\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(361))\).

	Total	New	Old
Modular forms	5667	5619	48
Cusp forms	5164	5150	14
Eisenstein series	503	469	34

Trace form

5150 * q - 156 * q^2 - 157 * q^3 - 160 * q^4 - 159 * q^5 - 165 * q^6 - 161 * q^7 - 168 * q^8 - 166 * q^9 - 171 * q^10 - 165 * q^11 - 157 * q^12 - 143 * q^13 - 141 * q^14 - 141 * q^15 - 112 * q^16 - 153 * q^17 - 120 * q^18 - 141 * q^19 - 267 * q^20 - 143 * q^21 - 135 * q^22 - 159 * q^23 - 141 * q^24 - 148 * q^25 - 159 * q^26 - 151 * q^27 - 131 * q^28 - 147 * q^29 - 99 * q^30 - 149 * q^31 - 126 * q^32 - 93 * q^33 - 117 * q^34 - 129 * q^35 - 28 * q^36 - 137 * q^37 - 99 * q^38 - 245 * q^39 - 81 * q^40 - 159 * q^41 - 69 * q^42 - 119 * q^43 - 93 * q^44 - 69 * q^45 - 63 * q^46 - 111 * q^47 - 25 * q^48 - 132 * q^49 - 48 * q^50 - 117 * q^51 - 119 * q^52 - 135 * q^53 - 111 * q^54 - 153 * q^55 - 39 * q^56 - 117 * q^57 - 315 * q^58 - 123 * q^59 - 15 * q^60 - 83 * q^61 - 51 * q^62 - 89 * q^63 - 4 * q^64 - 39 * q^65 - 9 * q^66 - 35 * q^67 - 27 * q^68 - 51 * q^69 - 9 * q^70 - 99 * q^71 + 48 * q^72 - 59 * q^73 - 87 * q^74 - 91 * q^75 - 72 * q^76 - 195 * q^77 - 33 * q^78 - 29 * q^79 - 15 * q^80 - 40 * q^81 + 63 * q^82 - 111 * q^83 + 55 * q^84 - 45 * q^85 - 87 * q^86 + 15 * q^87 - 9 * q^88 - 81 * q^89 + 27 * q^90 - 97 * q^91 - 87 * q^92 - 77 * q^93 - 63 * q^94 - 99 * q^95 - 117 * q^96 - 125 * q^97 + 18 * q^98 - 39 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(361))\)

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
361.2.a	\(\chi_{361}(1, \cdot)\)	361.2.a.a	1	1
		361.2.a.b	1
		361.2.a.c	2
		361.2.a.d	2
		361.2.a.e	2
		361.2.a.f	2
		361.2.a.g	3
		361.2.a.h	3
		361.2.a.i	4
361.2.c	\(\chi_{361}(68, \cdot)\)	361.2.c.a	2	2
		361.2.c.b	2
		361.2.c.c	2
		361.2.c.d	4
		361.2.c.e	4
		361.2.c.f	4
		361.2.c.g	4
		361.2.c.h	6
		361.2.c.i	6
		361.2.c.j	8
361.2.e	\(\chi_{361}(28, \cdot)\)	361.2.e.a	6	6
		361.2.e.b	6
		361.2.e.c	6
		361.2.e.d	6
		361.2.e.e	6
		361.2.e.f	6
		361.2.e.g	6
		361.2.e.h	6
		361.2.e.i	12
		361.2.e.j	12
		361.2.e.k	12
		361.2.e.l	12
		361.2.e.m	24
361.2.g	\(\chi_{361}(20, \cdot)\)	361.2.g.a	540	18
361.2.i	\(\chi_{361}(7, \cdot)\)	361.2.i.a	1080	36
361.2.k	\(\chi_{361}(4, \cdot)\)	361.2.k.a	3348	108

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(361))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(361)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)