Space of modular forms of level 371 and weight 2

• Label: 371.2
• Level: 371
• Weight: 2
• Dimension: 5121
• Nonzero newspaces: 12
• Newform subspaces: 30
• Sturm bound: 22464
• Trace bound: 3

Defining parameters

Level:	\( N \)	=	\( 371 = 7 \cdot 53 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 30 \)
Sturm bound:			\(22464\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(371))\).

	Total	New	Old
Modular forms	5928	5633	295
Cusp forms	5305	5121	184
Eisenstein series	623	512	111

Trace form

5121 * q - 107 * q^2 - 108 * q^3 - 111 * q^4 - 110 * q^5 - 116 * q^6 - 131 * q^7 - 275 * q^8 - 117 * q^9 - 122 * q^10 - 116 * q^11 - 132 * q^12 - 118 * q^13 - 133 * q^14 - 284 * q^15 - 135 * q^16 - 122 * q^17 - 143 * q^18 - 124 * q^19 - 146 * q^20 - 134 * q^21 - 296 * q^22 - 128 * q^23 - 164 * q^24 - 135 * q^25 - 146 * q^26 - 144 * q^27 - 137 * q^28 - 290 * q^29 - 176 * q^30 - 136 * q^31 - 167 * q^32 - 152 * q^33 - 158 * q^34 - 136 * q^35 - 351 * q^36 - 142 * q^37 - 164 * q^38 - 160 * q^39 - 116 * q^40 - 94 * q^41 - 38 * q^42 - 200 * q^43 + 20 * q^44 + 78 * q^45 - 72 * q^46 - 100 * q^47 + 292 * q^48 - 79 * q^49 - 119 * q^50 + 32 * q^51 + 162 * q^52 - q^53 - 16 * q^54 - 20 * q^55 + 11 * q^56 - 132 * q^57 + 40 * q^58 - 60 * q^59 + 248 * q^60 - 114 * q^61 - 96 * q^62 - 13 * q^63 - 179 * q^64 - 84 * q^65 - 40 * q^66 - 120 * q^67 - 152 * q^68 - 200 * q^69 - 148 * q^70 - 332 * q^71 - 299 * q^72 - 178 * q^73 - 218 * q^74 - 228 * q^75 - 244 * q^76 - 142 * q^77 - 428 * q^78 - 184 * q^79 - 290 * q^80 - 225 * q^81 - 230 * q^82 - 188 * q^83 - 158 * q^84 - 368 * q^85 - 236 * q^86 - 120 * q^87 - 24 * q^88 - 64 * q^89 + 78 * q^90 - 40 * q^91 + 40 * q^92 - 24 * q^93 + 376 * q^94 - 16 * q^95 + 164 * q^96 + 240 * q^97 - 107 * q^98 + 104 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(371))\)

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
371.2.a	\(\chi_{371}(1, \cdot)\)	371.2.a.a	1	1
		371.2.a.b	1
		371.2.a.c	2
		371.2.a.d	3
		371.2.a.e	9
		371.2.a.f	11
371.2.b	\(\chi_{371}(211, \cdot)\)	371.2.b.a	4	1
		371.2.b.b	10
		371.2.b.c	12
371.2.e	\(\chi_{371}(107, \cdot)\)	371.2.e.a	2	2
		371.2.e.b	32
		371.2.e.c	34
371.2.g	\(\chi_{371}(76, \cdot)\)	371.2.g.a	4	2
		371.2.g.b	4
		371.2.g.c	4
		371.2.g.d	4
		371.2.g.e	52
371.2.j	\(\chi_{371}(158, \cdot)\)	371.2.j.a	68	2
371.2.l	\(\chi_{371}(129, \cdot)\)	371.2.l.a	4	4
		371.2.l.b	4
		371.2.l.c	128
371.2.m	\(\chi_{371}(15, \cdot)\)	371.2.m.a	156	12
		371.2.m.b	180
371.2.p	\(\chi_{371}(29, \cdot)\)	371.2.p.a	144	12
		371.2.p.b	168
371.2.q	\(\chi_{371}(16, \cdot)\)	371.2.q.a	816	24
371.2.r	\(\chi_{371}(20, \cdot)\)	371.2.r.a	48	24
		371.2.r.b	768
371.2.t	\(\chi_{371}(4, \cdot)\)	371.2.t.a	816	24
371.2.w	\(\chi_{371}(3, \cdot)\)	371.2.w.a	1632	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(371))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(371)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(53))\)\(^{\oplus 2}\)