Space of modular forms of level 395 and weight 2

• Label: 395.2
• Level: 395
• Weight: 2
• Dimension: 5485
• Nonzero newspaces: 12
• Newform subspaces: 30
• Sturm bound: 24960
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 395 = 5 \cdot 79 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 12 \)
Newform subspaces:			\( 30 \)
Sturm bound:			\(24960\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(395))\).

	Total	New	Old
Modular forms	6552	5949	603
Cusp forms	5929	5485	444
Eisenstein series	623	464	159

Trace form

5485 * q - 81 * q^2 - 82 * q^3 - 85 * q^4 - 118 * q^5 - 246 * q^6 - 86 * q^7 - 93 * q^8 - 91 * q^9 - 120 * q^10 - 246 * q^11 - 106 * q^12 - 92 * q^13 - 102 * q^14 - 121 * q^15 - 265 * q^16 - 96 * q^17 - 117 * q^18 - 98 * q^19 - 124 * q^20 - 266 * q^21 - 114 * q^22 - 102 * q^23 - 138 * q^24 - 118 * q^25 - 276 * q^26 - 118 * q^27 - 134 * q^28 - 108 * q^29 - 129 * q^30 - 266 * q^31 - 141 * q^32 - 126 * q^33 - 132 * q^34 - 125 * q^35 - 325 * q^36 - 116 * q^37 - 138 * q^38 - 134 * q^39 - 132 * q^40 - 276 * q^41 - 174 * q^42 - 122 * q^43 - 162 * q^44 - 130 * q^45 - 306 * q^46 - 126 * q^47 - 202 * q^48 - 135 * q^49 - 120 * q^50 - 306 * q^51 - 176 * q^52 - 132 * q^53 - 198 * q^54 - 129 * q^55 - 354 * q^56 - 158 * q^57 - 168 * q^58 - 138 * q^59 - 145 * q^60 - 296 * q^61 - 174 * q^62 - 78 * q^63 + 107 * q^64 - 53 * q^65 - 66 * q^66 + 36 * q^67 + 108 * q^68 + 138 * q^69 + 171 * q^70 - 150 * q^71 + 507 * q^72 + 4 * q^73 + 120 * q^74 + 35 * q^75 + 354 * q^76 + 60 * q^77 + 144 * q^78 + 311 * q^79 + 125 * q^80 + 113 * q^81 + 108 * q^82 + 72 * q^83 + 426 * q^84 + 21 * q^85 - 54 * q^86 - 42 * q^87 + 522 * q^88 - 12 * q^89 + 156 * q^90 - 34 * q^91 + 66 * q^92 - 24 * q^93 + 90 * q^94 - 59 * q^95 - 174 * q^96 - 72 * q^97 - 249 * q^98 - 234 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(395))\)

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
395.2.a	\(\chi_{395}(1, \cdot)\)	395.2.a.a	1	1
		395.2.a.b	1
		395.2.a.c	1
		395.2.a.d	3
		395.2.a.e	3
		395.2.a.f	3
		395.2.a.g	4
		395.2.a.h	11
395.2.b	\(\chi_{395}(159, \cdot)\)	395.2.b.a	2	1
		395.2.b.b	12
		395.2.b.c	24
395.2.e	\(\chi_{395}(181, \cdot)\)	395.2.e.a	2	2
		395.2.e.b	24
		395.2.e.c	26
395.2.f	\(\chi_{395}(78, \cdot)\)	395.2.f.a	12	2
		395.2.f.b	20
		395.2.f.c	44
395.2.j	\(\chi_{395}(134, \cdot)\)	395.2.j.a	8	2
		395.2.j.b	68
395.2.l	\(\chi_{395}(103, \cdot)\)	395.2.l.a	4	4
		395.2.l.b	4
		395.2.l.c	144
395.2.m	\(\chi_{395}(21, \cdot)\)	395.2.m.a	168	12
		395.2.m.b	168
395.2.p	\(\chi_{395}(64, \cdot)\)	395.2.p.a	456	12
395.2.q	\(\chi_{395}(11, \cdot)\)	395.2.q.a	312	24
		395.2.q.b	312
395.2.s	\(\chi_{395}(12, \cdot)\)	395.2.s.a	912	24
395.2.t	\(\chi_{395}(4, \cdot)\)	395.2.t.a	912	24
395.2.w	\(\chi_{395}(3, \cdot)\)	395.2.w.a	1824	48

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(395))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(395)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(79))\)\(^{\oplus 2}\)