Space of modular forms of level 380 and weight 2

• Label: 380.2
• Level: 380
• Weight: 2
• Dimension: 2196
• Nonzero newspaces: 18
• Newform subspaces: 36
• Sturm bound: 17280
• Trace bound: 5

Defining parameters

Level:	\( N \)	=	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 18 \)
Newform subspaces:			\( 36 \)
Sturm bound:			\(17280\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(380))\).

	Total	New	Old
Modular forms	4680	2396	2284
Cusp forms	3961	2196	1765
Eisenstein series	719	200	519

Trace form

2196 * q - 14 * q^2 + 4 * q^3 - 18 * q^4 - 44 * q^5 - 54 * q^6 - 4 * q^7 - 26 * q^8 - 38 * q^9 - 39 * q^10 - 18 * q^12 - 12 * q^13 - 18 * q^14 + 14 * q^15 - 38 * q^16 - 18 * q^17 - 24 * q^18 + 46 * q^19 - 46 * q^20 - 58 * q^21 - 18 * q^22 + 6 * q^23 - 18 * q^24 - 50 * q^25 - 62 * q^26 - 2 * q^27 - 72 * q^28 - 84 * q^29 - 90 * q^30 - 28 * q^31 - 124 * q^32 - 144 * q^33 - 108 * q^34 - 32 * q^35 - 258 * q^36 - 84 * q^37 - 144 * q^38 - 100 * q^39 - 82 * q^40 - 124 * q^41 - 198 * q^42 - 46 * q^43 - 108 * q^44 - 91 * q^45 - 144 * q^46 + 30 * q^47 - 144 * q^48 - 24 * q^49 - 26 * q^50 + 48 * q^51 - 10 * q^52 + 12 * q^53 + 36 * q^54 + 36 * q^55 - 72 * q^56 + 46 * q^57 - 52 * q^58 + 66 * q^59 - 36 * q^60 - 172 * q^61 + 72 * q^62 + 20 * q^63 + 126 * q^64 - 63 * q^65 + 90 * q^66 - 34 * q^67 + 132 * q^68 - 246 * q^69 + 81 * q^70 + 42 * q^71 + 276 * q^72 - 152 * q^73 + 90 * q^74 - 8 * q^75 + 126 * q^76 - 342 * q^77 + 126 * q^78 - 136 * q^79 + 13 * q^80 - 284 * q^81 + 220 * q^82 - 102 * q^83 + 198 * q^84 - 282 * q^85 + 72 * q^86 - 192 * q^87 + 126 * q^88 - 186 * q^89 - 12 * q^90 - 128 * q^91 + 72 * q^92 - 280 * q^93 - 121 * q^95 - 252 * q^96 - 218 * q^97 - 244 * q^98 - 270 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(380))\)

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
380.2.a	\(\chi_{380}(1, \cdot)\)	380.2.a.a	1	1
		380.2.a.b	1
		380.2.a.c	2
		380.2.a.d	2
380.2.c	\(\chi_{380}(229, \cdot)\)	380.2.c.a	4	1
		380.2.c.b	6
380.2.d	\(\chi_{380}(379, \cdot)\)	380.2.d.a	16	1
		380.2.d.b	40
380.2.f	\(\chi_{380}(151, \cdot)\)	380.2.f.a	20	1
		380.2.f.b	20
380.2.i	\(\chi_{380}(121, \cdot)\)	380.2.i.a	2	2
		380.2.i.b	6
		380.2.i.c	8
380.2.k	\(\chi_{380}(267, \cdot)\)	380.2.k.a	2	2
		380.2.k.b	2
		380.2.k.c	52
		380.2.k.d	52
380.2.l	\(\chi_{380}(37, \cdot)\)	380.2.l.a	8	2
		380.2.l.b	12
380.2.n	\(\chi_{380}(31, \cdot)\)	380.2.n.a	40	2
		380.2.n.b	40
380.2.r	\(\chi_{380}(49, \cdot)\)	380.2.r.a	20	2
380.2.s	\(\chi_{380}(179, \cdot)\)	380.2.s.a	112	2
380.2.u	\(\chi_{380}(61, \cdot)\)	380.2.u.a	18	6
		380.2.u.b	18
380.2.v	\(\chi_{380}(7, \cdot)\)	380.2.v.a	4	4
		380.2.v.b	4
		380.2.v.c	216
380.2.y	\(\chi_{380}(217, \cdot)\)	380.2.y.a	4	4
		380.2.y.b	36
380.2.bb	\(\chi_{380}(59, \cdot)\)	380.2.bb.a	336	6
380.2.bd	\(\chi_{380}(9, \cdot)\)	380.2.bd.a	60	6
380.2.be	\(\chi_{380}(51, \cdot)\)	380.2.be.a	120	6
		380.2.be.b	120
380.2.bh	\(\chi_{380}(13, \cdot)\)	380.2.bh.a	120	12
380.2.bj	\(\chi_{380}(23, \cdot)\)	380.2.bj.a	672	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(380))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(380)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 2}\)