Space of modular forms of level 1520 and weight 1

• Label: 1520.1
• Level: 1520
• Weight: 1
• Dimension: 55
• Nonzero newspaces: 6
• Newform subspaces: 15
• Sturm bound: 138240
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	=	\( 1 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 15 \)
Sturm bound:			\(138240\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1520))\).

	Total	New	Old
Modular forms	2216	513	1703
Cusp forms	200	55	145
Eisenstein series	2016	458	1558

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	39	0	16	0

Trace form

55 * q + 5 * q^5 - 8 * q^6 + 2 * q^9 - 10 * q^11 - 2 * q^13 - 8 * q^16 - 2 * q^17 - 4 * q^20 + 2 * q^23 - 16 * q^24 - q^25 - 8 * q^26 - q^29 - 4 * q^30 + 8 * q^31 + 7 * q^35 - 4 * q^37 + 4 * q^39 + 4 * q^41 + 2 * q^43 - 4 * q^45 + 2 * q^47 - 19 * q^49 + 4 * q^51 + 4 * q^53 + 2 * q^55 - 8 * q^57 + 3 * q^59 - 11 * q^61 - 4 * q^65 + 16 * q^66 - 2 * q^67 + q^71 + 2 * q^73 - 8 * q^75 + 12 * q^77 + 3 * q^79 + 12 * q^80 - 26 * q^81 + 4 * q^83 + 13 * q^85 - 8 * q^87 + 5 * q^89 + 8 * q^95 + 24 * q^96 + 2 * q^97 + 15 * q^99

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1520))\)

We only show spaces with odd 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
1520.1.b	\(\chi_{1520}(569, \cdot)\)	None	0	1
1520.1.c	\(\chi_{1520}(191, \cdot)\)	None	0	1
1520.1.h	\(\chi_{1520}(721, \cdot)\)	None	0	1
1520.1.i	\(\chi_{1520}(39, \cdot)\)	None	0	1
1520.1.l	\(\chi_{1520}(951, \cdot)\)	None	0	1
1520.1.m	\(\chi_{1520}(1329, \cdot)\)	1520.1.m.a	1	1
		1520.1.m.b	2
		1520.1.m.c	2
1520.1.n	\(\chi_{1520}(799, \cdot)\)	None	0	1
1520.1.o	\(\chi_{1520}(1481, \cdot)\)	None	0	1
1520.1.s	\(\chi_{1520}(837, \cdot)\)	None	0	2
1520.1.u	\(\chi_{1520}(987, \cdot)\)	None	0	2
1520.1.v	\(\chi_{1520}(419, \cdot)\)	None	0	2
1520.1.x	\(\chi_{1520}(341, \cdot)\)	None	0	2
1520.1.z	\(\chi_{1520}(153, \cdot)\)	None	0	2
1520.1.ba	\(\chi_{1520}(303, \cdot)\)	1520.1.ba.a	2	2
		1520.1.ba.b	2
		1520.1.ba.c	4
		1520.1.ba.d	4
1520.1.bf	\(\chi_{1520}(913, \cdot)\)	None	0	2
1520.1.bg	\(\chi_{1520}(1063, \cdot)\)	None	0	2
1520.1.bh	\(\chi_{1520}(189, \cdot)\)	1520.1.bh.a	4	2
		1520.1.bh.b	4
		1520.1.bh.c	16
1520.1.bj	\(\chi_{1520}(571, \cdot)\)	None	0	2
1520.1.bm	\(\chi_{1520}(227, \cdot)\)	None	0	2
1520.1.bo	\(\chi_{1520}(77, \cdot)\)	None	0	2
1520.1.br	\(\chi_{1520}(369, \cdot)\)	1520.1.br.a	2	2
1520.1.bs	\(\chi_{1520}(311, \cdot)\)	None	0	2
1520.1.bt	\(\chi_{1520}(521, \cdot)\)	None	0	2
1520.1.bu	\(\chi_{1520}(159, \cdot)\)	1520.1.bu.a	2	2
		1520.1.bu.b	2
1520.1.bw	\(\chi_{1520}(1071, \cdot)\)	None	0	2
1520.1.bx	\(\chi_{1520}(1129, \cdot)\)	None	0	2
1520.1.cc	\(\chi_{1520}(919, \cdot)\)	None	0	2
1520.1.cd	\(\chi_{1520}(1281, \cdot)\)	None	0	2
1520.1.cg	\(\chi_{1520}(957, \cdot)\)	None	0	4
1520.1.ci	\(\chi_{1520}(787, \cdot)\)	None	0	4
1520.1.cj	\(\chi_{1520}(141, \cdot)\)	None	0	4
1520.1.cl	\(\chi_{1520}(539, \cdot)\)	None	0	4
1520.1.cp	\(\chi_{1520}(1033, \cdot)\)	None	0	4
1520.1.cq	\(\chi_{1520}(863, \cdot)\)	None	0	4
1520.1.cr	\(\chi_{1520}(273, \cdot)\)	1520.1.cr.a	4	4
		1520.1.cr.b	4
1520.1.cs	\(\chi_{1520}(103, \cdot)\)	None	0	4
1520.1.cv	\(\chi_{1520}(11, \cdot)\)	None	0	4
1520.1.cx	\(\chi_{1520}(69, \cdot)\)	None	0	4
1520.1.da	\(\chi_{1520}(27, \cdot)\)	None	0	4
1520.1.dc	\(\chi_{1520}(197, \cdot)\)	None	0	4
1520.1.de	\(\chi_{1520}(241, \cdot)\)	None	0	6
1520.1.df	\(\chi_{1520}(119, \cdot)\)	None	0	6
1520.1.dg	\(\chi_{1520}(479, \cdot)\)	None	0	6
1520.1.dh	\(\chi_{1520}(41, \cdot)\)	None	0	6
1520.1.dk	\(\chi_{1520}(631, \cdot)\)	None	0	6
1520.1.dl	\(\chi_{1520}(129, \cdot)\)	None	0	6
1520.1.dq	\(\chi_{1520}(89, \cdot)\)	None	0	6
1520.1.dr	\(\chi_{1520}(111, \cdot)\)	None	0	6
1520.1.du	\(\chi_{1520}(29, \cdot)\)	None	0	12
1520.1.dv	\(\chi_{1520}(131, \cdot)\)	None	0	12
1520.1.dw	\(\chi_{1520}(17, \cdot)\)	None	0	12
1520.1.dx	\(\chi_{1520}(167, \cdot)\)	None	0	12
1520.1.ea	\(\chi_{1520}(67, \cdot)\)	None	0	12
1520.1.eb	\(\chi_{1520}(157, \cdot)\)	None	0	12
1520.1.ee	\(\chi_{1520}(93, \cdot)\)	None	0	12
1520.1.ef	\(\chi_{1520}(3, \cdot)\)	None	0	12
1520.1.ei	\(\chi_{1520}(73, \cdot)\)	None	0	12
1520.1.ej	\(\chi_{1520}(127, \cdot)\)	None	0	12
1520.1.eo	\(\chi_{1520}(21, \cdot)\)	None	0	12
1520.1.ep	\(\chi_{1520}(99, \cdot)\)	None	0	12

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1520))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1520)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 10}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 8}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(190))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 2}\)