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Properties

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

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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

\( 55 q + 5 q^{5} - 8 q^{6} + 2 q^{9} + O(q^{10}) \) \( 55 q + 5 q^{5} - 8 q^{6} + 2 q^{9} - 10 q^{11} - 2 q^{13} - 8 q^{16} - 2 q^{17} - 4 q^{20} + 2 q^{23} - 16 q^{24} - q^{25} - 8 q^{26} - q^{29} - 4 q^{30} + 8 q^{31} + 7 q^{35} - 4 q^{37} + 4 q^{39} + 4 q^{41} + 2 q^{43} - 4 q^{45} + 2 q^{47} - 19 q^{49} + 4 q^{51} + 4 q^{53} + 2 q^{55} - 8 q^{57} + 3 q^{59} - 11 q^{61} - 4 q^{65} + 16 q^{66} - 2 q^{67} + q^{71} + 2 q^{73} - 8 q^{75} + 12 q^{77} + 3 q^{79} + 12 q^{80} - 26 q^{81} + 4 q^{83} + 13 q^{85} - 8 q^{87} + 5 q^{89} + 8 q^{95} + 24 q^{96} + 2 q^{97} + 15 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

\( S_{1}^{\mathrm{old}}(\Gamma_1(1520)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(95))\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(380))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(760))\)\(^{\oplus 2}\)