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Properties

Label 1120.1
Level 1120
Weight 1
Dimension 28
Nonzero newspaces 5
Newform subspaces 6
Sturm bound 73728
Trace bound 9

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Defining parameters

Level: \( N \) = \( 1120 = 2^{5} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 1 \)
Nonzero newspaces: \( 5 \)
Newform subspaces: \( 6 \)
Sturm bound: \(73728\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(\Gamma_1(1120))\).

Total New Old
Modular forms 1664 328 1336
Cusp forms 128 28 100
Eisenstein series 1536 300 1236

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

\(D_n\) \(A_4\) \(S_4\) \(A_5\)
Dimension 20 0 8 0

Trace form

\( 28 q - 4 q^{5} - 6 q^{9} + O(q^{10}) \) \( 28 q - 4 q^{5} - 6 q^{9} - 2 q^{11} + 4 q^{15} - 2 q^{19} + 4 q^{21} - 6 q^{25} - 4 q^{33} + 2 q^{35} - 8 q^{39} - 12 q^{41} + 12 q^{45} - 4 q^{53} + 8 q^{57} + 4 q^{59} - 4 q^{61} + 6 q^{65} + 4 q^{77} - 22 q^{81} - 16 q^{89} + 4 q^{91} + 4 q^{95} - 8 q^{97} + 4 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{1}^{\mathrm{new}}(\Gamma_1(1120))\)

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
1120.1.c \(\chi_{1120}(209, \cdot)\) 1120.1.c.a 4 1
1120.1.d \(\chi_{1120}(351, \cdot)\) None 0 1
1120.1.f \(\chi_{1120}(321, \cdot)\) None 0 1
1120.1.i \(\chi_{1120}(239, \cdot)\) None 0 1
1120.1.j \(\chi_{1120}(799, \cdot)\) None 0 1
1120.1.m \(\chi_{1120}(881, \cdot)\) None 0 1
1120.1.o \(\chi_{1120}(911, \cdot)\) None 0 1
1120.1.p \(\chi_{1120}(769, \cdot)\) 1120.1.p.a 4 1
1120.1.s \(\chi_{1120}(57, \cdot)\) None 0 2
1120.1.u \(\chi_{1120}(167, \cdot)\) None 0 2
1120.1.v \(\chi_{1120}(223, \cdot)\) None 0 2
1120.1.y \(\chi_{1120}(113, \cdot)\) None 0 2
1120.1.z \(\chi_{1120}(41, \cdot)\) None 0 2
1120.1.ba \(\chi_{1120}(519, \cdot)\) None 0 2
1120.1.bf \(\chi_{1120}(489, \cdot)\) None 0 2
1120.1.bg \(\chi_{1120}(71, \cdot)\) None 0 2
1120.1.bh \(\chi_{1120}(673, \cdot)\) None 0 2
1120.1.bk \(\chi_{1120}(783, \cdot)\) None 0 2
1120.1.bm \(\chi_{1120}(727, \cdot)\) None 0 2
1120.1.bo \(\chi_{1120}(617, \cdot)\) None 0 2
1120.1.bp \(\chi_{1120}(431, \cdot)\) None 0 2
1120.1.br \(\chi_{1120}(129, \cdot)\) 1120.1.br.a 8 2
1120.1.bt \(\chi_{1120}(319, \cdot)\) None 0 2
1120.1.bu \(\chi_{1120}(241, \cdot)\) None 0 2
1120.1.bx \(\chi_{1120}(481, \cdot)\) None 0 2
1120.1.by \(\chi_{1120}(79, \cdot)\) 1120.1.by.a 2 2
1120.1.by.b 2
1120.1.ca \(\chi_{1120}(369, \cdot)\) None 0 2
1120.1.cd \(\chi_{1120}(191, \cdot)\) None 0 2
1120.1.ce \(\chi_{1120}(69, \cdot)\) None 0 4
1120.1.cf \(\chi_{1120}(211, \cdot)\) None 0 4
1120.1.ck \(\chi_{1120}(197, \cdot)\) None 0 4
1120.1.cl \(\chi_{1120}(307, \cdot)\) None 0 4
1120.1.co \(\chi_{1120}(27, \cdot)\) None 0 4
1120.1.cp \(\chi_{1120}(477, \cdot)\) None 0 4
1120.1.cq \(\chi_{1120}(99, \cdot)\) None 0 4
1120.1.cr \(\chi_{1120}(181, \cdot)\) None 0 4
1120.1.cu \(\chi_{1120}(87, \cdot)\) None 0 4
1120.1.cw \(\chi_{1120}(137, \cdot)\) None 0 4
1120.1.cz \(\chi_{1120}(47, \cdot)\) None 0 4
1120.1.da \(\chi_{1120}(193, \cdot)\) 1120.1.da.a 8 4
1120.1.dc \(\chi_{1120}(151, \cdot)\) None 0 4
1120.1.dd \(\chi_{1120}(89, \cdot)\) None 0 4
1120.1.di \(\chi_{1120}(39, \cdot)\) None 0 4
1120.1.dj \(\chi_{1120}(201, \cdot)\) None 0 4
1120.1.dl \(\chi_{1120}(177, \cdot)\) None 0 4
1120.1.dm \(\chi_{1120}(383, \cdot)\) None 0 4
1120.1.do \(\chi_{1120}(233, \cdot)\) None 0 4
1120.1.dq \(\chi_{1120}(327, \cdot)\) None 0 4
1120.1.du \(\chi_{1120}(61, \cdot)\) None 0 8
1120.1.dv \(\chi_{1120}(179, \cdot)\) None 0 8
1120.1.dw \(\chi_{1120}(3, \cdot)\) None 0 8
1120.1.dx \(\chi_{1120}(53, \cdot)\) None 0 8
1120.1.ea \(\chi_{1120}(37, \cdot)\) None 0 8
1120.1.eb \(\chi_{1120}(227, \cdot)\) None 0 8
1120.1.eg \(\chi_{1120}(11, \cdot)\) None 0 8
1120.1.eh \(\chi_{1120}(229, \cdot)\) None 0 8

Decomposition of \(S_{1}^{\mathrm{old}}(\Gamma_1(1120))\) into lower level spaces

\( S_{1}^{\mathrm{old}}(\Gamma_1(1120)) \cong \) \(S_{1}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(112))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(224))\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(\Gamma_1(560))\)\(^{\oplus 2}\)