Properties

Label 160.2
Level 160
Weight 2
Dimension 366
Nonzero newspaces 10
Newform subspaces 18
Sturm bound 3072
Trace bound 9

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Defining parameters

Level: \( N \) = \( 160 = 2^{5} \cdot 5 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 10 \)
Newform subspaces: \( 18 \)
Sturm bound: \(3072\)
Trace bound: \(9\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(160))\).

Total New Old
Modular forms 896 426 470
Cusp forms 641 366 275
Eisenstein series 255 60 195

Trace form

\( 366 q - 8 q^{2} - 4 q^{3} - 8 q^{4} - 10 q^{5} - 24 q^{6} - 4 q^{7} - 8 q^{8} - 10 q^{9} - 20 q^{10} - 16 q^{11} - 40 q^{12} - 20 q^{13} - 40 q^{14} - 12 q^{15} - 64 q^{16} - 12 q^{17} - 48 q^{18} - 8 q^{19}+ \cdots - 112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)

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
160.2.a \(\chi_{160}(1, \cdot)\) 160.2.a.a 1 1
160.2.a.b 1
160.2.a.c 2
160.2.c \(\chi_{160}(129, \cdot)\) 160.2.c.a 2 1
160.2.c.b 4
160.2.d \(\chi_{160}(81, \cdot)\) 160.2.d.a 4 1
160.2.f \(\chi_{160}(49, \cdot)\) 160.2.f.a 4 1
160.2.j \(\chi_{160}(87, \cdot)\) None 0 2
160.2.l \(\chi_{160}(41, \cdot)\) None 0 2
160.2.n \(\chi_{160}(63, \cdot)\) 160.2.n.a 2 2
160.2.n.b 2
160.2.n.c 2
160.2.n.d 2
160.2.n.e 2
160.2.n.f 2
160.2.o \(\chi_{160}(47, \cdot)\) 160.2.o.a 8 2
160.2.q \(\chi_{160}(9, \cdot)\) None 0 2
160.2.s \(\chi_{160}(7, \cdot)\) None 0 2
160.2.u \(\chi_{160}(43, \cdot)\) 160.2.u.a 88 4
160.2.x \(\chi_{160}(21, \cdot)\) 160.2.x.a 64 4
160.2.z \(\chi_{160}(29, \cdot)\) 160.2.z.a 88 4
160.2.ba \(\chi_{160}(3, \cdot)\) 160.2.ba.a 88 4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(160))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(160)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 1}\)