Properties

Label 80.5
Level 80
Weight 5
Dimension 382
Nonzero newspaces 7
Newform subspaces 16
Sturm bound 1920
Trace bound 3

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Defining parameters

Level: \( N \) = \( 80 = 2^{4} \cdot 5 \)
Weight: \( k \) = \( 5 \)
Nonzero newspaces: \( 7 \)
Newform subspaces: \( 16 \)
Sturm bound: \(1920\)
Trace bound: \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(80))\).

Total New Old
Modular forms 824 410 414
Cusp forms 712 382 330
Eisenstein series 112 28 84

Trace form

\( 382 q - 4 q^{2} - 2 q^{3} + 8 q^{4} - 44 q^{5} - 144 q^{6} + 2 q^{7} + 176 q^{8} + 444 q^{9} + 92 q^{10} - 200 q^{11} + 656 q^{12} - 478 q^{13} - 96 q^{14} - 678 q^{15} + 320 q^{16} + 14 q^{17} - 2788 q^{18}+ \cdots - 45948 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(80))\)

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
80.5.b \(\chi_{80}(31, \cdot)\) 80.5.b.a 4 1
80.5.b.b 4
80.5.e \(\chi_{80}(39, \cdot)\) None 0 1
80.5.g \(\chi_{80}(71, \cdot)\) None 0 1
80.5.h \(\chi_{80}(79, \cdot)\) 80.5.h.a 2 1
80.5.h.b 2
80.5.h.c 8
80.5.i \(\chi_{80}(13, \cdot)\) 80.5.i.a 92 2
80.5.k \(\chi_{80}(19, \cdot)\) 80.5.k.a 92 2
80.5.m \(\chi_{80}(57, \cdot)\) None 0 2
80.5.p \(\chi_{80}(17, \cdot)\) 80.5.p.a 2 2
80.5.p.b 2
80.5.p.c 2
80.5.p.d 2
80.5.p.e 4
80.5.p.f 4
80.5.p.g 6
80.5.r \(\chi_{80}(11, \cdot)\) 80.5.r.a 64 2
80.5.t \(\chi_{80}(53, \cdot)\) 80.5.t.a 92 2

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(80))\) into lower level spaces

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