Properties

Label 55.6
Level 55
Weight 6
Dimension 514
Nonzero newspaces 6
Newform subspaces 12
Sturm bound 1440
Trace bound 1

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Defining parameters

Level: \( N \) = \( 55 = 5 \cdot 11 \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 6 \)
Newform subspaces: \( 12 \)
Sturm bound: \(1440\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(55))\).

Total New Old
Modular forms 640 570 70
Cusp forms 560 514 46
Eisenstein series 80 56 24

Trace form

\( 514 q - 14 q^{2} - 2 q^{3} + 94 q^{4} + 115 q^{5} - 502 q^{6} - 984 q^{7} - 90 q^{8} + 2156 q^{9} + 1770 q^{10} + 504 q^{11} + 396 q^{12} - 1592 q^{13} - 1372 q^{14} - 6195 q^{15} - 12566 q^{16} - 164 q^{17}+ \cdots + 570706 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(55))\)

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
55.6.a \(\chi_{55}(1, \cdot)\) 55.6.a.a 3 1
55.6.a.b 4
55.6.a.c 5
55.6.a.d 6
55.6.b \(\chi_{55}(34, \cdot)\) 55.6.b.a 10 1
55.6.b.b 14
55.6.e \(\chi_{55}(32, \cdot)\) 55.6.e.a 4 2
55.6.e.b 52
55.6.g \(\chi_{55}(16, \cdot)\) 55.6.g.a 40 4
55.6.g.b 40
55.6.j \(\chi_{55}(4, \cdot)\) 55.6.j.a 112 4
55.6.l \(\chi_{55}(2, \cdot)\) 55.6.l.a 224 8

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(55))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(55)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 2}\)