Properties

Label 135.4
Level 135
Weight 4
Dimension 1360
Nonzero newspaces 9
Newform subspaces 22
Sturm bound 5184
Trace bound 2

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Defining parameters

Level: \( N \) = \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 22 \)
Sturm bound: \(5184\)
Trace bound: \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(135))\).

Total New Old
Modular forms 2064 1456 608
Cusp forms 1824 1360 464
Eisenstein series 240 96 144

Trace form

\( 1360 q - 10 q^{2} - 12 q^{3} - 50 q^{4} - 37 q^{5} - 12 q^{6} + 54 q^{7} + 234 q^{8} + 84 q^{9} - 31 q^{10} - 262 q^{11} - 318 q^{12} - 138 q^{13} - 18 q^{14} + 12 q^{15} + 546 q^{16} + 890 q^{17} + 1254 q^{18}+ \cdots + 2580 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(135))\)

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
135.4.a \(\chi_{135}(1, \cdot)\) 135.4.a.a 1 1
135.4.a.b 1
135.4.a.c 1
135.4.a.d 1
135.4.a.e 3
135.4.a.f 3
135.4.a.g 3
135.4.a.h 3
135.4.b \(\chi_{135}(109, \cdot)\) 135.4.b.a 4 1
135.4.b.b 8
135.4.b.c 12
135.4.e \(\chi_{135}(46, \cdot)\) 135.4.e.a 4 2
135.4.e.b 6
135.4.e.c 14
135.4.f \(\chi_{135}(53, \cdot)\) 135.4.f.a 24 2
135.4.f.b 24
135.4.j \(\chi_{135}(19, \cdot)\) 135.4.j.a 32 2
135.4.k \(\chi_{135}(16, \cdot)\) 135.4.k.a 102 6
135.4.k.b 114
135.4.m \(\chi_{135}(8, \cdot)\) 135.4.m.a 64 4
135.4.p \(\chi_{135}(4, \cdot)\) 135.4.p.a 312 6
135.4.q \(\chi_{135}(2, \cdot)\) 135.4.q.a 624 12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(135))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(135)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(27))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 2}\)