Properties

Label 135.3
Level 135
Weight 3
Dimension 890
Nonzero newspaces 9
Newform subspaces 18
Sturm bound 3888
Trace bound 4

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Defining parameters

Level: \( N \) = \( 135 = 3^{3} \cdot 5 \)
Weight: \( k \) = \( 3 \)
Nonzero newspaces: \( 9 \)
Newform subspaces: \( 18 \)
Sturm bound: \(3888\)
Trace bound: \(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(135))\).

Total New Old
Modular forms 1416 986 430
Cusp forms 1176 890 286
Eisenstein series 240 96 144

Trace form

\( 890 q - 10 q^{2} - 12 q^{3} - 2 q^{4} + 5 q^{5} - 12 q^{6} - 6 q^{7} + 18 q^{8} - 24 q^{9} + q^{10} - 2 q^{11} + 6 q^{12} + 26 q^{13} + 30 q^{14} - 15 q^{15} - 62 q^{16} - 34 q^{17} - 150 q^{18} - 64 q^{19}+ \cdots + 150 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(135))\)

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
135.3.c \(\chi_{135}(26, \cdot)\) 135.3.c.a 2 1
135.3.c.b 4
135.3.c.c 4
135.3.d \(\chi_{135}(134, \cdot)\) 135.3.d.a 2 1
135.3.d.b 2
135.3.d.c 2
135.3.d.d 2
135.3.d.e 2
135.3.d.f 2
135.3.d.g 4
135.3.g \(\chi_{135}(28, \cdot)\) 135.3.g.a 16 2
135.3.g.b 16
135.3.h \(\chi_{135}(44, \cdot)\) 135.3.h.a 20 2
135.3.i \(\chi_{135}(71, \cdot)\) 135.3.i.a 16 2
135.3.l \(\chi_{135}(37, \cdot)\) 135.3.l.a 40 4
135.3.n \(\chi_{135}(14, \cdot)\) 135.3.n.a 204 6
135.3.o \(\chi_{135}(11, \cdot)\) 135.3.o.a 144 6
135.3.r \(\chi_{135}(7, \cdot)\) 135.3.r.a 408 12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(135))\) into lower level spaces

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