Properties

Label 147.4
Level 147
Weight 4
Dimension 1644
Nonzero newspaces 8
Newform subspaces 41
Sturm bound 6272
Trace bound 1

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Defining parameters

Level: \( N \) = \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) = \( 4 \)
Nonzero newspaces: \( 8 \)
Newform subspaces: \( 41 \)
Sturm bound: \(6272\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(147))\).

Total New Old
Modular forms 2472 1740 732
Cusp forms 2232 1644 588
Eisenstein series 240 96 144

Trace form

\( 1644 q - 27 q^{3} - 30 q^{4} + 48 q^{5} + 51 q^{6} + 12 q^{7} - 108 q^{8} - 99 q^{9} - 138 q^{10} + 171 q^{12} + 126 q^{13} + 312 q^{14} + 357 q^{15} + 210 q^{16} + 24 q^{17} - 561 q^{18} - 1158 q^{19}+ \cdots - 7128 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.4.a \(\chi_{147}(1, \cdot)\) 147.4.a.a 1 1
147.4.a.b 1
147.4.a.c 1
147.4.a.d 1
147.4.a.e 1
147.4.a.f 1
147.4.a.g 1
147.4.a.h 1
147.4.a.i 2
147.4.a.j 2
147.4.a.k 2
147.4.a.l 3
147.4.a.m 3
147.4.c \(\chi_{147}(146, \cdot)\) 147.4.c.a 12 1
147.4.c.b 24
147.4.e \(\chi_{147}(67, \cdot)\) 147.4.e.a 2 2
147.4.e.b 2
147.4.e.c 2
147.4.e.d 2
147.4.e.e 2
147.4.e.f 2
147.4.e.g 2
147.4.e.h 2
147.4.e.i 2
147.4.e.j 4
147.4.e.k 4
147.4.e.l 4
147.4.e.m 4
147.4.e.n 6
147.4.g \(\chi_{147}(68, \cdot)\) 147.4.g.a 2 2
147.4.g.b 2
147.4.g.c 8
147.4.g.d 12
147.4.g.e 48
147.4.i \(\chi_{147}(22, \cdot)\) 147.4.i.a 84 6
147.4.i.b 84
147.4.k \(\chi_{147}(20, \cdot)\) 147.4.k.a 12 6
147.4.k.b 312
147.4.m \(\chi_{147}(4, \cdot)\) 147.4.m.a 156 12
147.4.m.b 180
147.4.o \(\chi_{147}(5, \cdot)\) 147.4.o.a 648 12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_1(147)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)