Properties

Label 147.6
Level 147
Weight 6
Dimension 2773
Nonzero newspaces 8
Sturm bound 9408
Trace bound 1

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Defining parameters

Level: \( N \) = \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 8 \)
Sturm bound: \(9408\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(147))\).

Total New Old
Modular forms 4040 2869 1171
Cusp forms 3800 2773 1027
Eisenstein series 240 96 144

Trace form

\( 2773 q - 6 q^{2} - 24 q^{3} + 230 q^{4} - 126 q^{5} - 507 q^{6} - 268 q^{7} - 516 q^{8} + 1368 q^{9} + 6114 q^{10} + 264 q^{11} - 4209 q^{12} - 6096 q^{13} - 3720 q^{14} - 4737 q^{15} + 3010 q^{16} + 7386 q^{17}+ \cdots + 584928 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(147))\)

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
147.6.a \(\chi_{147}(1, \cdot)\) 147.6.a.a 1 1
147.6.a.b 1
147.6.a.c 1
147.6.a.d 1
147.6.a.e 1
147.6.a.f 1
147.6.a.g 1
147.6.a.h 2
147.6.a.i 2
147.6.a.j 2
147.6.a.k 2
147.6.a.l 4
147.6.a.m 4
147.6.a.n 6
147.6.a.o 6
147.6.c \(\chi_{147}(146, \cdot)\) 147.6.c.a 2 1
147.6.c.b 4
147.6.c.c 16
147.6.c.d 40
147.6.e \(\chi_{147}(67, \cdot)\) 147.6.e.a 2 2
147.6.e.b 2
147.6.e.c 2
147.6.e.d 2
147.6.e.e 2
147.6.e.f 2
147.6.e.g 2
147.6.e.h 2
147.6.e.i 2
147.6.e.j 2
147.6.e.k 2
147.6.e.l 4
147.6.e.m 4
147.6.e.n 4
147.6.e.o 8
147.6.e.p 12
147.6.e.q 12
147.6.g \(\chi_{147}(68, \cdot)\) n/a 126 2
147.6.i \(\chi_{147}(22, \cdot)\) n/a 276 6
147.6.k \(\chi_{147}(20, \cdot)\) n/a 552 6
147.6.m \(\chi_{147}(4, \cdot)\) n/a 564 12
147.6.o \(\chi_{147}(5, \cdot)\) n/a 1092 12

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(147))\) into lower level spaces

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