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