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