Defining parameters
Level: | \( N \) | = | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 4 \) |
Nonzero newspaces: | \( 8 \) | ||
Sturm bound: | \(18816\) | ||
Trace bound: | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(294))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7296 | 1693 | 5603 |
Cusp forms | 6816 | 1693 | 5123 |
Eisenstein series | 480 | 0 | 480 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(294))\)
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 |
---|---|---|---|---|
294.4.a | \(\chi_{294}(1, \cdot)\) | 294.4.a.a | 1 | 1 |
294.4.a.b | 1 | |||
294.4.a.c | 1 | |||
294.4.a.d | 1 | |||
294.4.a.e | 1 | |||
294.4.a.f | 1 | |||
294.4.a.g | 1 | |||
294.4.a.h | 1 | |||
294.4.a.i | 1 | |||
294.4.a.j | 2 | |||
294.4.a.k | 2 | |||
294.4.a.l | 2 | |||
294.4.a.m | 2 | |||
294.4.a.n | 2 | |||
294.4.a.o | 2 | |||
294.4.d | \(\chi_{294}(293, \cdot)\) | 294.4.d.a | 16 | 1 |
294.4.d.b | 24 | |||
294.4.e | \(\chi_{294}(67, \cdot)\) | 294.4.e.a | 2 | 2 |
294.4.e.b | 2 | |||
294.4.e.c | 2 | |||
294.4.e.d | 2 | |||
294.4.e.e | 2 | |||
294.4.e.f | 2 | |||
294.4.e.g | 2 | |||
294.4.e.h | 2 | |||
294.4.e.i | 2 | |||
294.4.e.j | 2 | |||
294.4.e.k | 4 | |||
294.4.e.l | 4 | |||
294.4.e.m | 4 | |||
294.4.e.n | 4 | |||
294.4.e.o | 4 | |||
294.4.f | \(\chi_{294}(215, \cdot)\) | 294.4.f.a | 16 | 2 |
294.4.f.b | 16 | |||
294.4.f.c | 48 | |||
294.4.i | \(\chi_{294}(43, \cdot)\) | n/a | 168 | 6 |
294.4.j | \(\chi_{294}(41, \cdot)\) | n/a | 336 | 6 |
294.4.m | \(\chi_{294}(25, \cdot)\) | n/a | 336 | 12 |
294.4.p | \(\chi_{294}(5, \cdot)\) | n/a | 672 | 12 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(294))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_1(294)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_1(147))\)\(^{\oplus 2}\)