Defining parameters
Level: | \( N \) | = | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | = | \( 3 \) |
Nonzero newspaces: | \( 12 \) | ||
Sturm bound: | \(170352\) | ||
Trace bound: | \(4\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(1014))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 57696 | 14028 | 43668 |
Cusp forms | 55872 | 14028 | 41844 |
Eisenstein series | 1824 | 0 | 1824 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(1014))\)
We only show spaces with odd 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 |
---|---|---|---|---|
1014.3.c | \(\chi_{1014}(677, \cdot)\) | n/a | 104 | 1 |
1014.3.d | \(\chi_{1014}(1013, \cdot)\) | n/a | 104 | 1 |
1014.3.f | \(\chi_{1014}(577, \cdot)\) | 1014.3.f.a | 4 | 2 |
1014.3.f.b | 4 | |||
1014.3.f.c | 4 | |||
1014.3.f.d | 4 | |||
1014.3.f.e | 4 | |||
1014.3.f.f | 4 | |||
1014.3.f.g | 4 | |||
1014.3.f.h | 8 | |||
1014.3.f.i | 8 | |||
1014.3.f.j | 8 | |||
1014.3.f.k | 24 | |||
1014.3.f.l | 24 | |||
1014.3.h | \(\chi_{1014}(191, \cdot)\) | n/a | 204 | 2 |
1014.3.j | \(\chi_{1014}(23, \cdot)\) | n/a | 204 | 2 |
1014.3.l | \(\chi_{1014}(19, \cdot)\) | n/a | 208 | 4 |
1014.3.n | \(\chi_{1014}(77, \cdot)\) | n/a | 1440 | 12 |
1014.3.o | \(\chi_{1014}(53, \cdot)\) | n/a | 1440 | 12 |
1014.3.s | \(\chi_{1014}(31, \cdot)\) | n/a | 1488 | 24 |
1014.3.t | \(\chi_{1014}(17, \cdot)\) | n/a | 2928 | 24 |
1014.3.v | \(\chi_{1014}(29, \cdot)\) | n/a | 2928 | 24 |
1014.3.w | \(\chi_{1014}(7, \cdot)\) | n/a | 2880 | 48 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(1014))\) into lower level spaces
\( S_{3}^{\mathrm{old}}(\Gamma_1(1014)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(169))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(338))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(507))\)\(^{\oplus 2}\)