Defining parameters
Level: | \( N \) | = | \( 3017 = 7 \cdot 431 \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 16 \) | ||
Sturm bound: | \(1486080\) | ||
Trace bound: | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3017))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 374100 | 358181 | 15919 |
Cusp forms | 368941 | 353889 | 15052 |
Eisenstein series | 5159 | 4292 | 867 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3017))\)
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 the newforms together with their dimension.
Label | \(\chi\) | Newforms | Dimension | \(\chi\) degree |
---|---|---|---|---|
3017.2.a | \(\chi_{3017}(1, \cdot)\) | 3017.2.a.a | 1 | 1 |
3017.2.a.b | 1 | |||
3017.2.a.c | 37 | |||
3017.2.a.d | 48 | |||
3017.2.a.e | 58 | |||
3017.2.a.f | 70 | |||
3017.2.c | \(\chi_{3017}(3016, \cdot)\) | n/a | 286 | 1 |
3017.2.e | \(\chi_{3017}(863, \cdot)\) | n/a | 572 | 2 |
3017.2.f | \(\chi_{3017}(526, \cdot)\) | n/a | 864 | 4 |
3017.2.i | \(\chi_{3017}(430, \cdot)\) | n/a | 572 | 2 |
3017.2.j | \(\chi_{3017}(888, \cdot)\) | n/a | 1144 | 4 |
3017.2.m | \(\chi_{3017}(95, \cdot)\) | n/a | 2288 | 8 |
3017.2.o | \(\chi_{3017}(26, \cdot)\) | n/a | 2288 | 8 |
3017.2.q | \(\chi_{3017}(8, \cdot)\) | n/a | 9072 | 42 |
3017.2.s | \(\chi_{3017}(188, \cdot)\) | n/a | 12012 | 42 |
3017.2.u | \(\chi_{3017}(2, \cdot)\) | n/a | 24024 | 84 |
3017.2.v | \(\chi_{3017}(15, \cdot)\) | n/a | 36288 | 168 |
3017.2.w | \(\chi_{3017}(47, \cdot)\) | n/a | 24024 | 84 |
3017.2.bb | \(\chi_{3017}(13, \cdot)\) | n/a | 48048 | 168 |
3017.2.bc | \(\chi_{3017}(11, \cdot)\) | n/a | 96096 | 336 |
3017.2.be | \(\chi_{3017}(17, \cdot)\) | n/a | 96096 | 336 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3017))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(3017)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(431))\)\(^{\oplus 2}\)