Defining parameters
Level: | \( N \) | = | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | = | \( 10 \) |
Nonzero newspaces: | \( 4 \) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(5880\) | ||
Trace bound: | \(1\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_1(98))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2706 | 847 | 1859 |
Cusp forms | 2586 | 847 | 1739 |
Eisenstein series | 120 | 0 | 120 |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_1(98))\)
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 |
---|---|---|---|---|
98.10.a | \(\chi_{98}(1, \cdot)\) | 98.10.a.a | 1 | 1 |
98.10.a.b | 1 | |||
98.10.a.c | 1 | |||
98.10.a.d | 2 | |||
98.10.a.e | 2 | |||
98.10.a.f | 2 | |||
98.10.a.g | 3 | |||
98.10.a.h | 3 | |||
98.10.a.i | 3 | |||
98.10.a.j | 3 | |||
98.10.a.k | 4 | |||
98.10.a.l | 6 | |||
98.10.c | \(\chi_{98}(67, \cdot)\) | 98.10.c.a | 2 | 2 |
98.10.c.b | 2 | |||
98.10.c.c | 2 | |||
98.10.c.d | 2 | |||
98.10.c.e | 2 | |||
98.10.c.f | 2 | |||
98.10.c.g | 4 | |||
98.10.c.h | 4 | |||
98.10.c.i | 4 | |||
98.10.c.j | 4 | |||
98.10.c.k | 6 | |||
98.10.c.l | 6 | |||
98.10.c.m | 8 | |||
98.10.c.n | 12 | |||
98.10.e | \(\chi_{98}(15, \cdot)\) | 98.10.e.a | 126 | 6 |
98.10.e.b | 126 | |||
98.10.g | \(\chi_{98}(9, \cdot)\) | 98.10.g.a | 252 | 12 |
98.10.g.b | 252 |
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_1(98))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_1(98)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 2}\)