Defining parameters
Level: | \( N \) | = | \( 4096 = 2^{12} \) |
Weight: | \( k \) | = | \( 2 \) |
Nonzero newspaces: | \( 10 \) | ||
Sturm bound: | \(2097152\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4096))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 528128 | 296000 | 232128 |
Cusp forms | 520449 | 293824 | 226625 |
Eisenstein series | 7679 | 2176 | 5503 |
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4096))\)
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 |
---|---|---|---|---|
4096.2.a | \(\chi_{4096}(1, \cdot)\) | 4096.2.a.a | 4 | 1 |
4096.2.a.b | 4 | |||
4096.2.a.c | 4 | |||
4096.2.a.d | 4 | |||
4096.2.a.e | 4 | |||
4096.2.a.f | 4 | |||
4096.2.a.g | 4 | |||
4096.2.a.h | 4 | |||
4096.2.a.i | 8 | |||
4096.2.a.j | 8 | |||
4096.2.a.k | 8 | |||
4096.2.a.l | 8 | |||
4096.2.a.m | 8 | |||
4096.2.a.n | 8 | |||
4096.2.a.o | 8 | |||
4096.2.a.p | 8 | |||
4096.2.a.q | 8 | |||
4096.2.a.r | 8 | |||
4096.2.a.s | 8 | |||
4096.2.b | \(\chi_{4096}(2049, \cdot)\) | n/a | 120 | 1 |
4096.2.e | \(\chi_{4096}(1025, \cdot)\) | n/a | 240 | 2 |
4096.2.g | \(\chi_{4096}(513, \cdot)\) | n/a | 480 | 4 |
4096.2.i | \(\chi_{4096}(257, \cdot)\) | n/a | 1024 | 8 |
4096.2.k | \(\chi_{4096}(129, \cdot)\) | n/a | 1920 | 16 |
4096.2.m | \(\chi_{4096}(65, \cdot)\) | n/a | 3968 | 32 |
4096.2.o | \(\chi_{4096}(33, \cdot)\) | n/a | 8064 | 64 |
4096.2.q | \(\chi_{4096}(17, \cdot)\) | n/a | 16256 | 128 |
4096.2.s | \(\chi_{4096}(9, \cdot)\) | None | 0 | 256 |
4096.2.u | \(\chi_{4096}(5, \cdot)\) | n/a | 261632 | 512 |
"n/a" means that newforms for that character have not been added to the database yet
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4096))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_1(4096)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(128))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(256))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(512))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1024))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2048))\)\(^{\oplus 2}\)