Defining parameters
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 16 \) | ||
Sturm bound: | \(640\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(384))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 592 | 72 | 520 |
Cusp forms | 560 | 72 | 488 |
Eisenstein series | 32 | 0 | 32 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | Fricke | Dim. |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(17\) |
\(+\) | \(-\) | \(-\) | \(19\) |
\(-\) | \(+\) | \(-\) | \(19\) |
\(-\) | \(-\) | \(+\) | \(17\) |
Plus space | \(+\) | \(34\) | |
Minus space | \(-\) | \(38\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(384))\) into newform subspaces
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(384))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_0(384)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 14}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 7}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 10}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 5}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 6}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(96))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(192))\)\(^{\oplus 2}\)