Defining parameters
Level: | \( N \) | \(=\) | \( 10000 = 2^{4} \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 10000.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 44 \) | ||
Sturm bound: | \(3000\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(10000))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1590 | 248 | 1342 |
Cusp forms | 1411 | 232 | 1179 |
Eisenstein series | 179 | 16 | 163 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(58\) |
\(+\) | \(-\) | $-$ | \(62\) |
\(-\) | \(+\) | $-$ | \(58\) |
\(-\) | \(-\) | $+$ | \(54\) |
Plus space | \(+\) | \(112\) | |
Minus space | \(-\) | \(120\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(10000))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(10000))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(10000)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(400))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(125))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(250))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(500))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(625))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1000))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1250))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2000))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2500))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(5000))\)\(^{\oplus 2}\)