Defining parameters
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 81 \) | ||
Sturm bound: | \(3360\) | ||
Trace bound: | \(23\) | ||
Distinguishing \(T_p\): | \(3\), \(11\), \(13\), \(19\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9800))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1776 | 195 | 1581 |
Cusp forms | 1585 | 195 | 1390 |
Eisenstein series | 191 | 0 | 191 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(5\) | \(7\) | Fricke | Dim. |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(19\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(26\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(28\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(24\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(25\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(22\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(24\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(27\) |
Plus space | \(+\) | \(89\) | ||
Minus space | \(-\) | \(106\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9800))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9800))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9800)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(245))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(280))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(490))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(700))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(980))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1400))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1960))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2450))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4900))\)\(^{\oplus 2}\)