Defining parameters
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 10 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(3\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(700))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 138 | 10 | 128 |
Cusp forms | 103 | 10 | 93 |
Eisenstein series | 35 | 0 | 35 |
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 |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | $-$ | \(2\) |
\(-\) | \(+\) | \(-\) | $+$ | \(2\) |
\(-\) | \(-\) | \(+\) | $+$ | \(3\) |
\(-\) | \(-\) | \(-\) | $-$ | \(3\) |
Plus space | \(+\) | \(5\) | ||
Minus space | \(-\) | \(5\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(700))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(700))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(700)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(100))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 2}\)