Defining parameters
Level: | \( N \) | \(=\) | \( 7175 = 5^{2} \cdot 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7175.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 33 \) | ||
Sturm bound: | \(1680\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\), \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(7175))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 852 | 380 | 472 |
Cusp forms | 829 | 380 | 449 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(7\) | \(41\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(36\) |
\(+\) | \(+\) | \(-\) | $-$ | \(57\) |
\(+\) | \(-\) | \(+\) | $-$ | \(54\) |
\(+\) | \(-\) | \(-\) | $+$ | \(33\) |
\(-\) | \(+\) | \(+\) | $-$ | \(56\) |
\(-\) | \(+\) | \(-\) | $+$ | \(42\) |
\(-\) | \(-\) | \(+\) | $+$ | \(44\) |
\(-\) | \(-\) | \(-\) | $-$ | \(58\) |
Plus space | \(+\) | \(155\) | ||
Minus space | \(-\) | \(225\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(7175))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(7175))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(7175)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(41))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(205))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(287))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1025))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1435))\)\(^{\oplus 2}\)