Defining parameters
Level: | \( N \) | \(=\) | \( 5175 = 3^{2} \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5175.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 62 \) | ||
Sturm bound: | \(1440\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(5175))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 744 | 173 | 571 |
Cusp forms | 697 | 173 | 524 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(5\) | \(23\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(17\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(17\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(17\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(17\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(29\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(20\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(25\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(31\) |
Plus space | \(+\) | \(79\) | ||
Minus space | \(-\) | \(94\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(5175))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(5175))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(5175)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(115))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(207))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(345))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(575))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1035))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1725))\)\(^{\oplus 2}\)