Defining parameters
Level: | \( N \) | \(=\) | \( 8325 = 3^{2} \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8325.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 76 \) | ||
Sturm bound: | \(2280\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(2\), \(7\), \(11\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8325))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1164 | 285 | 879 |
Cusp forms | 1117 | 285 | 832 |
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.
\(3\) | \(5\) | \(37\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(24\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(30\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(32\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(28\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(42\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(39\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(44\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(46\) |
Plus space | \(+\) | \(135\) | ||
Minus space | \(-\) | \(150\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8325))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8325))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8325)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(37))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(111))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(185))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(333))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(555))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(925))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1665))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2775))\)\(^{\oplus 2}\)