Defining parameters
Level: | \( N \) | \(=\) | \( 4624 = 2^{4} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4624.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 46 \) | ||
Sturm bound: | \(1224\) | ||
Trace bound: | \(15\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4624))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 666 | 143 | 523 |
Cusp forms | 559 | 128 | 431 |
Eisenstein series | 107 | 15 | 92 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(17\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(32\) |
\(+\) | \(-\) | $-$ | \(36\) |
\(-\) | \(+\) | $-$ | \(32\) |
\(-\) | \(-\) | $+$ | \(28\) |
Plus space | \(+\) | \(60\) | |
Minus space | \(-\) | \(68\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4624))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4624))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4624)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(289))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1156))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2312))\)\(^{\oplus 2}\)