Defining parameters
Level: | \( N \) | \(=\) | \( 4950 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4950.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 62 \) | ||
Sturm bound: | \(2160\) | ||
Trace bound: | \(19\) | ||
Distinguishing \(T_p\): | \(7\), \(13\), \(17\), \(19\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4950))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1128 | 81 | 1047 |
Cusp forms | 1033 | 81 | 952 |
Eisenstein series | 95 | 0 | 95 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(11\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(5\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(6\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(4\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(6\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(5\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(6\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(6\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(2\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(4\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(6\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(5\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(7\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(7\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(5\) |
Plus space | \(+\) | \(33\) | |||
Minus space | \(-\) | \(48\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4950))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4950))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4950)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(198))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(275))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(495))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(550))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(825))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(990))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1650))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2475))\)\(^{\oplus 2}\)