Defining parameters
Level: | \( N \) | \(=\) | \( 4840 = 2^{3} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4840.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 34 \) | ||
Sturm bound: | \(1584\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4840))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 840 | 109 | 731 |
Cusp forms | 745 | 109 | 636 |
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.
\(2\) | \(5\) | \(11\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(12\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(15\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(17\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(10\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(12\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(15\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(13\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(15\) |
Plus space | \(+\) | \(50\) | ||
Minus space | \(-\) | \(59\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4840))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4840))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4840)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(440))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(484))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(968))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2420))\)\(^{\oplus 2}\)