Defining parameters
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 11 \) | ||
Sturm bound: | \(2880\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8004))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1452 | 104 | 1348 |
Cusp forms | 1429 | 104 | 1325 |
Eisenstein series | 23 | 0 | 23 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(23\) | \(29\) | Fricke | Dim |
---|---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(14\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(10\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(12\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(16\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(10\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(18\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(16\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(8\) |
Plus space | \(+\) | \(40\) | |||
Minus space | \(-\) | \(64\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8004))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8004))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(92))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(116))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(174))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(276))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(348))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(667))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2001))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2668))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4002))\)\(^{\oplus 2}\)