Defining parameters
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 26 \) | ||
Sturm bound: | \(2688\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8008))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1360 | 180 | 1180 |
Cusp forms | 1329 | 180 | 1149 |
Eisenstein series | 31 | 0 | 31 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | \(11\) | \(13\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(10\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(15\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(11\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(14\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(9\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(10\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(12\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(10\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(13\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(11\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(11\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(14\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(11\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(10\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(10\) |
Plus space | \(+\) | \(86\) | |||
Minus space | \(-\) | \(94\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8008))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8008))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(52))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(88))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(91))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(104))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(182))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(308))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(364))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(572))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(616))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(728))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1001))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1144))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2002))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4004))\)\(^{\oplus 2}\)