Defining parameters
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 86 \) | ||
Sturm bound: | \(3168\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(3\), \(13\), \(17\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8470))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1632 | 218 | 1414 |
Cusp forms | 1537 | 218 | 1319 |
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.
\(2\) | \(5\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(12\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(15\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(13\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(15\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(13\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(15\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(12\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(15\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(17\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(10\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(12\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(15\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(12\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(15\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(17\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(10\) |
Plus space | \(+\) | \(98\) | |||
Minus space | \(-\) | \(120\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8470))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8470))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8470)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(385))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(770))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1694))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4235))\)\(^{\oplus 2}\)