Defining parameters
Level: | \( N \) | \(=\) | \( 8040 = 2^{3} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8040.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 29 \) | ||
Sturm bound: | \(3264\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8040))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1648 | 132 | 1516 |
Cusp forms | 1617 | 132 | 1485 |
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.
\(2\) | \(3\) | \(5\) | \(67\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(9\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(7\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(11\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(6\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(10\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(6\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(6\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(11\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(8\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(9\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(8\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(8\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(9\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(8\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(11\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(5\) |
Plus space | \(+\) | \(58\) | |||
Minus space | \(-\) | \(74\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8040))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8040))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8040)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(268))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(335))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(402))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(536))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(670))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(804))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1005))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1340))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1608))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2010))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2680))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4020))\)\(^{\oplus 2}\)