Defining parameters
Level: | \( N \) | \(=\) | \( 4080 = 2^{4} \cdot 3 \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4080.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 46 \) | ||
Sturm bound: | \(1728\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4080))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 888 | 64 | 824 |
Cusp forms | 841 | 64 | 777 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(17\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(4\) |
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(3\) |
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(4\) |
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(5\) |
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(4\) |
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(4\) |
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(3\) |
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(5\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(6\) |
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(6\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(2\) |
Plus space | \(+\) | \(26\) | |||
Minus space | \(-\) | \(38\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4080))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4080))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4080)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(48))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(51))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(68))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(85))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(102))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(136))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(170))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(204))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(240))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(255))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(272))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(340))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(408))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(510))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(680))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(816))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1020))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2040))\)\(^{\oplus 2}\)