Defining parameters
Level: | \( N \) | \(=\) | \( 6030 = 2 \cdot 3^{2} \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6030.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 51 \) | ||
Sturm bound: | \(2448\) | ||
Trace bound: | \(13\) | ||
Distinguishing \(T_p\): | \(7\), \(11\), \(13\), \(17\), \(23\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6030))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1240 | 110 | 1130 |
Cusp forms | 1209 | 110 | 1099 |
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 |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(4\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(8\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(6\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(4\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(9\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(7\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(8\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(9\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(6\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(4\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(4\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(8\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(8\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(9\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(9\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(7\) |
Plus space | \(+\) | \(46\) | |||
Minus space | \(-\) | \(64\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6030))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6030))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6030)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(201))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(67))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(134))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(335))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(402))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(603))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(670))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1005))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1206))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2010))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3015))\)\(^{\oplus 2}\)