Defining parameters
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 46 \) | ||
Sturm bound: | \(1584\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(7\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3630))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 840 | 74 | 766 |
Cusp forms | 745 | 74 | 671 |
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.
\(2\) | \(3\) | \(5\) | \(11\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(4\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(5\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(4\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(5\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(7\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(2\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(3\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(7\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(4\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(5\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(4\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(5\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(3\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(7\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(7\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(28\) | |||
Minus space | \(-\) | \(46\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3630))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3630))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3630)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(165))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(330))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(726))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1815))\)\(^{\oplus 2}\)