Defining parameters
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 39 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(5\), \(13\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3234))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 704 | 68 | 636 |
Cusp forms | 641 | 68 | 573 |
Eisenstein series | 63 | 0 | 63 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(7\) | \(11\) | Fricke | Dim |
---|---|---|---|---|---|
\(+\) | \(+\) | \(+\) | \(+\) | $+$ | \(5\) |
\(+\) | \(+\) | \(+\) | \(-\) | $-$ | \(4\) |
\(+\) | \(+\) | \(-\) | \(+\) | $-$ | \(4\) |
\(+\) | \(+\) | \(-\) | \(-\) | $+$ | \(4\) |
\(+\) | \(-\) | \(+\) | \(+\) | $-$ | \(6\) |
\(+\) | \(-\) | \(+\) | \(-\) | $+$ | \(3\) |
\(+\) | \(-\) | \(-\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | \(-\) | \(-\) | $-$ | \(5\) |
\(-\) | \(+\) | \(+\) | \(+\) | $-$ | \(5\) |
\(-\) | \(+\) | \(+\) | \(-\) | $+$ | \(4\) |
\(-\) | \(+\) | \(-\) | \(+\) | $+$ | \(3\) |
\(-\) | \(+\) | \(-\) | \(-\) | $-$ | \(6\) |
\(-\) | \(-\) | \(+\) | \(+\) | $+$ | \(2\) |
\(-\) | \(-\) | \(+\) | \(-\) | $-$ | \(7\) |
\(-\) | \(-\) | \(-\) | \(+\) | $-$ | \(7\) |
\(-\) | \(-\) | \(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(24\) | |||
Minus space | \(-\) | \(44\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3234))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3234))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3234)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(22))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(66))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(147))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(154))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(294))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(462))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(539))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1078))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1617))\)\(^{\oplus 2}\)