Defining parameters
Level: | \( N \) | \(=\) | \( 6272 = 2^{7} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6272.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 52 \) | ||
Sturm bound: | \(1792\) | ||
Trace bound: | \(29\) | ||
Distinguishing \(T_p\): | \(3\), \(5\), \(11\), \(13\), \(23\), \(29\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6272))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 960 | 164 | 796 |
Cusp forms | 833 | 164 | 669 |
Eisenstein series | 127 | 0 | 127 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(36\) |
\(+\) | \(-\) | $-$ | \(45\) |
\(-\) | \(+\) | $-$ | \(44\) |
\(-\) | \(-\) | $+$ | \(39\) |
Plus space | \(+\) | \(75\) | |
Minus space | \(-\) | \(89\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6272))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6272))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6272)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(32))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(56))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(98))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(112))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(128))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(196))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(224))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(392))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(448))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(784))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(896))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1568))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3136))\)\(^{\oplus 2}\)