Defining parameters
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 54 \) | ||
Sturm bound: | \(910\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(3\), \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4225))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 496 | 262 | 234 |
Cusp forms | 413 | 229 | 184 |
Eisenstein series | 83 | 33 | 50 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | \(13\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||
\(+\) | \(+\) | \(+\) | \(119\) | \(59\) | \(60\) | \(99\) | \(54\) | \(45\) | \(20\) | \(5\) | \(15\) | |||
\(+\) | \(-\) | \(-\) | \(128\) | \(63\) | \(65\) | \(107\) | \(57\) | \(50\) | \(21\) | \(6\) | \(15\) | |||
\(-\) | \(+\) | \(-\) | \(126\) | \(72\) | \(54\) | \(105\) | \(62\) | \(43\) | \(21\) | \(10\) | \(11\) | |||
\(-\) | \(-\) | \(+\) | \(123\) | \(68\) | \(55\) | \(102\) | \(56\) | \(46\) | \(21\) | \(12\) | \(9\) | |||
Plus space | \(+\) | \(242\) | \(127\) | \(115\) | \(201\) | \(110\) | \(91\) | \(41\) | \(17\) | \(24\) | ||||
Minus space | \(-\) | \(254\) | \(135\) | \(119\) | \(212\) | \(119\) | \(93\) | \(42\) | \(16\) | \(26\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4225))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4225))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4225)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(65))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(169))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(325))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(845))\)\(^{\oplus 2}\)