Defining parameters
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 44 \) | ||
Sturm bound: | \(704\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(5\), \(13\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2541))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 376 | 108 | 268 |
Cusp forms | 329 | 108 | 221 |
Eisenstein series | 47 | 0 | 47 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(7\) | \(11\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(42\) | \(12\) | \(30\) | \(37\) | \(12\) | \(25\) | \(5\) | \(0\) | \(5\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(51\) | \(15\) | \(36\) | \(45\) | \(15\) | \(30\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(48\) | \(12\) | \(36\) | \(42\) | \(12\) | \(30\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(47\) | \(15\) | \(32\) | \(41\) | \(15\) | \(26\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(52\) | \(16\) | \(36\) | \(46\) | \(16\) | \(30\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(43\) | \(10\) | \(33\) | \(37\) | \(10\) | \(27\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(46\) | \(8\) | \(38\) | \(40\) | \(8\) | \(32\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(47\) | \(20\) | \(27\) | \(41\) | \(20\) | \(21\) | \(6\) | \(0\) | \(6\) | |||
Plus space | \(+\) | \(178\) | \(45\) | \(133\) | \(155\) | \(45\) | \(110\) | \(23\) | \(0\) | \(23\) | |||||
Minus space | \(-\) | \(198\) | \(63\) | \(135\) | \(174\) | \(63\) | \(111\) | \(24\) | \(0\) | \(24\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2541))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2541))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2541)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(77))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(231))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(847))\)\(^{\oplus 2}\)