Defining parameters
Level: | \( N \) | \(=\) | \( 3174 = 2 \cdot 3 \cdot 23^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3174.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 30 \) | ||
Sturm bound: | \(1104\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(3174))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 600 | 83 | 517 |
Cusp forms | 505 | 83 | 422 |
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.
\(2\) | \(3\) | \(23\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(66\) | \(7\) | \(59\) | \(55\) | \(7\) | \(48\) | \(11\) | \(0\) | \(11\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(84\) | \(14\) | \(70\) | \(72\) | \(14\) | \(58\) | \(12\) | \(0\) | \(12\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(78\) | \(11\) | \(67\) | \(66\) | \(11\) | \(55\) | \(12\) | \(0\) | \(12\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(72\) | \(10\) | \(62\) | \(60\) | \(10\) | \(50\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(78\) | \(13\) | \(65\) | \(66\) | \(13\) | \(53\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(72\) | \(8\) | \(64\) | \(60\) | \(8\) | \(52\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(78\) | \(5\) | \(73\) | \(66\) | \(5\) | \(61\) | \(12\) | \(0\) | \(12\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(72\) | \(15\) | \(57\) | \(60\) | \(15\) | \(45\) | \(12\) | \(0\) | \(12\) | |||
Plus space | \(+\) | \(288\) | \(30\) | \(258\) | \(241\) | \(30\) | \(211\) | \(47\) | \(0\) | \(47\) | |||||
Minus space | \(-\) | \(312\) | \(53\) | \(259\) | \(264\) | \(53\) | \(211\) | \(48\) | \(0\) | \(48\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(3174))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(3174))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(3174)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(46))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(138))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(529))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1058))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1587))\)\(^{\oplus 2}\)