Defining parameters
Level: | \( N \) | \(=\) | \( 8349 = 3 \cdot 11^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8349.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 41 \) | ||
Sturm bound: | \(2112\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(2\), \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(8349))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1080 | 398 | 682 |
Cusp forms | 1033 | 398 | 635 |
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.
\(3\) | \(11\) | \(23\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | |||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(120\) | \(44\) | \(76\) | \(115\) | \(44\) | \(71\) | \(5\) | \(0\) | \(5\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(150\) | \(56\) | \(94\) | \(144\) | \(56\) | \(88\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(150\) | \(55\) | \(95\) | \(144\) | \(55\) | \(89\) | \(6\) | \(0\) | \(6\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(120\) | \(45\) | \(75\) | \(114\) | \(45\) | \(69\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(132\) | \(52\) | \(80\) | \(126\) | \(52\) | \(74\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(138\) | \(40\) | \(98\) | \(132\) | \(40\) | \(92\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(138\) | \(48\) | \(90\) | \(132\) | \(48\) | \(84\) | \(6\) | \(0\) | \(6\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(132\) | \(58\) | \(74\) | \(126\) | \(58\) | \(68\) | \(6\) | \(0\) | \(6\) | |||
Plus space | \(+\) | \(516\) | \(177\) | \(339\) | \(493\) | \(177\) | \(316\) | \(23\) | \(0\) | \(23\) | |||||
Minus space | \(-\) | \(564\) | \(221\) | \(343\) | \(540\) | \(221\) | \(319\) | \(24\) | \(0\) | \(24\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(8349))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(8349))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(8349)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(11))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(33))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(69))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(121))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(253))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(363))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(759))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(2783))\)\(^{\oplus 2}\)