Defining parameters
Level: | \( N \) | \(=\) | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9450.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 128 \) | ||
Sturm bound: | \(4320\) | ||
Trace bound: | \(17\) | ||
Distinguishing \(T_p\): | \(11\), \(13\), \(17\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(9450))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2232 | 152 | 2080 |
Cusp forms | 2089 | 152 | 1937 |
Eisenstein series | 143 | 0 | 143 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | \(7\) | Fricke | Total | Cusp | Eisenstein | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
All | New | Old | All | New | Old | All | New | Old | ||||||||
\(+\) | \(+\) | \(+\) | \(+\) | \(+\) | \(129\) | \(8\) | \(121\) | \(121\) | \(8\) | \(113\) | \(8\) | \(0\) | \(8\) | |||
\(+\) | \(+\) | \(+\) | \(-\) | \(-\) | \(141\) | \(10\) | \(131\) | \(132\) | \(10\) | \(122\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(+\) | \(-\) | \(+\) | \(-\) | \(146\) | \(10\) | \(136\) | \(137\) | \(10\) | \(127\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(+\) | \(-\) | \(-\) | \(+\) | \(139\) | \(10\) | \(129\) | \(130\) | \(10\) | \(120\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(-\) | \(+\) | \(+\) | \(-\) | \(147\) | \(10\) | \(137\) | \(138\) | \(10\) | \(128\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(-\) | \(+\) | \(-\) | \(+\) | \(141\) | \(8\) | \(133\) | \(132\) | \(8\) | \(124\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(-\) | \(-\) | \(+\) | \(+\) | \(134\) | \(10\) | \(124\) | \(125\) | \(10\) | \(115\) | \(9\) | \(0\) | \(9\) | |||
\(+\) | \(-\) | \(-\) | \(-\) | \(-\) | \(139\) | \(10\) | \(129\) | \(130\) | \(10\) | \(120\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(+\) | \(+\) | \(+\) | \(-\) | \(141\) | \(11\) | \(130\) | \(132\) | \(11\) | \(121\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(+\) | \(+\) | \(-\) | \(+\) | \(138\) | \(7\) | \(131\) | \(129\) | \(7\) | \(122\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(+\) | \(-\) | \(+\) | \(+\) | \(139\) | \(8\) | \(131\) | \(130\) | \(8\) | \(122\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(+\) | \(-\) | \(-\) | \(-\) | \(143\) | \(12\) | \(131\) | \(134\) | \(12\) | \(122\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(-\) | \(+\) | \(+\) | \(+\) | \(141\) | \(7\) | \(134\) | \(132\) | \(7\) | \(125\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(-\) | \(+\) | \(-\) | \(-\) | \(138\) | \(11\) | \(127\) | \(129\) | \(11\) | \(118\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(-\) | \(-\) | \(+\) | \(-\) | \(139\) | \(12\) | \(127\) | \(130\) | \(12\) | \(118\) | \(9\) | \(0\) | \(9\) | |||
\(-\) | \(-\) | \(-\) | \(-\) | \(+\) | \(137\) | \(8\) | \(129\) | \(128\) | \(8\) | \(120\) | \(9\) | \(0\) | \(9\) | |||
Plus space | \(+\) | \(1098\) | \(66\) | \(1032\) | \(1027\) | \(66\) | \(961\) | \(71\) | \(0\) | \(71\) | ||||||
Minus space | \(-\) | \(1134\) | \(86\) | \(1048\) | \(1062\) | \(86\) | \(976\) | \(72\) | \(0\) | \(72\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(9450))\) into newform subspaces
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(9450))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(9450)) \simeq \) \(S_{2}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(27))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(35))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(45))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(54))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(70))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(75))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(90))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(105))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(135))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(150))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(175))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(189))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(225))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(270))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(315))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(350))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(378))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(450))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(525))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(630))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(675))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(945))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1050))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1350))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1575))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1890))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(3150))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(4725))\)\(^{\oplus 2}\)