Defining parameters
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(192\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(252))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 8 | 148 |
Cusp forms | 132 | 8 | 124 |
Eisenstein series | 24 | 0 | 24 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(7\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | \(-\) | \(2\) |
\(-\) | \(+\) | \(-\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(+\) | \(+\) | \(2\) |
\(-\) | \(-\) | \(-\) | \(-\) | \(2\) |
Plus space | \(+\) | \(4\) | ||
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(252))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 7 | |||||||
252.4.a.a | $1$ | $14.868$ | \(\Q\) | None | \(0\) | \(0\) | \(-14\) | \(-7\) | $-$ | $-$ | $+$ | \(q-14q^{5}-7q^{7}-4q^{11}+54q^{13}+\cdots\) | |
252.4.a.b | $1$ | $14.868$ | \(\Q\) | None | \(0\) | \(0\) | \(-6\) | \(7\) | $-$ | $-$ | $-$ | \(q-6q^{5}+7q^{7}-6^{2}q^{11}+62q^{13}+\cdots\) | |
252.4.a.c | $1$ | $14.868$ | \(\Q\) | None | \(0\) | \(0\) | \(-6\) | \(7\) | $-$ | $-$ | $-$ | \(q-6q^{5}+7q^{7}+12q^{11}-82q^{13}+\cdots\) | |
252.4.a.d | $1$ | $14.868$ | \(\Q\) | None | \(0\) | \(0\) | \(8\) | \(-7\) | $-$ | $-$ | $+$ | \(q+8q^{5}-7q^{7}+40q^{11}-12q^{13}+\cdots\) | |
252.4.a.e | $2$ | $14.868$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(0\) | \(-14\) | $-$ | $+$ | $+$ | \(q+\beta q^{5}-7q^{7}-13\beta q^{11}-30q^{13}+\cdots\) | |
252.4.a.f | $2$ | $14.868$ | \(\Q(\sqrt{7}) \) | None | \(0\) | \(0\) | \(0\) | \(14\) | $-$ | $+$ | $-$ | \(q+\beta q^{5}+7q^{7}+\beta q^{11}+26q^{13}-5\beta q^{17}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(252))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(252)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(21))\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(42))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(63))\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(84))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(126))\)\(^{\oplus 2}\)