Defining parameters
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(72\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(72))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 68 | 6 | 62 |
Cusp forms | 52 | 6 | 46 |
Eisenstein series | 16 | 0 | 16 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(2\) |
Plus space | \(+\) | \(3\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(72))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
72.6.a.a | $1$ | $11.548$ | \(\Q\) | None | \(0\) | \(0\) | \(-94\) | \(144\) | $+$ | $-$ | \(q-94q^{5}+12^{2}q^{7}+380q^{11}+814q^{13}+\cdots\) | |
72.6.a.b | $1$ | $11.548$ | \(\Q\) | None | \(0\) | \(0\) | \(-38\) | \(120\) | $-$ | $-$ | \(q-38q^{5}+120q^{7}-524q^{11}-962q^{13}+\cdots\) | |
72.6.a.c | $1$ | $11.548$ | \(\Q\) | None | \(0\) | \(0\) | \(-16\) | \(12\) | $+$ | $+$ | \(q-2^{4}q^{5}+12q^{7}-448q^{11}-206q^{13}+\cdots\) | |
72.6.a.d | $1$ | $11.548$ | \(\Q\) | None | \(0\) | \(0\) | \(16\) | \(12\) | $-$ | $+$ | \(q+2^{4}q^{5}+12q^{7}+448q^{11}-206q^{13}+\cdots\) | |
72.6.a.e | $1$ | $11.548$ | \(\Q\) | None | \(0\) | \(0\) | \(34\) | \(-240\) | $-$ | $-$ | \(q+34q^{5}-240q^{7}+124q^{11}+46q^{13}+\cdots\) | |
72.6.a.f | $1$ | $11.548$ | \(\Q\) | None | \(0\) | \(0\) | \(74\) | \(-24\) | $+$ | $-$ | \(q+74q^{5}-24q^{7}-124q^{11}+478q^{13}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(72))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(72)) \simeq \) \(S_{6}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(8))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(9))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(18))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(24))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_0(36))\)\(^{\oplus 2}\)