Defining parameters
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{8}(\Gamma_0(60))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 90 | 4 | 86 |
Cusp forms | 78 | 4 | 74 |
Eisenstein series | 12 | 0 | 12 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(5\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | $-$ | \(1\) |
\(-\) | \(+\) | \(-\) | $+$ | \(1\) |
\(-\) | \(-\) | \(+\) | $+$ | \(1\) |
\(-\) | \(-\) | \(-\) | $-$ | \(1\) |
Plus space | \(+\) | \(2\) | ||
Minus space | \(-\) | \(2\) |
Trace form
Decomposition of \(S_{8}^{\mathrm{new}}(\Gamma_0(60))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 5 | |||||||
60.8.a.a | $1$ | $18.743$ | \(\Q\) | None | \(0\) | \(-27\) | \(-125\) | \(1028\) | $-$ | $+$ | $+$ | \(q-3^{3}q^{3}-5^{3}q^{5}+1028q^{7}+3^{6}q^{9}+\cdots\) | |
60.8.a.b | $1$ | $18.743$ | \(\Q\) | None | \(0\) | \(-27\) | \(125\) | \(-832\) | $-$ | $+$ | $-$ | \(q-3^{3}q^{3}+5^{3}q^{5}-832q^{7}+3^{6}q^{9}+\cdots\) | |
60.8.a.c | $1$ | $18.743$ | \(\Q\) | None | \(0\) | \(27\) | \(-125\) | \(92\) | $-$ | $-$ | $+$ | \(q+3^{3}q^{3}-5^{3}q^{5}+92q^{7}+3^{6}q^{9}+\cdots\) | |
60.8.a.d | $1$ | $18.743$ | \(\Q\) | None | \(0\) | \(27\) | \(125\) | \(-1408\) | $-$ | $-$ | $-$ | \(q+3^{3}q^{3}+5^{3}q^{5}-1408q^{7}+3^{6}q^{9}+\cdots\) |
Decomposition of \(S_{8}^{\mathrm{old}}(\Gamma_0(60))\) into lower level spaces
\( S_{8}^{\mathrm{old}}(\Gamma_0(60)) \cong \) \(S_{8}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 8}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 6}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(10))\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(12))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 3}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(20))\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(\Gamma_0(30))\)\(^{\oplus 2}\)