Defining parameters
Level: | \( N \) | \(=\) | \( 534 = 2 \cdot 3 \cdot 89 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 534.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(180\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(534))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 94 | 15 | 79 |
Cusp forms | 87 | 15 | 72 |
Eisenstein series | 7 | 0 | 7 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(89\) | Fricke | Dim |
---|---|---|---|---|
\(+\) | \(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(+\) | \(-\) | $-$ | \(2\) |
\(+\) | \(-\) | \(+\) | $-$ | \(4\) |
\(-\) | \(+\) | \(+\) | $-$ | \(2\) |
\(-\) | \(+\) | \(-\) | $+$ | \(1\) |
\(-\) | \(-\) | \(-\) | $-$ | \(4\) |
Plus space | \(+\) | \(3\) | ||
Minus space | \(-\) | \(12\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(534))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 89 | |||||||
534.2.a.a | $1$ | $4.264$ | \(\Q\) | None | \(1\) | \(-1\) | \(-2\) | \(-2\) | $-$ | $+$ | $-$ | \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}-2q^{7}+\cdots\) | |
534.2.a.b | $2$ | $4.264$ | \(\Q(\sqrt{2}) \) | None | \(-2\) | \(-2\) | \(-4\) | \(4\) | $+$ | $+$ | $+$ | \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+(2+\beta )q^{7}+\cdots\) | |
534.2.a.c | $2$ | $4.264$ | \(\Q(\sqrt{13}) \) | None | \(-2\) | \(-2\) | \(3\) | \(-2\) | $+$ | $+$ | $-$ | \(q-q^{2}-q^{3}+q^{4}+(1+\beta )q^{5}+q^{6}+\cdots\) | |
534.2.a.d | $2$ | $4.264$ | \(\Q(\sqrt{5}) \) | None | \(2\) | \(-2\) | \(1\) | \(2\) | $-$ | $+$ | $+$ | \(q+q^{2}-q^{3}+q^{4}+\beta q^{5}-q^{6}+2\beta q^{7}+\cdots\) | |
534.2.a.e | $4$ | $4.264$ | 4.4.106168.1 | None | \(-4\) | \(4\) | \(3\) | \(2\) | $+$ | $-$ | $+$ | \(q-q^{2}+q^{3}+q^{4}+(1+\beta _{2})q^{5}-q^{6}+\cdots\) | |
534.2.a.f | $4$ | $4.264$ | 4.4.5225.1 | None | \(4\) | \(4\) | \(1\) | \(4\) | $-$ | $-$ | $-$ | \(q+q^{2}+q^{3}+q^{4}+(\beta _{1}-\beta _{3})q^{5}+q^{6}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(534))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(534)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(89))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(178))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(267))\)\(^{\oplus 2}\)