Defining parameters
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 80 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(20\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{80}(\Gamma_0(2))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 21 | 7 | 14 |
Cusp forms | 19 | 7 | 12 |
Eisenstein series | 2 | 0 | 2 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | Dim |
---|---|
\(+\) | \(4\) |
\(-\) | \(3\) |
Trace form
Decomposition of \(S_{80}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
2.80.a.a | $3$ | $79.047$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(16\!\cdots\!64\) | \(-45\!\cdots\!36\) | \(-40\!\cdots\!50\) | \(14\!\cdots\!12\) | $-$ | \(q+2^{39}q^{2}+(-1528323113916241812+\cdots)q^{3}+\cdots\) | |
2.80.a.b | $4$ | $79.047$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(-21\!\cdots\!52\) | \(43\!\cdots\!88\) | \(-20\!\cdots\!80\) | \(25\!\cdots\!04\) | $+$ | \(q-2^{39}q^{2}+(1099291558848636972+\cdots)q^{3}+\cdots\) |
Decomposition of \(S_{80}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces
\( S_{80}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{80}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)