Defining parameters
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 52 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(13\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{52}(\Gamma_0(2))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 14 | 4 | 10 |
Cusp forms | 12 | 4 | 8 |
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 |
---|---|
\(+\) | \(2\) |
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{52}^{\mathrm{new}}(\Gamma_0(2))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | |||||||
2.52.a.a | $2$ | $32.946$ | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) | None | \(-67108864\) | \(187290382776\) | \(-12\!\cdots\!00\) | \(-41\!\cdots\!52\) | $+$ | \(q-2^{25}q^{2}+(93645191388-17\beta )q^{3}+\cdots\) | |
2.52.a.b | $2$ | $32.946$ | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) | None | \(67108864\) | \(889619774904\) | \(-50\!\cdots\!00\) | \(-64\!\cdots\!08\) | $-$ | \(q+2^{25}q^{2}+(444809887452-\beta )q^{3}+\cdots\) |
Decomposition of \(S_{52}^{\mathrm{old}}(\Gamma_0(2))\) into lower level spaces
\( S_{52}^{\mathrm{old}}(\Gamma_0(2)) \cong \) \(S_{52}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)