Defining parameters
Level: | \( N \) | \(=\) | \( 68 = 2^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 68.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(90\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(68))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 84 | 12 | 72 |
Cusp forms | 78 | 12 | 66 |
Eisenstein series | 6 | 0 | 6 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(17\) | Fricke | Dim |
---|---|---|---|
\(-\) | \(+\) | $-$ | \(7\) |
\(-\) | \(-\) | $+$ | \(5\) |
Plus space | \(+\) | \(5\) | |
Minus space | \(-\) | \(7\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(68))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 17 | |||||||
68.10.a.a | $5$ | $35.022$ | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) | None | \(0\) | \(-236\) | \(-1138\) | \(3712\) | $-$ | $-$ | \(q+(-47+\beta _{1})q^{3}+(-227+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\) | |
68.10.a.b | $7$ | $35.022$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | \(0\) | \(-74\) | \(1480\) | \(5132\) | $-$ | $+$ | \(q+(-11+\beta _{1})q^{3}+(212-\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\) |
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(68))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_0(68)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 4}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(17))\)\(^{\oplus 3}\)\(\oplus\)\(S_{10}^{\mathrm{new}}(\Gamma_0(34))\)\(^{\oplus 2}\)