Defining parameters
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(32\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(69))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 26 | 12 | 14 |
Cusp forms | 22 | 12 | 10 |
Eisenstein series | 4 | 0 | 4 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(3\) | \(23\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(4\) |
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(4\) |
Plus space | \(+\) | \(8\) | |
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(69))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 23 | |||||||
69.4.a.a | $2$ | $4.071$ | \(\Q(\sqrt{5}) \) | None | \(-4\) | \(6\) | \(-26\) | \(-10\) | $-$ | $+$ | \(q+(-2-\beta )q^{2}+3q^{3}+(1+4\beta )q^{4}+\cdots\) | |
69.4.a.b | $2$ | $4.071$ | \(\Q(\sqrt{2}) \) | None | \(-2\) | \(-6\) | \(8\) | \(-28\) | $+$ | $-$ | \(q+(-1+\beta )q^{2}-3q^{3}+(1-2\beta )q^{4}+\cdots\) | |
69.4.a.c | $4$ | $4.071$ | 4.4.1140200.1 | None | \(-2\) | \(-12\) | \(-2\) | \(32\) | $+$ | $+$ | \(q+\beta _{1}q^{2}-3q^{3}+(6-\beta _{1}-2\beta _{2})q^{4}+\cdots\) | |
69.4.a.d | $4$ | $4.071$ | 4.4.2009704.1 | None | \(4\) | \(12\) | \(4\) | \(-14\) | $-$ | $-$ | \(q+(1-\beta _{1})q^{2}+3q^{3}+(7-2\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(69))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(69)) \cong \) \(S_{4}^{\mathrm{new}}(\Gamma_0(23))\)\(^{\oplus 2}\)