Defining parameters
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(6\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(5))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 7 | 3 | 4 |
Cusp forms | 5 | 3 | 2 |
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.
\(5\) | Dim |
---|---|
\(+\) | \(2\) |
\(-\) | \(1\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(5))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | |||||||
5.12.a.a | $1$ | $3.842$ | \(\Q\) | None | \(34\) | \(-792\) | \(3125\) | \(-17556\) | $-$ | \(q+34q^{2}-792q^{3}-892q^{4}+5^{5}q^{5}+\cdots\) | |
5.12.a.b | $2$ | $3.842$ | \(\Q(\sqrt{151}) \) | None | \(-20\) | \(-220\) | \(-6250\) | \(57900\) | $+$ | \(q+(-10+3\beta )q^{2}+(-110+2^{4}\beta )q^{3}+\cdots\) |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(5))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(5)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)