Defining parameters
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(15))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 24 | 8 | 16 |
Cusp forms | 20 | 8 | 12 |
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.
\(3\) | \(5\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(2\) |
\(+\) | \(-\) | $-$ | \(1\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(3\) |
Plus space | \(+\) | \(5\) | |
Minus space | \(-\) | \(3\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(15))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | 5 | |||||||
15.12.a.a | $1$ | $11.525$ | \(\Q\) | None | \(-56\) | \(-243\) | \(3125\) | \(27984\) | $+$ | $-$ | \(q-56q^{2}-3^{5}q^{3}+1088q^{4}+5^{5}q^{5}+\cdots\) | |
15.12.a.b | $2$ | $11.525$ | \(\Q(\sqrt{1609}) \) | None | \(-22\) | \(486\) | \(-6250\) | \(-10864\) | $-$ | $+$ | \(q+(-11-\beta )q^{2}+3^{5}q^{3}+(-318+22\beta )q^{4}+\cdots\) | |
15.12.a.c | $2$ | $11.525$ | \(\Q(\sqrt{1801}) \) | None | \(-13\) | \(-486\) | \(-6250\) | \(7784\) | $+$ | $+$ | \(q+(-6-\beta )q^{2}-3^{5}q^{3}+(-1562+13\beta )q^{4}+\cdots\) | |
15.12.a.d | $3$ | $11.525$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(-1\) | \(729\) | \(9375\) | \(-14608\) | $-$ | $-$ | \(q-\beta _{1}q^{2}+3^{5}q^{3}+(1585+3\beta _{1}+\beta _{2})q^{4}+\cdots\) |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(15))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(15)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)