Defining parameters
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(24\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{12}(\Gamma_0(12))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 25 | 2 | 23 |
Cusp forms | 19 | 2 | 17 |
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.
\(2\) | \(3\) | Fricke | Dim |
---|---|---|---|
\(-\) | \(+\) | $-$ | \(1\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(1\) | |
Minus space | \(-\) | \(1\) |
Trace form
Decomposition of \(S_{12}^{\mathrm{new}}(\Gamma_0(12))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | |||||||
12.12.a.a | $1$ | $9.220$ | \(\Q\) | None | \(0\) | \(-243\) | \(9990\) | \(-86128\) | $-$ | $+$ | \(q-3^{5}q^{3}+9990q^{5}-86128q^{7}+3^{10}q^{9}+\cdots\) | |
12.12.a.b | $1$ | $9.220$ | \(\Q\) | None | \(0\) | \(243\) | \(2862\) | \(9128\) | $-$ | $-$ | \(q+3^{5}q^{3}+2862q^{5}+9128q^{7}+3^{10}q^{9}+\cdots\) |
Decomposition of \(S_{12}^{\mathrm{old}}(\Gamma_0(12))\) into lower level spaces
\( S_{12}^{\mathrm{old}}(\Gamma_0(12)) \cong \) \(S_{12}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 6}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(3))\)\(^{\oplus 3}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(4))\)\(^{\oplus 2}\)\(\oplus\)\(S_{12}^{\mathrm{new}}(\Gamma_0(6))\)\(^{\oplus 2}\)