Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(4\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(3))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 5 | 3 | 2 |
Cusp forms | 3 | 3 | 0 |
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.
\(3\) | Dim |
---|---|
\(+\) | \(1\) |
\(-\) | \(2\) |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
3.14.a.a | $1$ | $3.217$ | \(\Q\) | None | \(-12\) | \(-729\) | \(-30210\) | \(235088\) | $+$ | \(q-12q^{2}-3^{6}q^{3}-8048q^{4}-30210q^{5}+\cdots\) | |
3.14.a.b | $2$ | $3.217$ | \(\Q(\sqrt{1969}) \) | None | \(-54\) | \(1458\) | \(40716\) | \(-21008\) | $-$ | \(q+(-3^{3}-\beta )q^{2}+3^{6}q^{3}+(10258+54\beta )q^{4}+\cdots\) |