Defining parameters
Level: | \( N \) | \(=\) | \( 14 = 2 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 14.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(28\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{14}(\Gamma_0(14))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 28 | 6 | 22 |
Cusp forms | 24 | 6 | 18 |
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.
\(2\) | \(7\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(1\) |
\(+\) | \(-\) | $-$ | \(2\) |
\(-\) | \(+\) | $-$ | \(2\) |
\(-\) | \(-\) | $+$ | \(1\) |
Plus space | \(+\) | \(2\) | |
Minus space | \(-\) | \(4\) |
Trace form
Decomposition of \(S_{14}^{\mathrm{new}}(\Gamma_0(14))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 7 | |||||||
14.14.a.a | $1$ | $15.012$ | \(\Q\) | None | \(-64\) | \(1626\) | \(-36400\) | \(-117649\) | $+$ | $+$ | \(q-2^{6}q^{2}+1626q^{3}+2^{12}q^{4}-36400q^{5}+\cdots\) | |
14.14.a.b | $1$ | $15.012$ | \(\Q\) | None | \(64\) | \(-1026\) | \(4320\) | \(117649\) | $-$ | $-$ | \(q+2^{6}q^{2}-1026q^{3}+2^{12}q^{4}+4320q^{5}+\cdots\) | |
14.14.a.c | $2$ | $15.012$ | \(\Q(\sqrt{100129}) \) | None | \(-128\) | \(952\) | \(32004\) | \(235298\) | $+$ | $-$ | \(q-2^{6}q^{2}+(476-\beta )q^{3}+2^{12}q^{4}+(16002+\cdots)q^{5}+\cdots\) | |
14.14.a.d | $2$ | $15.012$ | \(\Q(\sqrt{78985}) \) | None | \(128\) | \(1106\) | \(75530\) | \(-235298\) | $-$ | $+$ | \(q+2^{6}q^{2}+(553-5\beta )q^{3}+2^{12}q^{4}+\cdots\) |
Decomposition of \(S_{14}^{\mathrm{old}}(\Gamma_0(14))\) into lower level spaces
\( S_{14}^{\mathrm{old}}(\Gamma_0(14)) \cong \) \(S_{14}^{\mathrm{new}}(\Gamma_0(2))\)\(^{\oplus 2}\)\(\oplus\)\(S_{14}^{\mathrm{new}}(\Gamma_0(7))\)\(^{\oplus 2}\)