Defining parameters
Level: | \( N \) | \(=\) | \( 26 = 2 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 26.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(14\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(26))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13 | 3 | 10 |
Cusp forms | 9 | 3 | 6 |
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.
\(2\) | \(13\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | \(+\) | \(1\) |
\(-\) | \(-\) | \(+\) | \(2\) |
Plus space | \(+\) | \(3\) | |
Minus space | \(-\) | \(0\) |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(26))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 13 | |||||||
26.4.a.a | $1$ | $1.534$ | \(\Q\) | None | \(-2\) | \(3\) | \(11\) | \(19\) | $+$ | $+$ | \(q-2q^{2}+3q^{3}+4q^{4}+11q^{5}-6q^{6}+\cdots\) | |
26.4.a.b | $1$ | $1.534$ | \(\Q\) | None | \(2\) | \(-1\) | \(17\) | \(-35\) | $-$ | $-$ | \(q+2q^{2}-q^{3}+4q^{4}+17q^{5}-2q^{6}+\cdots\) | |
26.4.a.c | $1$ | $1.534$ | \(\Q\) | None | \(2\) | \(4\) | \(-18\) | \(20\) | $-$ | $-$ | \(q+2q^{2}+4q^{3}+4q^{4}-18q^{5}+8q^{6}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(26))\) into lower level spaces
\( S_{4}^{\mathrm{old}}(\Gamma_0(26)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(13))\)\(^{\oplus 2}\)