Defining parameters
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(15\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(29))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 13 | 11 | 2 |
Cusp forms | 11 | 11 | 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.
\(29\) | Dim |
---|---|
\(+\) | \(4\) |
\(-\) | \(7\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(29))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 29 | |||||||
29.6.a.a | $4$ | $4.651$ | 4.4.3257317.1 | None | \(0\) | \(-28\) | \(-68\) | \(-208\) | $+$ | \(q-\beta _{2}q^{2}+(-7+\beta _{1}+\beta _{2})q^{3}+(2-3\beta _{1}+\cdots)q^{4}+\cdots\) | |
29.6.a.b | $7$ | $4.651$ | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) | None | \(4\) | \(26\) | \(32\) | \(184\) | $-$ | \(q+(1-\beta _{1})q^{2}+(4+\beta _{5})q^{3}+(23-3\beta _{1}+\cdots)q^{4}+\cdots\) |