Defining parameters
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 42 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(14\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{42}(\Gamma_0(3))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15 | 7 | 8 |
Cusp forms | 13 | 7 | 6 |
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 |
---|---|
\(+\) | \(3\) |
\(-\) | \(4\) |
Trace form
Decomposition of \(S_{42}^{\mathrm{new}}(\Gamma_0(3))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 3 | |||||||
3.42.a.a | $3$ | $31.942$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(-289380\) | \(-10460353203\) | \(38\!\cdots\!26\) | \(-44\!\cdots\!68\) | $+$ | \(q+(-96460-\beta _{1})q^{2}-3^{20}q^{3}+(-751422059600+\cdots)q^{4}+\cdots\) | |
3.42.a.b | $4$ | $31.942$ | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) | None | \(-69822\) | \(13947137604\) | \(11\!\cdots\!80\) | \(15\!\cdots\!36\) | $-$ | \(q+(-17455-\beta _{1})q^{2}+3^{20}q^{3}+(1338237117038+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{42}^{\mathrm{old}}(\Gamma_0(3))\) into lower level spaces
\( S_{42}^{\mathrm{old}}(\Gamma_0(3)) \cong \) \(S_{42}^{\mathrm{new}}(\Gamma_0(1))\)\(^{\oplus 2}\)