Defining parameters
Level: | \( N \) | \(=\) | \( 3744 = 2^{5} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3744.g (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(1344\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3744, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 704 | 60 | 644 |
Cusp forms | 640 | 60 | 580 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3744, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3744.2.g.a | $2$ | $29.896$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(-6\) | \(q+3 i q^{5}-3 q^{7}-i q^{13}+7 q^{17}+\cdots\) |
3744.2.g.b | $4$ | $29.896$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(12\) | \(q+2\beta_{2} q^{5}+(\beta_{3}+3)q^{7}+(\beta_{2}-3\beta_1)q^{11}+\cdots\) |
3744.2.g.c | $6$ | $29.896$ | 6.0.399424.1 | None | \(0\) | \(0\) | \(0\) | \(-2\) | \(q-\beta _{2}q^{5}+\beta _{1}q^{7}+(2\beta _{2}-\beta _{3}+\beta _{5})q^{11}+\cdots\) |
3744.2.g.d | $8$ | $29.896$ | \(\Q(\zeta_{20})\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+(\beta_{2}-\beta_1)q^{5}+(-\beta_{5}-1)q^{7}+\cdots\) |
3744.2.g.e | $16$ | $29.896$ | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q+\beta _{12}q^{5}-\beta _{5}q^{7}+\beta _{10}q^{11}-\beta _{6}q^{13}+\cdots\) |
3744.2.g.f | $24$ | $29.896$ | None | \(0\) | \(0\) | \(0\) | \(8\) |
Decomposition of \(S_{2}^{\mathrm{old}}(3744, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3744, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(96, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(288, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(312, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(936, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1248, [\chi])\)\(^{\oplus 2}\)