Defining parameters
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 33 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(88\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(363, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 56 | 44 | 12 |
Cusp forms | 32 | 28 | 4 |
Eisenstein series | 24 | 16 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(363, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
363.2.d.a | $2$ | $2.899$ | \(\Q(\sqrt{-2}) \) | None | \(-2\) | \(2\) | \(0\) | \(0\) | \(q-q^{2}+(1+\beta )q^{3}-q^{4}+2\beta q^{5}+(-1+\cdots)q^{6}+\cdots\) |
363.2.d.b | $2$ | $2.899$ | \(\Q(\sqrt{-2}) \) | None | \(2\) | \(2\) | \(0\) | \(0\) | \(q+q^{2}+(1+\beta )q^{3}-q^{4}+2\beta q^{5}+(1+\cdots)q^{6}+\cdots\) |
363.2.d.c | $4$ | $2.899$ | \(\Q(\sqrt{-2}, \sqrt{-3})\) | None | \(0\) | \(-6\) | \(0\) | \(0\) | \(q+(-2\beta _{1}+\beta _{3})q^{2}+(-1-\beta _{2})q^{3}+\cdots\) |
363.2.d.d | $4$ | $2.899$ | \(\Q(\sqrt{-2}, \sqrt{3})\) | \(\Q(\sqrt{-3}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{3}-2q^{4}-\beta _{2}q^{7}+3q^{9}+2\beta _{1}q^{12}+\cdots\) |
363.2.d.e | $8$ | $2.899$ | 8.0.3588489216.5 | None | \(0\) | \(-4\) | \(0\) | \(0\) | \(q-\beta _{3}q^{2}+(-1-\beta _{7})q^{3}+(2-\beta _{4}-\beta _{7})q^{4}+\cdots\) |
363.2.d.f | $8$ | $2.899$ | \(\Q(\zeta_{20})\) | None | \(0\) | \(4\) | \(0\) | \(0\) | \(q-\beta_{6} q^{2}+(\beta_{5}+\beta_{3}-\beta_1+1)q^{3}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(363, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(363, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(33, [\chi])\)\(^{\oplus 2}\)