Defining parameters
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 152 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(480\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1368, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 248 | 102 | 146 |
Cusp forms | 232 | 98 | 134 |
Eisenstein series | 16 | 4 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1368.2.e.a | $2$ | $10.924$ | \(\Q(\sqrt{-2}) \) | \(\Q(\sqrt{-2}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta q^{2}-2q^{4}+2\beta q^{8}-6q^{11}+4q^{16}+\cdots\) |
1368.2.e.b | $4$ | $10.924$ | \(\Q(\sqrt{-3}, \sqrt{5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+(1-\beta _{3})q^{4}+(-1+2\beta _{3})q^{7}+\cdots\) |
1368.2.e.c | $8$ | $10.924$ | 8.0.\(\cdots\).11 | \(\Q(\sqrt{-114}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{8}+\cdots\) |
1368.2.e.d | $8$ | $10.924$ | 8.0.207360000.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{1}-\beta _{5})q^{2}+(-1-\beta _{4})q^{4}+2\beta _{4}q^{7}+\cdots\) |
1368.2.e.e | $12$ | $10.924$ | 12.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{5}-\beta _{8})q^{5}-\beta _{8}q^{7}+\cdots\) |
1368.2.e.f | $24$ | $10.924$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
1368.2.e.g | $40$ | $10.924$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1368, [\chi]) \cong \)