Defining parameters
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.o (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1368, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 496 | 50 | 446 |
Cusp forms | 464 | 50 | 414 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1368, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1368.3.o.a | $2$ | $37.275$ | \(\Q(\sqrt{-2}) \) | None | \(0\) | \(0\) | \(-14\) | \(22\) | \(q-7q^{5}+11q^{7}-3q^{11}+2\beta q^{13}+\cdots\) |
1368.3.o.b | $8$ | $37.275$ | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) | None | \(0\) | \(0\) | \(14\) | \(-6\) | \(q+(2+\beta _{4})q^{5}+(-1+\beta _{3})q^{7}+(4+\beta _{4}+\cdots)q^{11}+\cdots\) |
1368.3.o.c | $20$ | $37.275$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-16\) | \(q-\beta _{4}q^{5}+(-1-\beta _{3})q^{7}+(-1-\beta _{1}+\cdots)q^{11}+\cdots\) |
1368.3.o.d | $20$ | $37.275$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-16\) | \(q-\beta _{10}q^{5}+(-1+\beta _{3})q^{7}+\beta _{14}q^{11}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1368, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(57, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(114, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(342, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(456, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(684, [\chi])\)\(^{\oplus 2}\)