Defining parameters
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.i (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 67 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(272\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(5\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(804, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 284 | 22 | 262 |
Cusp forms | 260 | 22 | 238 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(804, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
804.2.i.a | $2$ | $6.420$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-2\) | \(-4\) | \(3\) | \(q-q^{3}-2q^{5}+3\zeta_{6}q^{7}+q^{9}-3\zeta_{6}q^{11}+\cdots\) |
804.2.i.b | $2$ | $6.420$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-2\) | \(4\) | \(-5\) | \(q-q^{3}+2q^{5}-5\zeta_{6}q^{7}+q^{9}-5\zeta_{6}q^{11}+\cdots\) |
804.2.i.c | $2$ | $6.420$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(2\) | \(4\) | \(3\) | \(q+q^{3}+2q^{5}+3\zeta_{6}q^{7}+q^{9}-\zeta_{6}q^{11}+\cdots\) |
804.2.i.d | $8$ | $6.420$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(-8\) | \(2\) | \(1\) | \(q-q^{3}+\beta _{6}q^{5}+(-\beta _{1}+\beta _{6})q^{7}+q^{9}+\cdots\) |
804.2.i.e | $8$ | $6.420$ | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) | None | \(0\) | \(8\) | \(-6\) | \(0\) | \(q+q^{3}+(-1-\beta _{2}+\beta _{5}-\beta _{6})q^{5}-\beta _{3}q^{7}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(804, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(804, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(67, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(134, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(201, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(268, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(402, [\chi])\)\(^{\oplus 2}\)