Defining parameters
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.be (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 95 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(240\) | ||
Trace bound: | \(4\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(855, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 256 | 104 | 152 |
Cusp forms | 224 | 96 | 128 |
Eisenstein series | 32 | 8 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(855, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
855.2.be.a | $4$ | $6.827$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(-2\) | \(0\) | \(q+\zeta_{12}q^{2}+2\zeta_{12}^{2}q^{4}+(-1-\zeta_{12}+\cdots)q^{5}+\cdots\) |
855.2.be.b | $8$ | $6.827$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{5}q^{2}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{5}+\cdots\) |
855.2.be.c | $8$ | $6.827$ | 8.0.12960000.1 | \(\Q(\sqrt{-15}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\beta _{4}+\beta _{5}-\beta _{7})q^{2}+(-1+\beta _{1}-2\beta _{2}+\cdots)q^{4}+\cdots\) |
855.2.be.d | $12$ | $6.827$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(2\) | \(0\) | \(q+\beta _{5}q^{2}+(-\beta _{2}+\beta _{3}-\beta _{8}-\beta _{9})q^{4}+\cdots\) |
855.2.be.e | $24$ | $6.827$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
855.2.be.f | $40$ | $6.827$ | None | \(0\) | \(0\) | \(2\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(855, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(855, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(95, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)