Defining parameters
Level: | \( N \) | \(=\) | \( 95 = 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 95.e (of order \(3\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 19 \) |
Character field: | \(\Q(\zeta_{3})\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(40\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{4}(95, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 64 | 40 | 24 |
Cusp forms | 56 | 40 | 16 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{4}^{\mathrm{new}}(95, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
95.4.e.a | $2$ | $5.605$ | \(\Q(\sqrt{-3}) \) | None | \(1\) | \(5\) | \(-5\) | \(44\) | \(q+(1-\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}+7\zeta_{6}q^{4}+\cdots\) |
95.4.e.b | $18$ | $5.605$ | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) | None | \(6\) | \(2\) | \(-45\) | \(-90\) | \(q+(1-\beta _{1}+\beta _{4})q^{2}+\beta _{11}q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\) |
95.4.e.c | $20$ | $5.605$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-3\) | \(-5\) | \(50\) | \(6\) | \(q+(\beta _{1}+\beta _{3})q^{2}-\beta _{2}q^{3}+(4\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\) |
Decomposition of \(S_{4}^{\mathrm{old}}(95, [\chi])\) into lower level spaces
\( S_{4}^{\mathrm{old}}(95, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)