Defining parameters
Level: | \( N \) | \(=\) | \( 308 = 2^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 308.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 77 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(96\) | ||
Trace bound: | \(9\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(308, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 54 | 8 | 46 |
Cusp forms | 42 | 8 | 34 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(308, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
308.2.c.a | $4$ | $2.459$ | \(\Q(\sqrt{2}, \sqrt{-5})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{3}q^{3}-\beta _{3}q^{5}+(\beta _{1}-\beta _{2})q^{7}-2q^{9}+\cdots\) |
308.2.c.b | $4$ | $2.459$ | \(\Q(\sqrt{-2}, \sqrt{-7})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{3}-2\beta _{2}q^{5}-\beta _{3}q^{7}+q^{9}+(2+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(308, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(308, [\chi]) \cong \)