Defining parameters
Level: | \( N \) | \(=\) | \( 2368 = 2^{6} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2368.c (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(608\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2368, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 316 | 72 | 244 |
Cusp forms | 292 | 72 | 220 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2368, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
2368.2.c.a | $12$ | $18.909$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+\beta _{11}q^{3}+\beta _{9}q^{5}+(-1+\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\) |
2368.2.c.b | $12$ | $18.909$ | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+\beta _{11}q^{3}-\beta _{9}q^{5}+(1-\beta _{1}+\beta _{4})q^{7}+\cdots\) |
2368.2.c.c | $24$ | $18.909$ | None | \(0\) | \(0\) | \(0\) | \(-16\) | ||
2368.2.c.d | $24$ | $18.909$ | None | \(0\) | \(0\) | \(0\) | \(16\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2368, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1184, [\chi])\)\(^{\oplus 2}\)