Defining parameters
Level: | \( N \) | \(=\) | \( 2368 = 2^{6} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2368.e (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 296 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(608\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2368, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 316 | 76 | 240 |
Cusp forms | 292 | 76 | 216 |
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.e.a | $8$ | $18.909$ | 8.0.8540717056.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{5}q^{7}+2q^{9}+\beta _{1}q^{11}+\cdots\) |
2368.2.e.b | $20$ | $18.909$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | \(\Q(\sqrt{-74}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{8}q^{3}+\beta _{11}q^{5}+(-3+\beta _{2})q^{9}+\cdots\) |
2368.2.e.c | $48$ | $18.909$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2368, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2368, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(296, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(592, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1184, [\chi])\)\(^{\oplus 2}\)