Defining parameters
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.v (of order \(18\) and degree \(6\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 185 \) |
Character field: | \(\Q(\zeta_{18})\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(114\) | ||
Trace bound: | \(5\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(370, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 360 | 120 | 240 |
Cusp forms | 312 | 120 | 192 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(370, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
370.2.v.a | $60$ | $2.954$ | None | \(0\) | \(0\) | \(-3\) | \(0\) | ||
370.2.v.b | $60$ | $2.954$ | None | \(0\) | \(0\) | \(6\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(370, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(370, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(185, [\chi])\)\(^{\oplus 2}\)