Defining parameters
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.e (of order \(4\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 55 \) |
Character field: | \(\Q(i)\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(132\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(605, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 156 | 124 | 32 |
Cusp forms | 108 | 92 | 16 |
Eisenstein series | 48 | 32 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(605, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
605.2.e.a | $20$ | $4.831$ | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) | None | \(0\) | \(4\) | \(4\) | \(0\) | \(q+\beta _{1}q^{2}-\beta _{12}q^{3}+(-\beta _{4}+\beta _{10}-\beta _{13}+\cdots)q^{4}+\cdots\) |
605.2.e.b | $32$ | $4.831$ | None | \(0\) | \(-4\) | \(8\) | \(0\) | ||
605.2.e.c | $40$ | $4.831$ | None | \(0\) | \(8\) | \(-4\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(605, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(605, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 2}\)