Defining parameters
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 93 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(384\) | ||
Trace bound: | \(6\) | ||
Distinguishing \(T_p\): | \(7\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(930, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 400 | 88 | 312 |
Cusp forms | 368 | 88 | 280 |
Eisenstein series | 32 | 0 | 32 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(930, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
930.2.o.a | $4$ | $7.426$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(-6\) | \(0\) | \(8\) | \(q+\zeta_{12}^{3}q^{2}+(-1-\zeta_{12}^{2})q^{3}-q^{4}+\cdots\) |
930.2.o.b | $4$ | $7.426$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+\zeta_{12}^{3}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\cdots\) |
930.2.o.c | $4$ | $7.426$ | \(\Q(\zeta_{12})\) | None | \(0\) | \(0\) | \(0\) | \(2\) | \(q+\zeta_{12}^{3}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}-q^{4}+\cdots\) |
930.2.o.d | $36$ | $7.426$ | None | \(0\) | \(0\) | \(0\) | \(-8\) | ||
930.2.o.e | $40$ | $7.426$ | None | \(0\) | \(6\) | \(0\) | \(-12\) |
Decomposition of \(S_{2}^{\mathrm{old}}(930, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(930, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(93, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(186, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(465, [\chi])\)\(^{\oplus 2}\)