Defining parameters
Level: | \( N \) | \(=\) | \( 270 = 2 \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 270.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 15 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(162\) | ||
Trace bound: | \(10\) | ||
Distinguishing \(T_p\): | \(7\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(270, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 120 | 16 | 104 |
Cusp forms | 96 | 16 | 80 |
Eisenstein series | 24 | 0 | 24 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(270, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
270.3.b.a | $4$ | $7.357$ | 4.0.31744.1 | None | \(0\) | \(0\) | \(-12\) | \(0\) | \(q-\beta _{2}q^{2}+2q^{4}+(-3-\beta _{1}-\beta _{2})q^{5}+\cdots\) |
270.3.b.b | $4$ | $7.357$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(3\zeta_{8}-4\zeta_{8}^{3})q^{5}+\cdots\) |
270.3.b.c | $4$ | $7.357$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}+5\zeta_{8}^{2}q^{7}+\cdots\) |
270.3.b.d | $4$ | $7.357$ | 4.0.31744.1 | None | \(0\) | \(0\) | \(12\) | \(0\) | \(q+\beta _{2}q^{2}+2q^{4}+(3-\beta _{1}+\beta _{2})q^{5}+\cdots\) |
Decomposition of \(S_{3}^{\mathrm{old}}(270, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(270, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(30, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(45, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(90, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(135, [\chi])\)\(^{\oplus 2}\)