Defining parameters
Level: | \( N \) | \(=\) | \( 1320 = 2^{3} \cdot 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1320.w (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 8 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(576\) | ||
Trace bound: | \(22\) | ||
Distinguishing \(T_p\): | \(7\), \(23\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(1320, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 296 | 80 | 216 |
Cusp forms | 280 | 80 | 200 |
Eisenstein series | 16 | 0 | 16 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(1320, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1320.2.w.a | $2$ | $10.540$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(0\) | \(0\) | \(-4\) | \(q+(1+i)q^{2}-iq^{3}+2iq^{4}-iq^{5}+\cdots\) |
1320.2.w.b | $2$ | $10.540$ | \(\Q(\sqrt{-1}) \) | None | \(2\) | \(0\) | \(0\) | \(-4\) | \(q+(1+i)q^{2}-iq^{3}+2iq^{4}-iq^{5}+\cdots\) |
1320.2.w.c | $12$ | $10.540$ | \(\Q(\zeta_{28})\) | None | \(-2\) | \(0\) | \(0\) | \(4\) | \(q-\zeta_{28}^{9}q^{2}-\zeta_{28}^{5}q^{3}-\zeta_{28}^{4}q^{4}+\cdots\) |
1320.2.w.d | $18$ | $10.540$ | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{1}q^{2}+\beta _{11}q^{3}+\beta _{2}q^{4}-\beta _{11}q^{5}+\cdots\) |
1320.2.w.e | $20$ | $10.540$ | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) | None | \(-2\) | \(0\) | \(0\) | \(4\) | \(q+\beta _{2}q^{2}+\beta _{11}q^{3}+\beta _{4}q^{4}+\beta _{11}q^{5}+\cdots\) |
1320.2.w.f | $26$ | $10.540$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(1320, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(1320, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(40, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(88, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(264, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(440, [\chi])\)\(^{\oplus 2}\)