Defining parameters
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.d (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(1536\) | ||
Trace bound: | \(7\) | ||
Distinguishing \(T_p\): | \(11\), \(19\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3360, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 800 | 64 | 736 |
Cusp forms | 736 | 64 | 672 |
Eisenstein series | 64 | 0 | 64 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3360, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3360.2.d.a | $16$ | $26.830$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(-16\) | \(0\) | \(0\) | \(q-q^{3}+\beta _{5}q^{5}-\beta _{10}q^{7}+q^{9}+(-\beta _{5}+\cdots)q^{11}+\cdots\) |
3360.2.d.b | $16$ | $26.830$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(-16\) | \(0\) | \(8\) | \(q-q^{3}-\beta _{3}q^{5}+\beta _{14}q^{7}+q^{9}+\beta _{12}q^{11}+\cdots\) |
3360.2.d.c | $16$ | $26.830$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(16\) | \(0\) | \(-8\) | \(q+q^{3}+\beta _{3}q^{5}+(-1+\beta _{13})q^{7}+q^{9}+\cdots\) |
3360.2.d.d | $16$ | $26.830$ | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) | None | \(0\) | \(16\) | \(0\) | \(0\) | \(q+q^{3}-\beta _{5}q^{5}-\beta _{12}q^{7}+q^{9}+(-\beta _{5}+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(3360, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3360, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(560, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(672, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1120, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1680, [\chi])\)\(^{\oplus 2}\)