Defining parameters
Level: | \( N \) | \(=\) | \( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2340.j (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 65 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(1008\) | ||
Trace bound: | \(25\) | ||
Distinguishing \(T_p\): | \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2340, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 528 | 36 | 492 |
Cusp forms | 480 | 36 | 444 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2340, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
2340.2.j.a | $4$ | $18.685$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}-2q^{7}+\zeta_{8}^{2}q^{11}+\cdots\) |
2340.2.j.b | $4$ | $18.685$ | \(\Q(\zeta_{8})\) | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{5}+2q^{7}+\zeta_{8}^{2}q^{11}+\cdots\) |
2340.2.j.c | $8$ | $18.685$ | 8.0.4569760000.1 | \(\Q(\sqrt{-195}) \) | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{5}q^{5}+\beta _{1}q^{7}+(-\beta _{2}-\beta _{5})q^{11}+\cdots\) |
2340.2.j.d | $8$ | $18.685$ | 8.0.\(\cdots\).3 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{5}q^{5}+(-\beta _{5}+\beta _{6})q^{7}-\beta _{7}q^{11}+\cdots\) |
2340.2.j.e | $12$ | $18.685$ | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\beta _{11}q^{5}+\beta _{10}q^{7}+\beta _{9}q^{11}+(-\beta _{4}+\cdots)q^{13}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2340, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2340, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(390, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(585, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(780, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1170, [\chi])\)\(^{\oplus 2}\)