Defining parameters
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bf (of order \(6\) and degree \(2\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 21 \) |
Character field: | \(\Q(\zeta_{6})\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(1440\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(11\), \(37\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(3150, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 1536 | 104 | 1432 |
Cusp forms | 1344 | 104 | 1240 |
Eisenstein series | 192 | 0 | 192 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(3150, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
3150.2.bf.a | $8$ | $25.153$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(-4\) | \(q-\zeta_{24}q^{2}+\zeta_{24}^{2}q^{4}+(-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{7}+\cdots\) |
3150.2.bf.b | $8$ | $25.153$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(\zeta_{24}-3\zeta_{24}^{5}+\cdots)q^{7}+\cdots\) |
3150.2.bf.c | $8$ | $25.153$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(-\zeta_{24}+3\zeta_{24}^{5}+\cdots)q^{7}+\cdots\) |
3150.2.bf.d | $24$ | $25.153$ | None | \(0\) | \(0\) | \(0\) | \(-4\) | ||
3150.2.bf.e | $24$ | $25.153$ | None | \(0\) | \(0\) | \(0\) | \(4\) | ||
3150.2.bf.f | $32$ | $25.153$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(3150, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(3150, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(630, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1575, [\chi])\)\(^{\oplus 2}\)