Defining parameters
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.h (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 3 \) | ||
Sturm bound: | \(720\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{3}(1050, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 504 | 48 | 456 |
Cusp forms | 456 | 48 | 408 |
Eisenstein series | 48 | 0 | 48 |
Trace form
Decomposition of \(S_{3}^{\mathrm{new}}(1050, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
1050.3.h.a | $8$ | $28.610$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}q^{2}-\zeta_{24}^{2}q^{3}-2q^{4}-\zeta_{24}^{7}q^{6}+\cdots\) |
1050.3.h.b | $16$ | $28.610$ | 16.0.\(\cdots\).1 | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+\beta _{2}q^{2}-\beta _{3}q^{3}-2q^{4}+\beta _{11}q^{6}+\cdots\) |
1050.3.h.c | $24$ | $28.610$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{3}^{\mathrm{old}}(1050, [\chi])\) into lower level spaces
\( S_{3}^{\mathrm{old}}(1050, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 2}\)