Defining parameters
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.ce (of order \(12\) and degree \(4\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 35 \) |
Character field: | \(\Q(\zeta_{12})\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(960\) | ||
Trace bound: | \(21\) | ||
Distinguishing \(T_p\): | \(11\), \(17\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2100, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 2064 | 96 | 1968 |
Cusp forms | 1776 | 96 | 1680 |
Eisenstein series | 288 | 0 | 288 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2100, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
2100.2.ce.a | $8$ | $16.769$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q+(\zeta_{24}^{3}-\zeta_{24}^{7})q^{3}+(-3\zeta_{24}^{3}+\zeta_{24}^{7})q^{7}+\cdots\) |
2100.2.ce.b | $8$ | $16.769$ | \(\Q(\zeta_{24})\) | None | \(0\) | \(0\) | \(0\) | \(0\) | \(q-\zeta_{24}q^{3}+(-3\zeta_{24}+2\zeta_{24}^{5})q^{7}+\cdots\) |
2100.2.ce.c | $24$ | $16.769$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
2100.2.ce.d | $24$ | $16.769$ | None | \(0\) | \(0\) | \(0\) | \(0\) | ||
2100.2.ce.e | $32$ | $16.769$ | None | \(0\) | \(0\) | \(0\) | \(0\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2100, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2100, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(35, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(70, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(140, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(175, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(210, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(350, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(420, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(525, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(700, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1050, [\chi])\)\(^{\oplus 2}\)