Defining parameters
Level: | \( N \) | \(=\) | \( 2014 = 2 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2014.b (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 53 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(540\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(3\), \(7\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(2014, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 274 | 82 | 192 |
Cusp forms | 266 | 82 | 184 |
Eisenstein series | 8 | 0 | 8 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(2014, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
2014.2.b.a | $2$ | $16.082$ | \(\Q(\sqrt{-1}) \) | None | \(0\) | \(0\) | \(0\) | \(-8\) | \(q+iq^{2}-q^{4}+iq^{5}-4q^{7}-iq^{8}+\cdots\) |
2014.2.b.b | $6$ | $16.082$ | 6.0.62094400.1 | None | \(0\) | \(0\) | \(0\) | \(8\) | \(q+\beta _{4}q^{2}-q^{4}+\beta _{4}q^{5}+(1+\beta _{2})q^{7}+\cdots\) |
2014.2.b.c | $30$ | $16.082$ | None | \(0\) | \(0\) | \(0\) | \(6\) | ||
2014.2.b.d | $44$ | $16.082$ | None | \(0\) | \(0\) | \(0\) | \(-14\) |
Decomposition of \(S_{2}^{\mathrm{old}}(2014, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(2014, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(53, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(106, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(1007, [\chi])\)\(^{\oplus 2}\)