Defining parameters
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 6 \) | ||
Sturm bound: | \(706\) | ||
Trace bound: | \(1\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(4009))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 354 | 315 | 39 |
Cusp forms | 351 | 315 | 36 |
Eisenstein series | 3 | 0 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(19\) | \(211\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(75\) |
\(+\) | \(-\) | $-$ | \(84\) |
\(-\) | \(+\) | $-$ | \(82\) |
\(-\) | \(-\) | $+$ | \(74\) |
Plus space | \(+\) | \(149\) | |
Minus space | \(-\) | \(166\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(4009))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 19 | 211 | |||||||
4009.2.a.a | $1$ | $32.012$ | \(\Q\) | None | \(-1\) | \(2\) | \(3\) | \(0\) | $+$ | $-$ | \(q-q^{2}+2q^{3}-q^{4}+3q^{5}-2q^{6}+3q^{8}+\cdots\) | |
4009.2.a.b | $3$ | $32.012$ | \(\Q(\zeta_{14})^+\) | None | \(2\) | \(-2\) | \(-3\) | \(3\) | $-$ | $-$ | \(q+(1-\beta _{1})q^{2}+(-1+\beta _{1})q^{3}+(1-2\beta _{1}+\cdots)q^{4}+\cdots\) | |
4009.2.a.c | $71$ | $32.012$ | None | \(-15\) | \(-8\) | \(-18\) | \(-19\) | $-$ | $-$ | |||
4009.2.a.d | $75$ | $32.012$ | None | \(-11\) | \(-4\) | \(-18\) | \(-19\) | $+$ | $+$ | |||
4009.2.a.e | $82$ | $32.012$ | None | \(15\) | \(12\) | \(9\) | \(14\) | $-$ | $+$ | |||
4009.2.a.f | $83$ | $32.012$ | None | \(11\) | \(0\) | \(15\) | \(19\) | $+$ | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(4009))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(4009)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(19))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(211))\)\(^{\oplus 2}\)