Defining parameters
Level: | \( N \) | \(=\) | \( 2004 = 2^{2} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2004.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(672\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(5\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2004))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 342 | 28 | 314 |
Cusp forms | 331 | 28 | 303 |
Eisenstein series | 11 | 0 | 11 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(2\) | \(3\) | \(167\) | Fricke | Dim |
---|---|---|---|---|
\(-\) | \(+\) | \(+\) | $-$ | \(9\) |
\(-\) | \(+\) | \(-\) | $+$ | \(5\) |
\(-\) | \(-\) | \(+\) | $+$ | \(5\) |
\(-\) | \(-\) | \(-\) | $-$ | \(9\) |
Plus space | \(+\) | \(10\) | ||
Minus space | \(-\) | \(18\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2004))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 2 | 3 | 167 | |||||||
2004.2.a.a | $5$ | $16.002$ | 5.5.149169.1 | None | \(0\) | \(-5\) | \(-3\) | \(-2\) | $-$ | $+$ | $-$ | \(q-q^{3}+(-\beta _{1}+\beta _{3}-\beta _{4})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\) | |
2004.2.a.b | $5$ | $16.002$ | 5.5.161121.1 | None | \(0\) | \(5\) | \(-7\) | \(-2\) | $-$ | $-$ | $+$ | \(q+q^{3}+(-1-\beta _{3}-\beta _{4})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\) | |
2004.2.a.c | $9$ | $16.002$ | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) | None | \(0\) | \(-9\) | \(1\) | \(2\) | $-$ | $+$ | $+$ | \(q-q^{3}+\beta _{1}q^{5}+(-\beta _{3}-\beta _{6})q^{7}+q^{9}+\cdots\) | |
2004.2.a.d | $9$ | $16.002$ | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) | None | \(0\) | \(9\) | \(9\) | \(2\) | $-$ | $-$ | $-$ | \(q+q^{3}+(1-\beta _{1})q^{5}-\beta _{6}q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2004))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2004)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(167))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(334))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(501))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(668))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_0(1002))\)\(^{\oplus 2}\)