Defining parameters
Level: | \( N \) | \(=\) | \( 2005 = 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2005.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(402\) | ||
Trace bound: | \(11\) | ||
Distinguishing \(T_p\): | \(2\), \(11\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(2005))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 202 | 133 | 69 |
Cusp forms | 199 | 133 | 66 |
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.
\(5\) | \(401\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(29\) |
\(+\) | \(-\) | $-$ | \(37\) |
\(-\) | \(+\) | $-$ | \(37\) |
\(-\) | \(-\) | $+$ | \(30\) |
Plus space | \(+\) | \(59\) | |
Minus space | \(-\) | \(74\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(2005))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | 401 | |||||||
2005.2.a.a | $1$ | $16.010$ | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\) | |
2005.2.a.b | $1$ | $16.010$ | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(0\) | $-$ | $-$ | \(q-q^{2}-q^{4}+q^{5}+3q^{8}-3q^{9}-q^{10}+\cdots\) | |
2005.2.a.c | $3$ | $16.010$ | \(\Q(\zeta_{18})^+\) | None | \(-3\) | \(-3\) | \(3\) | \(-3\) | $-$ | $-$ | \(q+(-1+\beta _{1})q^{2}+(-1-2\beta _{1}+\beta _{2})q^{3}+\cdots\) | |
2005.2.a.d | $25$ | $16.010$ | None | \(-5\) | \(-10\) | \(25\) | \(-31\) | $-$ | $-$ | |||
2005.2.a.e | $29$ | $16.010$ | None | \(-5\) | \(-3\) | \(-29\) | \(12\) | $+$ | $+$ | |||
2005.2.a.f | $37$ | $16.010$ | None | \(7\) | \(3\) | \(-37\) | \(-16\) | $+$ | $-$ | |||
2005.2.a.g | $37$ | $16.010$ | None | \(11\) | \(13\) | \(37\) | \(34\) | $-$ | $+$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(2005))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(2005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(401))\)\(^{\oplus 2}\)