Defining parameters
Level: | \( N \) | \(=\) | \( 6005 = 5 \cdot 1201 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6005.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 7 \) | ||
Sturm bound: | \(1202\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(6005))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 602 | 401 | 201 |
Cusp forms | 599 | 401 | 198 |
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.
\(5\) | \(1201\) | Fricke | Dim |
---|---|---|---|
\(+\) | \(+\) | $+$ | \(87\) |
\(+\) | \(-\) | $-$ | \(113\) |
\(-\) | \(+\) | $-$ | \(113\) |
\(-\) | \(-\) | $+$ | \(88\) |
Plus space | \(+\) | \(175\) | |
Minus space | \(-\) | \(226\) |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(6005))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | 1201 | |||||||
6005.2.a.a | $1$ | $47.950$ | \(\Q\) | None | \(-2\) | \(-2\) | \(1\) | \(-2\) | $-$ | $+$ | \(q-2q^{2}-2q^{3}+2q^{4}+q^{5}+4q^{6}+\cdots\) | |
6005.2.a.b | $1$ | $47.950$ | \(\Q\) | None | \(-1\) | \(0\) | \(1\) | \(4\) | $-$ | $+$ | \(q-q^{2}-q^{4}+q^{5}+4q^{7}+3q^{8}-3q^{9}+\cdots\) | |
6005.2.a.c | $4$ | $47.950$ | 4.4.2777.1 | None | \(2\) | \(-2\) | \(-4\) | \(-7\) | $+$ | $+$ | \(q+(1-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{3})q^{3}+\cdots\) | |
6005.2.a.d | $83$ | $47.950$ | None | \(1\) | \(-4\) | \(-83\) | \(2\) | $+$ | $+$ | |||
6005.2.a.e | $88$ | $47.950$ | None | \(-14\) | \(-34\) | \(88\) | \(-35\) | $-$ | $-$ | |||
6005.2.a.f | $111$ | $47.950$ | None | \(20\) | \(40\) | \(111\) | \(39\) | $-$ | $+$ | |||
6005.2.a.g | $113$ | $47.950$ | None | \(-3\) | \(6\) | \(-113\) | \(7\) | $+$ | $-$ |
Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_0(6005))\) into lower level spaces
\( S_{2}^{\mathrm{old}}(\Gamma_0(6005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_0(1201))\)\(^{\oplus 2}\)