Defining parameters
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 4 \) | ||
Sturm bound: | \(15\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_0(25))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 15 | 10 | 5 |
Cusp forms | 9 | 7 | 2 |
Eisenstein series | 6 | 3 | 3 |
The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.
\(5\) | Dim |
---|---|
\(+\) | \(3\) |
\(-\) | \(4\) |
Trace form
Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_0(25))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | |||||||
25.6.a.a | $1$ | $4.010$ | \(\Q\) | None | \(-2\) | \(4\) | \(0\) | \(-192\) | $+$ | \(q-2q^{2}+4q^{3}-28q^{4}-8q^{6}-192q^{7}+\cdots\) | |
25.6.a.b | $2$ | $4.010$ | \(\Q(\sqrt{241}) \) | None | \(-5\) | \(-20\) | \(0\) | \(-200\) | $+$ | \(q+(-2-\beta )q^{2}+(-11+2\beta )q^{3}+(2^{5}+\cdots)q^{4}+\cdots\) | |
25.6.a.c | $2$ | $4.010$ | \(\Q(\sqrt{11}) \) | None | \(0\) | \(0\) | \(0\) | \(0\) | $-$ | \(q+\beta q^{2}+3\beta q^{3}+12q^{4}+132q^{6}+\cdots\) | |
25.6.a.d | $2$ | $4.010$ | \(\Q(\sqrt{241}) \) | None | \(5\) | \(20\) | \(0\) | \(200\) | $-$ | \(q+(3-\beta )q^{2}+(9+2\beta )q^{3}+(37-5\beta )q^{4}+\cdots\) |
Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces
\( S_{6}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)