Defining parameters
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.a (trivial) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 5 \) | ||
Sturm bound: | \(25\) | ||
Trace bound: | \(2\) | ||
Distinguishing \(T_p\): | \(2\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{10}(\Gamma_0(25))\).
Total | New | Old | |
---|---|---|---|
Modular forms | 25 | 16 | 9 |
Cusp forms | 19 | 13 | 6 |
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 |
---|---|
\(+\) | \(6\) |
\(-\) | \(7\) |
Trace form
Decomposition of \(S_{10}^{\mathrm{new}}(\Gamma_0(25))\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | A-L signs | $q$-expansion | ||||
---|---|---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | 5 | |||||||
25.10.a.a | $1$ | $12.876$ | \(\Q\) | None | \(8\) | \(114\) | \(0\) | \(-4242\) | $+$ | \(q+8q^{2}+114q^{3}-448q^{4}+912q^{6}+\cdots\) | |
25.10.a.b | $2$ | $12.876$ | \(\Q(\sqrt{1009}) \) | None | \(10\) | \(-260\) | \(0\) | \(-1700\) | $+$ | \(q+(5-\beta )q^{2}+(-130+2\beta )q^{3}+(522+\cdots)q^{4}+\cdots\) | |
25.10.a.c | $3$ | $12.876$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(-33\) | \(-89\) | \(0\) | \(-5258\) | $+$ | \(q+(-11-\beta _{1})q^{2}+(-30-2\beta _{1}+\beta _{2})q^{3}+\cdots\) | |
25.10.a.d | $3$ | $12.876$ | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) | None | \(33\) | \(89\) | \(0\) | \(5258\) | $-$ | \(q+(11+\beta _{1})q^{2}+(30+2\beta _{1}-\beta _{2})q^{3}+\cdots\) | |
25.10.a.e | $4$ | $12.876$ | 4.4.49740556.1 | None | \(0\) | \(0\) | \(0\) | \(0\) | $-$ | \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(342-\beta _{3})q^{4}+\cdots\) |
Decomposition of \(S_{10}^{\mathrm{old}}(\Gamma_0(25))\) into lower level spaces
\( S_{10}^{\mathrm{old}}(\Gamma_0(25)) \cong \) \(S_{10}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 2}\)