Properties

Label 125.2.a
Level $125$
Weight $2$
Character orbit 125.a
Rep. character $\chi_{125}(1,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $3$
Sturm bound $25$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 125 = 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 125.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 3 \)
Sturm bound: \(25\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(125))\).

Total New Old
Modular forms 17 8 9
Cusp forms 8 8 0
Eisenstein series 9 0 9

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.
\(+\)\(2\)
\(-\)\(6\)

Trace form

\( 8 q + 6 q^{4} - 4 q^{6} + 4 q^{9} + O(q^{10}) \) \( 8 q + 6 q^{4} - 4 q^{6} + 4 q^{9} - 4 q^{11} - 8 q^{14} - 2 q^{16} + 10 q^{19} + 6 q^{21} - 20 q^{24} - 14 q^{26} - 10 q^{29} + 6 q^{31} - 18 q^{34} - 22 q^{36} - 2 q^{39} - 14 q^{41} + 22 q^{44} + 26 q^{46} + 6 q^{49} + 26 q^{51} + 10 q^{54} + 10 q^{56} + 30 q^{59} - 4 q^{61} + 16 q^{64} + 2 q^{66} - 32 q^{69} - 24 q^{71} + 12 q^{74} + 20 q^{76} + 40 q^{79} - 32 q^{81} - 8 q^{84} + 56 q^{86} - 30 q^{89} + 46 q^{91} + 2 q^{94} - 34 q^{96} - 2 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(125))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5
125.2.a.a 125.a 1.a $2$ $0.998$ \(\Q(\sqrt{5}) \) None \(-1\) \(-3\) \(0\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+(-2+\beta )q^{3}+(-1+\beta )q^{4}+\cdots\)
125.2.a.b 125.a 1.a $2$ $0.998$ \(\Q(\sqrt{5}) \) None \(1\) \(3\) \(0\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(2-\beta )q^{3}+(-1+\beta )q^{4}+(-1+\cdots)q^{6}+\cdots\)
125.2.a.c 125.a 1.a $4$ $0.998$ 4.4.4400.1 None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+(1-2\beta _{2})q^{4}+(1+\cdots)q^{6}+\cdots\)