↑

Properties

Label 125.2.b
Level $125$
Weight $2$
Character orbit 125.b
Rep. character $\chi_{125}(124,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $25$
Trace bound $4$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 125 = 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 125.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(25\)
Trace bound: \(4\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(125, [\chi])\).

Total New Old
Modular forms 18 8 10
Cusp forms 8 8 0
Eisenstein series 10 0 10

Trace form

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

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(125, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
125.2.b.a 125.b 5.b $4$ $0.998$ 4.0.4400.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+(-1-2\beta _{2})q^{4}+\cdots\)
125.2.b.b 125.b 5.b $4$ $0.998$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(\beta _{1}+2\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots\)