Properties

Label 169.2.b
Level $169$
Weight $2$
Character orbit 169.b
Rep. character $\chi_{169}(168,\cdot)$
Character field $\Q$
Dimension $8$
Newform subspaces $2$
Sturm bound $30$
Trace bound $1$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(169, [\chi])\).

Total New Old
Modular forms 22 18 4
Cusp forms 8 8 0
Eisenstein series 14 10 4

Trace form

\( 8 q - 2 q^{4} - 4 q^{9} + O(q^{10}) \) \( 8 q - 2 q^{4} - 4 q^{9} - 4 q^{10} - 4 q^{12} - 10 q^{14} - 6 q^{16} - 2 q^{17} + 6 q^{22} - 2 q^{23} + 14 q^{25} - 6 q^{27} + 4 q^{29} + 14 q^{30} + 8 q^{35} + 12 q^{36} - 12 q^{38} + 16 q^{42} - 10 q^{43} - 18 q^{48} + 22 q^{49} - 10 q^{51} - 4 q^{53} + 12 q^{55} + 8 q^{56} + 10 q^{61} - 14 q^{62} + 20 q^{64} + 10 q^{66} - 36 q^{68} - 12 q^{69} + 14 q^{74} - 22 q^{75} - 16 q^{77} - 2 q^{79} - 24 q^{81} + 10 q^{82} - 24 q^{87} - 30 q^{88} + 30 q^{90} + 12 q^{92} + 22 q^{94} - 18 q^{95} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(169, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
169.2.b.a 169.b 13.b $2$ $1.349$ \(\Q(\sqrt{-3}) \) None 13.2.e.a \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{6}q^{2}+2q^{3}-q^{4}+\zeta_{6}q^{5}-2\zeta_{6}q^{6}+\cdots\)
169.2.b.b 169.b 13.b $6$ $1.349$ 6.0.153664.1 None 169.2.a.b \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}+\beta _{5})q^{2}+(-1+\beta _{4})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)