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 $1$

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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

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

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
169.2.b.a \(2\) \(1.349\) \(\Q(\sqrt{-3}) \) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{6}q^{2}+2q^{3}-q^{4}+\zeta_{6}q^{5}-2\zeta_{6}q^{6}+\cdots\)
169.2.b.b \(6\) \(1.349\) 6.0.153664.1 None \(0\) \(-4\) \(0\) \(0\) \(q+(\beta _{3}+\beta _{5})q^{2}+(-1+\beta _{4})q^{3}+(1-2\beta _{2}+\cdots)q^{4}+\cdots\)