Properties

Label 169.2.e
Level $169$
Weight $2$
Character orbit 169.e
Rep. character $\chi_{169}(23,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $14$
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.e (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{6})\)
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 46 34 12
Cusp forms 18 14 4
Eisenstein series 28 20 8

Trace form

\( 14q + 3q^{2} + 2q^{3} + q^{4} - 6q^{6} + 5q^{9} + O(q^{10}) \) \( 14q + 3q^{2} + 2q^{3} + q^{4} - 6q^{6} + 5q^{9} + 7q^{10} - 4q^{12} - 20q^{14} - 6q^{15} + q^{16} - q^{17} + 6q^{19} - 3q^{20} - 6q^{22} - 4q^{23} + 6q^{24} + 24q^{25} - 4q^{27} - q^{29} - 8q^{30} + 9q^{32} - 8q^{35} - 13q^{36} - 15q^{37} - 36q^{38} - 6q^{40} + 9q^{41} - 16q^{42} + 18q^{43} + 3q^{45} + 18q^{46} + 8q^{48} - 15q^{49} + 6q^{50} - 8q^{51} - 2q^{53} - 12q^{54} - 12q^{55} - 8q^{56} - 9q^{58} - 12q^{59} - 9q^{61} + 8q^{62} + 42q^{64} + 20q^{66} - 6q^{67} + 39q^{68} - 6q^{71} - 3q^{72} + q^{74} + 26q^{75} + 6q^{76} - 32q^{77} - 12q^{79} + 15q^{80} + 13q^{81} - 19q^{82} - 9q^{85} + 30q^{87} + 30q^{88} + 12q^{89} + 54q^{90} + 12q^{92} + 12q^{93} - 16q^{94} + 12q^{95} - 12q^{97} - 21q^{98} + O(q^{100}) \)

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.e.a \(2\) \(1.349\) \(\Q(\sqrt{-3}) \) None \(3\) \(-2\) \(0\) \(0\) \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
169.2.e.b \(12\) \(1.349\) 12.0.\(\cdots\).1 None \(0\) \(4\) \(0\) \(0\) \(q+(-\beta _{1}+\beta _{8}+\beta _{10})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(169, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(169, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)