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 $1$

Related objects

Downloads

Learn more

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

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

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.e.a 169.e 13.e $2$ $1.349$ \(\Q(\sqrt{-3}) \) None 13.2.e.a \(3\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\zeta_{6})q^{2}+(-2+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
169.2.e.b 169.e 13.e $12$ $1.349$ 12.0.\(\cdots\).1 None 169.2.a.b \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{1}+\beta _{8}+\beta _{10})q^{2}+(1-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)

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

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