Properties

Label 169.2.c
Level $169$
Weight $2$
Character orbit 169.c
Rep. character $\chi_{169}(22,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $16$
Newform subspaces $3$
Sturm bound $30$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 169.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(30\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 44 36 8
Cusp forms 16 16 0
Eisenstein series 28 20 8

Trace form

\( 16 q - 2 q^{4} + 4 q^{9} + O(q^{10}) \) \( 16 q - 2 q^{4} + 4 q^{9} - 4 q^{10} + 8 q^{12} - 20 q^{14} + 6 q^{16} - 2 q^{17} - 6 q^{22} - 2 q^{23} - 28 q^{25} - 12 q^{27} - 4 q^{29} + 14 q^{30} - 8 q^{35} + 12 q^{36} + 24 q^{38} - 16 q^{42} - 10 q^{43} + 18 q^{48} + 22 q^{49} + 20 q^{51} - 8 q^{53} - 12 q^{55} + 8 q^{56} - 10 q^{61} - 14 q^{62} - 40 q^{64} + 20 q^{66} + 36 q^{68} - 12 q^{69} - 14 q^{74} - 22 q^{75} + 32 q^{77} - 4 q^{79} + 24 q^{81} + 10 q^{82} + 24 q^{87} - 30 q^{88} - 60 q^{90} + 24 q^{92} - 22 q^{94} - 18 q^{95} + O(q^{100}) \)

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.c.a 169.c 13.c $4$ $1.349$ \(\Q(\zeta_{12})\) None 13.2.e.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{2}-2\zeta_{12}q^{3}+(-1+\zeta_{12}+\cdots)q^{4}+\cdots\)
169.2.c.b 169.c 13.c $6$ $1.349$ 6.0.64827.1 None 169.2.a.b \(-2\) \(2\) \(8\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{4}+\beta _{5})q^{2}+(1-\beta _{1}-\beta _{5})q^{3}+\cdots\)
169.2.c.c 169.c 13.c $6$ $1.349$ 6.0.64827.1 None 169.2.a.b \(2\) \(2\) \(-8\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{4})q^{2}+(1-\beta _{4}-\beta _{5})q^{3}+(2\beta _{1}+\cdots)q^{4}+\cdots\)