Properties

Label 26.2.c
Level $26$
Weight $2$
Character orbit 26.c
Rep. character $\chi_{26}(3,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $2$
Newform subspaces $1$
Sturm bound $7$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 26.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 1 \)
Sturm bound: \(7\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(26, [\chi])\).

Total New Old
Modular forms 10 2 8
Cusp forms 2 2 0
Eisenstein series 8 0 8

Trace form

\( 2 q - q^{2} - q^{4} - 2 q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9} + O(q^{10}) \) \( 2 q - q^{2} - q^{4} - 2 q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} - 4 q^{11} + 7 q^{13} + 8 q^{14} - q^{16} - 3 q^{17} - 6 q^{18} + q^{20} - 4 q^{22} + 4 q^{23} - 8 q^{25} - 5 q^{26} - 4 q^{28} + q^{29} + 8 q^{31} - q^{32} + 6 q^{34} + 4 q^{35} + 3 q^{36} - 3 q^{37} - 2 q^{40} + 9 q^{41} + 8 q^{43} + 8 q^{44} - 3 q^{45} + 4 q^{46} - 16 q^{47} - 9 q^{49} + 4 q^{50} - 2 q^{52} - 18 q^{53} + 4 q^{55} - 4 q^{56} + q^{58} + 4 q^{59} - 7 q^{61} - 4 q^{62} + 12 q^{63} + 2 q^{64} - 7 q^{65} - 4 q^{67} - 3 q^{68} - 8 q^{70} + 8 q^{71} + 3 q^{72} + 22 q^{73} - 3 q^{74} + 32 q^{77} - 8 q^{79} + q^{80} - 9 q^{81} + 9 q^{82} + 3 q^{85} - 16 q^{86} - 4 q^{88} + 6 q^{89} + 6 q^{90} - 8 q^{91} - 8 q^{92} + 8 q^{94} - 2 q^{97} - 9 q^{98} - 24 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(26, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
26.2.c.a $2$ $0.208$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-2\) \(-4\) \(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-q^{5}-4\zeta_{6}q^{7}+\cdots\)