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Properties

Label 26.2.b
Level $26$
Weight $2$
Character orbit 26.b
Rep. character $\chi_{26}(25,\cdot)$
Character field $\Q$
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.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q\)
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 6 2 4
Cusp forms 2 2 0
Eisenstein series 4 0 4

Trace form

\( 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{3} - 2 q^{4} - 4 q^{9} + 6 q^{10} + 2 q^{12} + 4 q^{13} - 6 q^{14} + 2 q^{16} + 6 q^{17} - 12 q^{23} - 8 q^{25} - 6 q^{26} + 10 q^{27} - 6 q^{30} + 18 q^{35} + 4 q^{36} + 12 q^{38} - 4 q^{39} - 6 q^{40} + 6 q^{42} - 2 q^{43} - 2 q^{48} - 4 q^{49} - 6 q^{51} - 4 q^{52} - 12 q^{53} + 6 q^{56} - 16 q^{61} - 2 q^{64} + 18 q^{65} - 6 q^{68} + 12 q^{69} - 6 q^{74} + 8 q^{75} + 6 q^{78} + 20 q^{79} + 2 q^{81} - 12 q^{90} - 18 q^{91} + 12 q^{92} - 6 q^{94} - 36 q^{95} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
26.2.b.a 26.b 13.b $2$ $0.208$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)