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

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

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.b.a \(2\) \(0.208\) \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)