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Properties

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

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Defining parameters

Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 26.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(7\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_0(26))\).

Total New Old
Modular forms 5 2 3
Cusp forms 2 2 0
Eisenstein series 3 0 3

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(2\)\(13\)FrickeDim
\(+\)\(-\)$-$\(1\)
\(-\)\(+\)$-$\(1\)
Plus space\(+\)\(0\)
Minus space\(-\)\(2\)

Trace form

\( 2 q - 2 q^{3} + 2 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{9} + O(q^{10}) \) \( 2 q - 2 q^{3} + 2 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 2 q^{14} + 2 q^{16} - 6 q^{17} + 8 q^{18} + 8 q^{19} - 4 q^{20} - 4 q^{21} - 8 q^{22} - 4 q^{23} - 4 q^{24} - 2 q^{26} - 14 q^{27} + 8 q^{29} + 6 q^{30} + 12 q^{33} + 2 q^{35} + 4 q^{36} - 4 q^{37} + 4 q^{38} + 4 q^{39} + 2 q^{40} - 2 q^{42} - 6 q^{43} + 4 q^{44} - 4 q^{46} + 16 q^{47} - 2 q^{48} - 12 q^{49} - 8 q^{50} + 6 q^{51} + 12 q^{53} - 4 q^{54} - 16 q^{55} + 2 q^{56} - 16 q^{57} - 4 q^{58} - 16 q^{59} + 8 q^{62} + 8 q^{63} + 2 q^{64} - 2 q^{65} + 12 q^{67} - 6 q^{68} + 12 q^{69} - 4 q^{70} - 8 q^{71} + 8 q^{72} - 8 q^{73} + 10 q^{74} + 16 q^{75} + 8 q^{76} - 8 q^{77} + 2 q^{78} + 4 q^{79} - 4 q^{80} + 10 q^{81} + 12 q^{83} - 4 q^{84} + 12 q^{85} - 4 q^{86} - 8 q^{88} - 12 q^{90} - 2 q^{91} - 4 q^{92} - 16 q^{93} + 10 q^{94} - 12 q^{95} - 4 q^{96} + 4 q^{97} - 24 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\) into newform subspaces

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