Properties

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

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 26 = 2 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 26.a (trivial)
Character field: \(\Q\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_0(26))\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces A-L signs $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\) 2 13
26.2.a.a \(1\) \(0.208\) \(\Q\) None \(-1\) \(1\) \(-3\) \(-1\) \(+\) \(-\) \(q-q^{2}+q^{3}+q^{4}-3q^{5}-q^{6}-q^{7}+\cdots\)
26.2.a.b \(1\) \(0.208\) \(\Q\) None \(1\) \(-3\) \(-1\) \(1\) \(-\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)