Properties

Label 26.2.a
Level 26
Weight 2
Character orbit 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

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

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

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 \(1\) \(-3\) \(-1\) \(1\) \(-\) \(+\) \(q+q^{2}-3q^{3}+q^{4}-q^{5}-3q^{6}+q^{7}+\cdots\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T \))(\( 1 - T \))
$3$ (\( 1 - T + 3 T^{2} \))(\( 1 + 3 T + 3 T^{2} \))
$5$ (\( 1 + 3 T + 5 T^{2} \))(\( 1 + T + 5 T^{2} \))
$7$ (\( 1 + T + 7 T^{2} \))(\( 1 - T + 7 T^{2} \))
$11$ (\( 1 - 6 T + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))
$13$ (\( 1 - T \))(\( 1 + T \))
$17$ (\( 1 + 3 T + 17 T^{2} \))(\( 1 + 3 T + 17 T^{2} \))
$19$ (\( 1 - 2 T + 19 T^{2} \))(\( 1 - 6 T + 19 T^{2} \))
$23$ (\( 1 + 23 T^{2} \))(\( 1 + 4 T + 23 T^{2} \))
$29$ (\( 1 - 6 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))
$31$ (\( 1 + 4 T + 31 T^{2} \))(\( 1 - 4 T + 31 T^{2} \))
$37$ (\( 1 + 7 T + 37 T^{2} \))(\( 1 - 3 T + 37 T^{2} \))
$41$ (\( 1 + 41 T^{2} \))(\( 1 + 41 T^{2} \))
$43$ (\( 1 + T + 43 T^{2} \))(\( 1 + 5 T + 43 T^{2} \))
$47$ (\( 1 - 3 T + 47 T^{2} \))(\( 1 - 13 T + 47 T^{2} \))
$53$ (\( 1 + 53 T^{2} \))(\( 1 - 12 T + 53 T^{2} \))
$59$ (\( 1 + 6 T + 59 T^{2} \))(\( 1 + 10 T + 59 T^{2} \))
$61$ (\( 1 - 8 T + 61 T^{2} \))(\( 1 + 8 T + 61 T^{2} \))
$67$ (\( 1 - 14 T + 67 T^{2} \))(\( 1 + 2 T + 67 T^{2} \))
$71$ (\( 1 + 3 T + 71 T^{2} \))(\( 1 + 5 T + 71 T^{2} \))
$73$ (\( 1 - 2 T + 73 T^{2} \))(\( 1 + 10 T + 73 T^{2} \))
$79$ (\( 1 - 8 T + 79 T^{2} \))(\( 1 + 4 T + 79 T^{2} \))
$83$ (\( 1 - 12 T + 83 T^{2} \))(\( 1 + 83 T^{2} \))
$89$ (\( 1 + 6 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))
$97$ (\( 1 + 10 T + 97 T^{2} \))(\( 1 - 14 T + 97 T^{2} \))
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