Properties

Label 26.2.b
Level 26
Weight 2
Character orbit 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 \(0\) \(-2\) \(0\) \(0\) \(q+iq^{2}-q^{3}-q^{4}-3iq^{5}-iq^{6}+\cdots\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ \( 1 + T^{2} \)
$3$ \( ( 1 + T + 3 T^{2} )^{2} \)
$5$ \( 1 - T^{2} + 25 T^{4} \)
$7$ \( 1 - 5 T^{2} + 49 T^{4} \)
$11$ \( ( 1 - 11 T^{2} )^{2} \)
$13$ \( 1 - 4 T + 13 T^{2} \)
$17$ \( ( 1 - 3 T + 17 T^{2} )^{2} \)
$19$ \( 1 - 2 T^{2} + 361 T^{4} \)
$23$ \( ( 1 + 6 T + 23 T^{2} )^{2} \)
$29$ \( ( 1 + 29 T^{2} )^{2} \)
$31$ \( ( 1 - 31 T^{2} )^{2} \)
$37$ \( 1 - 65 T^{2} + 1369 T^{4} \)
$41$ \( ( 1 - 41 T^{2} )^{2} \)
$43$ \( ( 1 + T + 43 T^{2} )^{2} \)
$47$ \( 1 - 85 T^{2} + 2209 T^{4} \)
$53$ \( ( 1 + 6 T + 53 T^{2} )^{2} \)
$59$ \( 1 - 82 T^{2} + 3481 T^{4} \)
$61$ \( ( 1 + 8 T + 61 T^{2} )^{2} \)
$67$ \( 1 + 10 T^{2} + 4489 T^{4} \)
$71$ \( 1 + 83 T^{2} + 5041 T^{4} \)
$73$ \( ( 1 - 16 T + 73 T^{2} )( 1 + 16 T + 73 T^{2} ) \)
$79$ \( ( 1 - 10 T + 79 T^{2} )^{2} \)
$83$ \( 1 - 130 T^{2} + 6889 T^{4} \)
$89$ \( 1 - 142 T^{2} + 7921 T^{4} \)
$97$ \( 1 - 50 T^{2} + 9409 T^{4} \)
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