Properties

Label 26.3.d
Level 26
Weight 3
Character orbit d
Rep. character \(\chi_{26}(5,\cdot)\)
Character field \(\Q(\zeta_{4})\)
Dimension 2
Newform subspaces 1
Sturm bound 10
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 26 = 2 \cdot 13 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 26.d (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 13 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 1 \)
Sturm bound: \(10\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(26, [\chi])\).

Total New Old
Modular forms 18 2 16
Cusp forms 10 2 8
Eisenstein series 8 0 8

Trace form

\( 2q + 2q^{2} - 6q^{5} + 4q^{7} - 4q^{8} - 18q^{9} + O(q^{10}) \) \( 2q + 2q^{2} - 6q^{5} + 4q^{7} - 4q^{8} - 18q^{9} + 12q^{11} + 8q^{14} - 8q^{16} - 18q^{18} + 52q^{19} + 12q^{20} + 24q^{22} - 26q^{26} + 8q^{28} - 96q^{29} - 28q^{31} - 8q^{32} - 12q^{34} - 24q^{35} + 74q^{37} + 24q^{40} - 18q^{41} + 24q^{44} + 54q^{45} + 48q^{46} + 84q^{47} + 14q^{50} - 52q^{52} + 60q^{53} - 72q^{55} - 96q^{58} - 108q^{59} - 36q^{61} - 36q^{63} + 78q^{65} - 44q^{67} - 24q^{68} - 24q^{70} + 12q^{71} + 36q^{72} + 34q^{73} + 148q^{74} - 104q^{76} - 216q^{79} + 24q^{80} + 162q^{81} + 156q^{83} + 36q^{85} - 72q^{86} - 18q^{89} + 52q^{91} + 96q^{92} + 168q^{94} - 94q^{97} - 82q^{98} - 108q^{99} + O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(26, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
26.3.d.a \(2\) \(0.708\) \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-6\) \(4\) \(q+(1+i)q^{2}+2iq^{4}+(-3-3i)q^{5}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(26, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(26, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ \( 1 - 2 T + 2 T^{2} \)
$3$ \( ( 1 + 9 T^{2} )^{2} \)
$5$ \( 1 + 6 T + 18 T^{2} + 150 T^{3} + 625 T^{4} \)
$7$ \( 1 - 4 T + 8 T^{2} - 196 T^{3} + 2401 T^{4} \)
$11$ \( 1 - 12 T + 72 T^{2} - 1452 T^{3} + 14641 T^{4} \)
$13$ \( 1 + 169 T^{2} \)
$17$ \( 1 - 542 T^{2} + 83521 T^{4} \)
$19$ \( 1 - 52 T + 1352 T^{2} - 18772 T^{3} + 130321 T^{4} \)
$23$ \( 1 - 482 T^{2} + 279841 T^{4} \)
$29$ \( ( 1 + 48 T + 841 T^{2} )^{2} \)
$31$ \( 1 + 28 T + 392 T^{2} + 26908 T^{3} + 923521 T^{4} \)
$37$ \( ( 1 - 37 T )^{2}( 1 + 1369 T^{2} ) \)
$41$ \( 1 + 18 T + 162 T^{2} + 30258 T^{3} + 2825761 T^{4} \)
$43$ \( 1 - 2402 T^{2} + 3418801 T^{4} \)
$47$ \( 1 - 84 T + 3528 T^{2} - 185556 T^{3} + 4879681 T^{4} \)
$53$ \( ( 1 - 30 T + 2809 T^{2} )^{2} \)
$59$ \( 1 + 108 T + 5832 T^{2} + 375948 T^{3} + 12117361 T^{4} \)
$61$ \( ( 1 + 18 T + 3721 T^{2} )^{2} \)
$67$ \( 1 + 44 T + 968 T^{2} + 197516 T^{3} + 20151121 T^{4} \)
$71$ \( 1 - 12 T + 72 T^{2} - 60492 T^{3} + 25411681 T^{4} \)
$73$ \( 1 - 34 T + 578 T^{2} - 181186 T^{3} + 28398241 T^{4} \)
$79$ \( ( 1 + 108 T + 6241 T^{2} )^{2} \)
$83$ \( 1 - 156 T + 12168 T^{2} - 1074684 T^{3} + 47458321 T^{4} \)
$89$ \( 1 + 18 T + 162 T^{2} + 142578 T^{3} + 62742241 T^{4} \)
$97$ \( 1 + 94 T + 4418 T^{2} + 884446 T^{3} + 88529281 T^{4} \)
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