Properties

Label 26.3.f
Level 26
Weight 3
Character orbit f
Rep. character \(\chi_{26}(7,\cdot)\)
Character field \(\Q(\zeta_{12})\)
Dimension 12
Newforms 2
Sturm bound 10
Trace bound 1

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Defining parameters

Level: \( N \) = \( 26 = 2 \cdot 13 \)
Weight: \( k \) = \( 3 \)
Character orbit: \([\chi]\) = 26.f (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 13 \)
Character field: \(\Q(\zeta_{12})\)
Newforms: \( 2 \)
Sturm bound: \(10\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

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

Total New Old
Modular forms 36 12 24
Cusp forms 20 12 8
Eisenstein series 16 0 16

Trace form

\(12q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 30q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 6q^{5} \) \(\mathstrut -\mathstrut 24q^{7} \) \(\mathstrut -\mathstrut 8q^{8} \) \(\mathstrut -\mathstrut 30q^{9} \) \(\mathstrut -\mathstrut 30q^{10} \) \(\mathstrut -\mathstrut 24q^{11} \) \(\mathstrut +\mathstrut 24q^{13} \) \(\mathstrut +\mathstrut 16q^{14} \) \(\mathstrut +\mathstrut 72q^{15} \) \(\mathstrut +\mathstrut 24q^{16} \) \(\mathstrut +\mathstrut 36q^{17} \) \(\mathstrut +\mathstrut 108q^{18} \) \(\mathstrut -\mathstrut 12q^{19} \) \(\mathstrut +\mathstrut 12q^{20} \) \(\mathstrut -\mathstrut 60q^{21} \) \(\mathstrut -\mathstrut 24q^{22} \) \(\mathstrut -\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 26q^{26} \) \(\mathstrut +\mathstrut 72q^{27} \) \(\mathstrut -\mathstrut 48q^{28} \) \(\mathstrut -\mathstrut 60q^{29} \) \(\mathstrut -\mathstrut 192q^{30} \) \(\mathstrut -\mathstrut 96q^{31} \) \(\mathstrut +\mathstrut 8q^{32} \) \(\mathstrut +\mathstrut 12q^{33} \) \(\mathstrut -\mathstrut 84q^{34} \) \(\mathstrut -\mathstrut 36q^{35} \) \(\mathstrut -\mathstrut 48q^{36} \) \(\mathstrut -\mathstrut 66q^{37} \) \(\mathstrut -\mathstrut 24q^{40} \) \(\mathstrut +\mathstrut 132q^{41} \) \(\mathstrut +\mathstrut 144q^{42} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 120q^{44} \) \(\mathstrut +\mathstrut 276q^{45} \) \(\mathstrut +\mathstrut 144q^{46} \) \(\mathstrut +\mathstrut 192q^{47} \) \(\mathstrut +\mathstrut 300q^{49} \) \(\mathstrut +\mathstrut 232q^{50} \) \(\mathstrut +\mathstrut 72q^{52} \) \(\mathstrut -\mathstrut 300q^{53} \) \(\mathstrut -\mathstrut 360q^{54} \) \(\mathstrut -\mathstrut 156q^{55} \) \(\mathstrut -\mathstrut 96q^{56} \) \(\mathstrut -\mathstrut 396q^{57} \) \(\mathstrut -\mathstrut 66q^{58} \) \(\mathstrut +\mathstrut 24q^{59} \) \(\mathstrut -\mathstrut 96q^{60} \) \(\mathstrut +\mathstrut 114q^{61} \) \(\mathstrut -\mathstrut 72q^{62} \) \(\mathstrut -\mathstrut 192q^{63} \) \(\mathstrut -\mathstrut 420q^{65} \) \(\mathstrut +\mathstrut 96q^{66} \) \(\mathstrut +\mathstrut 12q^{67} \) \(\mathstrut +\mathstrut 36q^{68} \) \(\mathstrut +\mathstrut 132q^{69} \) \(\mathstrut +\mathstrut 240q^{70} \) \(\mathstrut -\mathstrut 132q^{71} \) \(\mathstrut +\mathstrut 156q^{72} \) \(\mathstrut +\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 70q^{74} \) \(\mathstrut +\mathstrut 120q^{75} \) \(\mathstrut +\mathstrut 24q^{76} \) \(\mathstrut +\mathstrut 216q^{78} \) \(\mathstrut +\mathstrut 96q^{79} \) \(\mathstrut +\mathstrut 24q^{80} \) \(\mathstrut -\mathstrut 30q^{81} \) \(\mathstrut -\mathstrut 330q^{82} \) \(\mathstrut -\mathstrut 48q^{83} \) \(\mathstrut -\mathstrut 168q^{84} \) \(\mathstrut -\mathstrut 66q^{85} \) \(\mathstrut -\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 264q^{87} \) \(\mathstrut +\mathstrut 234q^{89} \) \(\mathstrut +\mathstrut 336q^{91} \) \(\mathstrut -\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 492q^{93} \) \(\mathstrut +\mathstrut 72q^{94} \) \(\mathstrut +\mathstrut 672q^{95} \) \(\mathstrut +\mathstrut 222q^{97} \) \(\mathstrut -\mathstrut 158q^{98} \) \(\mathstrut +\mathstrut 144q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(26, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
26.3.f.a \(4\) \(0.708\) \(\Q(\zeta_{12})\) None \(2\) \(0\) \(0\) \(-22\) \(q+(\zeta_{12}+\zeta_{12}^{2}-\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
26.3.f.b \(8\) \(0.708\) 8.0.\(\cdots\).1 None \(-4\) \(0\) \(6\) \(-2\) \(q+(-\beta _{3}-\beta _{4})q^{2}+(-\beta _{2}+\beta _{4}-\beta _{5}+\cdots)q^{3}+\cdots\)

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

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