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
Newforms 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: \(\Q(i)\)
Newforms: \( 1 \)
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

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

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.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

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