Properties

Label 27.4.c
Level 27
Weight 4
Character orbit c
Rep. character \(\chi_{27}(10,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newforms 1
Sturm bound 12
Trace bound 0

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Defining parameters

Level: \( N \) = \( 27 = 3^{3} \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 27.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 9 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(27, [\chi])\).

Total New Old
Modular forms 24 8 16
Cusp forms 12 4 8
Eisenstein series 12 4 8

Trace form

\( 4q + 3q^{2} - 5q^{4} + 15q^{5} - 7q^{7} - 66q^{8} + O(q^{10}) \) \( 4q + 3q^{2} - 5q^{4} + 15q^{5} - 7q^{7} - 66q^{8} + 12q^{10} + 66q^{11} + 11q^{13} + 60q^{14} + 7q^{16} - 198q^{17} - 154q^{19} - 12q^{20} + 33q^{22} + 33q^{23} + 121q^{25} + 528q^{26} + 332q^{28} - 51q^{29} - 43q^{31} - 423q^{32} - 297q^{34} - 6q^{35} - 100q^{37} - 561q^{38} - 264q^{40} + 132q^{41} - 88q^{43} + 462q^{44} - 528q^{46} + 399q^{47} + 513q^{49} - 429q^{50} + 770q^{52} - 108q^{53} + 1254q^{55} + 66q^{56} + 60q^{58} + 798q^{59} - 439q^{61} - 228q^{62} - 1454q^{64} + 165q^{65} - 988q^{67} + 693q^{68} - 318q^{70} - 2736q^{71} - 910q^{73} + 816q^{74} + 1529q^{76} - 165q^{77} + 803q^{79} - 192q^{80} + 3630q^{82} + 813q^{83} - 594q^{85} + 33q^{86} - 1221q^{88} + 792q^{89} - 1562q^{91} - 858q^{92} - 2100q^{94} - 132q^{95} - 736q^{97} + 846q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(27, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
27.4.c.a \(4\) \(1.593\) \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(3\) \(0\) \(15\) \(-7\) \(q+(\beta _{1}+\beta _{3})q^{2}+(-4+\beta _{1}-3\beta _{2}+3\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(27, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)