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Properties

Label 14.4.c
Level 14
Weight 4
Character orbit c
Rep. character \(\chi_{14}(9,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 4
Newform subspaces 2
Sturm bound 8
Trace bound 2

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Defining parameters

Level: \( N \) = \( 14 = 2 \cdot 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 14.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(8\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(14, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4q + 6q^{3} - 8q^{4} + 2q^{5} - 16q^{6} - 48q^{7} + 28q^{9} + O(q^{10}) \) \( 4q + 6q^{3} - 8q^{4} + 2q^{5} - 16q^{6} - 48q^{7} + 28q^{9} + 32q^{10} + 22q^{11} + 24q^{12} - 8q^{13} + 104q^{14} + 76q^{15} - 32q^{16} - 110q^{17} - 48q^{18} - 142q^{19} - 16q^{20} - 2q^{21} - 368q^{22} - 62q^{23} + 32q^{24} + 120q^{25} + 272q^{26} + 396q^{27} + 120q^{28} + 440q^{29} - 104q^{30} - 98q^{31} - 250q^{33} - 32q^{34} - 434q^{35} - 224q^{36} + 242q^{37} + 264q^{38} - 284q^{39} + 128q^{40} - 1080q^{41} + 240q^{42} + 272q^{43} + 88q^{44} + 164q^{45} - 152q^{46} - 30q^{47} - 192q^{48} - 188q^{49} + 128q^{50} + 314q^{51} + 16q^{52} + 810q^{53} - 184q^{54} + 1516q^{55} - 64q^{56} - 324q^{57} - 16q^{58} - 202q^{59} - 152q^{60} + 658q^{61} - 208q^{62} + 372q^{63} + 256q^{64} - 1092q^{65} - 640q^{66} - 858q^{67} - 440q^{68} - 676q^{69} - 392q^{70} - 1760q^{71} - 192q^{72} + 18q^{73} + 528q^{74} - 296q^{75} + 1136q^{76} + 1694q^{77} + 1664q^{78} + 34q^{79} + 32q^{80} + 22q^{81} - 912q^{82} + 688q^{83} - 632q^{84} - 92q^{85} + 768q^{86} + 676q^{87} + 736q^{88} + 1890q^{89} + 800q^{90} + 640q^{91} + 496q^{92} + 190q^{93} - 744q^{94} - 914q^{95} + 128q^{96} - 4248q^{97} - 2640q^{98} - 1592q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(14, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
14.4.c.a \(2\) \(0.826\) \(\Q(\sqrt{-3}) \) None \(-2\) \(5\) \(9\) \(-28\) \(q+(-2+2\zeta_{6})q^{2}+5\zeta_{6}q^{3}-4\zeta_{6}q^{4}+\cdots\)
14.4.c.b \(2\) \(0.826\) \(\Q(\sqrt{-3}) \) None \(2\) \(1\) \(-7\) \(-20\) \(q+(2-2\zeta_{6})q^{2}+\zeta_{6}q^{3}-4\zeta_{6}q^{4}+(-7+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(14, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(14, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(7, [\chi])\)\(^{\oplus 2}\)