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
Newforms 2
Sturm bound 8
Trace bound 2

Related objects

Downloads

Learn more about

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: \(\Q(\zeta_{3})\)
Newforms: \( 2 \)
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

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

Decomposition of \(S_{4}^{\mathrm{new}}(14, [\chi])\) into irreducible Hecke orbits

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

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