Properties

Label 7.4.c
Level 7
Weight 4
Character orbit c
Rep. character \(\chi_{7}(2,\cdot)\)
Character field \(\Q(\zeta_{3})\)
Dimension 2
Newforms 1
Sturm bound 2
Trace bound 0

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Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 4 \)
Character orbit: \([\chi]\) = 7.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{3})\)
Newforms: \( 1 \)
Sturm bound: \(2\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(7, [\chi])\).

Total New Old
Modular forms 6 6 0
Cusp forms 2 2 0
Eisenstein series 4 4 0

Trace form

\(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 28q^{6} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut -\mathstrut 48q^{8} \) \(\mathstrut -\mathstrut 22q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut -\mathstrut 7q^{3} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut -\mathstrut 7q^{5} \) \(\mathstrut +\mathstrut 28q^{6} \) \(\mathstrut +\mathstrut 28q^{7} \) \(\mathstrut -\mathstrut 48q^{8} \) \(\mathstrut -\mathstrut 22q^{9} \) \(\mathstrut -\mathstrut 14q^{10} \) \(\mathstrut +\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 28q^{12} \) \(\mathstrut -\mathstrut 28q^{13} \) \(\mathstrut +\mathstrut 14q^{14} \) \(\mathstrut +\mathstrut 98q^{15} \) \(\mathstrut +\mathstrut 16q^{16} \) \(\mathstrut +\mathstrut 21q^{17} \) \(\mathstrut -\mathstrut 44q^{18} \) \(\mathstrut -\mathstrut 49q^{19} \) \(\mathstrut -\mathstrut 56q^{20} \) \(\mathstrut -\mathstrut 245q^{21} \) \(\mathstrut -\mathstrut 20q^{22} \) \(\mathstrut +\mathstrut 159q^{23} \) \(\mathstrut +\mathstrut 168q^{24} \) \(\mathstrut +\mathstrut 76q^{25} \) \(\mathstrut +\mathstrut 28q^{26} \) \(\mathstrut -\mathstrut 70q^{27} \) \(\mathstrut +\mathstrut 140q^{28} \) \(\mathstrut +\mathstrut 116q^{29} \) \(\mathstrut -\mathstrut 98q^{30} \) \(\mathstrut -\mathstrut 147q^{31} \) \(\mathstrut -\mathstrut 160q^{32} \) \(\mathstrut +\mathstrut 35q^{33} \) \(\mathstrut -\mathstrut 84q^{34} \) \(\mathstrut +\mathstrut 49q^{35} \) \(\mathstrut -\mathstrut 176q^{36} \) \(\mathstrut -\mathstrut 219q^{37} \) \(\mathstrut -\mathstrut 98q^{38} \) \(\mathstrut +\mathstrut 98q^{39} \) \(\mathstrut +\mathstrut 168q^{40} \) \(\mathstrut +\mathstrut 700q^{41} \) \(\mathstrut +\mathstrut 392q^{42} \) \(\mathstrut -\mathstrut 248q^{43} \) \(\mathstrut -\mathstrut 20q^{44} \) \(\mathstrut -\mathstrut 154q^{45} \) \(\mathstrut +\mathstrut 318q^{46} \) \(\mathstrut -\mathstrut 525q^{47} \) \(\mathstrut -\mathstrut 224q^{48} \) \(\mathstrut +\mathstrut 98q^{49} \) \(\mathstrut -\mathstrut 304q^{50} \) \(\mathstrut +\mathstrut 147q^{51} \) \(\mathstrut -\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 303q^{53} \) \(\mathstrut +\mathstrut 70q^{54} \) \(\mathstrut -\mathstrut 70q^{55} \) \(\mathstrut -\mathstrut 672q^{56} \) \(\mathstrut +\mathstrut 686q^{57} \) \(\mathstrut -\mathstrut 116q^{58} \) \(\mathstrut +\mathstrut 105q^{59} \) \(\mathstrut +\mathstrut 196q^{60} \) \(\mathstrut +\mathstrut 413q^{61} \) \(\mathstrut +\mathstrut 588q^{62} \) \(\mathstrut +\mathstrut 154q^{63} \) \(\mathstrut +\mathstrut 896q^{64} \) \(\mathstrut +\mathstrut 98q^{65} \) \(\mathstrut +\mathstrut 70q^{66} \) \(\mathstrut -\mathstrut 415q^{67} \) \(\mathstrut -\mathstrut 84q^{68} \) \(\mathstrut -\mathstrut 2226q^{69} \) \(\mathstrut -\mathstrut 490q^{70} \) \(\mathstrut -\mathstrut 864q^{71} \) \(\mathstrut +\mathstrut 528q^{72} \) \(\mathstrut +\mathstrut 1113q^{73} \) \(\mathstrut -\mathstrut 438q^{74} \) \(\mathstrut +\mathstrut 532q^{75} \) \(\mathstrut -\mathstrut 392q^{76} \) \(\mathstrut +\mathstrut 175q^{77} \) \(\mathstrut -\mathstrut 392q^{78} \) \(\mathstrut +\mathstrut 103q^{79} \) \(\mathstrut +\mathstrut 112q^{80} \) \(\mathstrut +\mathstrut 839q^{81} \) \(\mathstrut -\mathstrut 700q^{82} \) \(\mathstrut +\mathstrut 2184q^{83} \) \(\mathstrut -\mathstrut 196q^{84} \) \(\mathstrut -\mathstrut 294q^{85} \) \(\mathstrut +\mathstrut 248q^{86} \) \(\mathstrut -\mathstrut 406q^{87} \) \(\mathstrut -\mathstrut 120q^{88} \) \(\mathstrut +\mathstrut 329q^{89} \) \(\mathstrut +\mathstrut 616q^{90} \) \(\mathstrut -\mathstrut 392q^{91} \) \(\mathstrut +\mathstrut 1272q^{92} \) \(\mathstrut -\mathstrut 1029q^{93} \) \(\mathstrut -\mathstrut 1050q^{94} \) \(\mathstrut -\mathstrut 343q^{95} \) \(\mathstrut -\mathstrut 1120q^{96} \) \(\mathstrut -\mathstrut 1764q^{97} \) \(\mathstrut +\mathstrut 1078q^{98} \) \(\mathstrut -\mathstrut 220q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(7, [\chi])\) into irreducible Hecke orbits

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.4.c.a \(2\) \(0.413\) \(\Q(\sqrt{-3}) \) None \(-2\) \(-7\) \(-7\) \(28\) \(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)