Properties

Label 7.7.d
Level 7
Weight 7
Character orbit d
Rep. character \(\chi_{7}(3,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 6
Newforms 2
Sturm bound 4
Trace bound 1

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 7 \)
Weight: \( k \) = \( 7 \)
Character orbit: \([\chi]\) = 7.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 7 \)
Character field: \(\Q(\zeta_{6})\)
Newforms: \( 2 \)
Sturm bound: \(4\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(2\)

Dimensions

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

Total New Old
Modular forms 10 10 0
Cusp forms 6 6 0
Eisenstein series 4 4 0

Trace form

\( 6q + 4q^{2} - 3q^{3} - 20q^{4} + 165q^{5} - 406q^{7} - 1312q^{8} + 42q^{9} + O(q^{10}) \) \( 6q + 4q^{2} - 3q^{3} - 20q^{4} + 165q^{5} - 406q^{7} - 1312q^{8} + 42q^{9} + 2580q^{10} + 403q^{11} + 5964q^{12} - 5936q^{14} - 20910q^{15} + 3064q^{16} + 8229q^{17} + 6672q^{18} + 29985q^{19} - 8967q^{21} - 63584q^{22} + 8383q^{23} + 28872q^{24} + 19950q^{25} + 33768q^{26} - 18004q^{28} - 26588q^{29} - 10560q^{30} - 39399q^{31} - 39072q^{32} - 36711q^{33} + 46305q^{35} + 175488q^{36} + 17707q^{37} + 60960q^{38} + 16548q^{39} - 137280q^{40} - 22344q^{42} + 285388q^{43} - 122652q^{44} - 370530q^{45} - 184592q^{46} - 407823q^{47} + 375438q^{49} + 578800q^{50} + 64809q^{51} + 128856q^{52} + 165043q^{53} - 44496q^{54} - 214480q^{56} - 141534q^{57} - 11696q^{58} - 436299q^{59} - 207900q^{60} + 141201q^{61} + 380898q^{63} - 778720q^{64} + 10500q^{65} + 1025532q^{66} + 701271q^{67} + 799596q^{68} - 1634640q^{70} - 1277684q^{71} + 141072q^{72} - 421599q^{73} - 688900q^{74} + 826050q^{75} + 1149967q^{77} - 1268736q^{78} + 573759q^{79} + 2654040q^{80} + 872505q^{81} + 2585016q^{82} - 1982148q^{84} - 1677390q^{85} - 947680q^{86} - 1909746q^{87} - 556648q^{88} - 2990823q^{89} + 711480q^{91} + 1178376q^{92} + 551337q^{93} + 223584q^{94} + 958485q^{95} + 972720q^{96} + 1050364q^{98} + 1879428q^{99} + O(q^{100}) \)

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

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
7.7.d.a \(2\) \(1.610\) \(\Q(\sqrt{-3}) \) None \(12\) \(-21\) \(315\) \(-686\) \(q+12\zeta_{6}q^{2}+(-7-7\zeta_{6})q^{3}+(-80+\cdots)q^{4}+\cdots\)
7.7.d.b \(4\) \(1.610\) \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-8\) \(18\) \(-150\) \(280\) \(q+(-4-4\beta _{1}+\beta _{2}+\beta _{3})q^{2}+(6+3\beta _{1}+\cdots)q^{3}+\cdots\)