Properties

Label 43.7.h
Level 43
Weight 7
Character orbit h
Rep. character \(\chi_{43}(3,\cdot)\)
Character field \(\Q(\zeta_{42})\)
Dimension 252
Newform subspaces 1
Sturm bound 25
Trace bound 0

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Defining parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.h (of order \(42\) and degree \(12\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 43 \)
Character field: \(\Q(\zeta_{42})\)
Newform subspaces: \( 1 \)
Sturm bound: \(25\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(43, [\chi])\).

Total New Old
Modular forms 276 276 0
Cusp forms 252 252 0
Eisenstein series 24 24 0

Trace form

\( 252q - 14q^{2} - 11q^{3} + 1180q^{4} - 11q^{5} - 118q^{6} + 126q^{7} - 2254q^{8} - 8178q^{9} + O(q^{10}) \) \( 252q - 14q^{2} - 11q^{3} + 1180q^{4} - 11q^{5} - 118q^{6} + 126q^{7} - 2254q^{8} - 8178q^{9} + 967q^{10} + 4090q^{11} - 484q^{12} + 1527q^{13} + 7812q^{14} - 8923q^{15} - 13760q^{16} - 3655q^{17} + 5596q^{18} + 38605q^{19} + 26085q^{20} + 24873q^{21} - 25214q^{22} + 27991q^{23} - 20480q^{24} - 24146q^{25} - 34923q^{26} - 14q^{27} - 77634q^{28} - 112735q^{29} + 375072q^{30} + 290647q^{31} - 344064q^{32} - 152174q^{33} - 198311q^{34} - 182471q^{35} - 930891q^{36} + 282762q^{37} + 487342q^{38} + 857290q^{39} + 745459q^{40} + 27674q^{41} + 148802q^{43} - 1255832q^{44} - 191310q^{45} - 1344785q^{46} + 69166q^{47} - 871241q^{48} + 1786604q^{49} + 837705q^{50} - 182756q^{51} + 2906416q^{52} + 7779q^{53} + 487154q^{54} - 529592q^{55} - 2464007q^{56} - 767855q^{57} - 1523780q^{58} + 1531338q^{59} - 1858647q^{60} + 646957q^{61} - 448559q^{62} - 2007847q^{63} + 3937366q^{64} - 1473542q^{65} + 1513319q^{66} - 575523q^{67} + 2717157q^{68} + 967041q^{69} + 4624473q^{70} - 2149319q^{71} - 9986371q^{72} - 514565q^{73} - 882972q^{74} - 6655138q^{75} + 1152658q^{76} - 341803q^{77} + 6322388q^{78} - 2476742q^{79} + 10750038q^{80} + 4308941q^{81} + 5079172q^{82} + 2318609q^{83} + 5578407q^{84} + 585292q^{86} - 1990710q^{87} - 2864890q^{88} - 4561993q^{89} - 17681545q^{90} - 4648506q^{91} - 1991714q^{92} - 8868294q^{93} - 10200218q^{94} + 10091737q^{95} + 6250318q^{96} - 1676750q^{97} + 7512700q^{98} + 18452884q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(43, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
43.7.h.a \(252\) \(9.892\) None \(-14\) \(-11\) \(-11\) \(126\)

Hecke characteristic polynomials

There are no characteristic polynomials of Hecke operators in the database