Properties

Label 38.7.f
Level $38$
Weight $7$
Character orbit 38.f
Rep. character $\chi_{38}(3,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $60$
Newform subspaces $1$
Sturm bound $35$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 38.f (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(35\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(38, [\chi])\).

Total New Old
Modular forms 192 60 132
Cusp forms 168 60 108
Eisenstein series 24 0 24

Trace form

\( 60q + 30q^{3} - 240q^{6} + 432q^{7} + 690q^{9} + O(q^{10}) \) \( 60q + 30q^{3} - 240q^{6} + 432q^{7} + 690q^{9} - 3360q^{11} + 9660q^{13} + 2496q^{14} - 37464q^{15} + 7704q^{17} + 46704q^{19} + 21504q^{20} + 78732q^{21} - 20304q^{22} - 54120q^{23} + 7680q^{24} - 41328q^{25} - 25536q^{26} - 124830q^{27} + 65280q^{28} - 21840q^{29} + 30780q^{31} - 54582q^{33} - 70560q^{34} - 56796q^{35} - 22080q^{36} + 52080q^{38} + 496344q^{39} + 83394q^{41} + 38880q^{42} - 294384q^{43} - 8448q^{44} - 391824q^{45} + 738720q^{46} + 639264q^{47} + 61440q^{48} - 85530q^{49} - 689472q^{50} - 215478q^{51} - 456960q^{52} - 1189428q^{53} - 907200q^{54} - 316512q^{55} + 517776q^{57} + 440640q^{58} + 957390q^{59} + 586752q^{60} + 1390404q^{61} + 978384q^{62} + 2002152q^{63} + 983040q^{64} - 878940q^{65} - 976992q^{66} - 2920854q^{67} - 78144q^{68} - 2667600q^{69} - 643392q^{70} + 1585980q^{71} + 706560q^{72} + 1734648q^{73} - 1167552q^{74} - 411264q^{76} - 1481400q^{77} - 2170608q^{78} + 4991952q^{79} + 40002q^{81} + 2299392q^{82} - 30672q^{83} + 1313280q^{84} + 815976q^{85} - 1424976q^{86} - 125892q^{87} - 6804636q^{89} - 2283456q^{90} - 3838704q^{91} - 244992q^{92} - 3271128q^{93} - 4631640q^{95} + 2112390q^{97} + 7177728q^{98} + 21467982q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.7.f.a \(60\) \(8.742\) None \(0\) \(30\) \(0\) \(432\)

Decomposition of \(S_{7}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)