Properties

Label 38.6.e
Level $38$
Weight $6$
Character orbit 38.e
Rep. character $\chi_{38}(5,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $54$
Newform subspaces $2$
Sturm bound $30$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{9})\)
Newform subspaces: \( 2 \)
Sturm bound: \(30\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(38, [\chi])\).

Total New Old
Modular forms 162 54 108
Cusp forms 138 54 84
Eisenstein series 24 0 24

Trace form

\( 54q + 33q^{3} - 12q^{6} + 354q^{7} - 192q^{8} + 33q^{9} + O(q^{10}) \) \( 54q + 33q^{3} - 12q^{6} + 354q^{7} - 192q^{8} + 33q^{9} + 474q^{11} - 4272q^{13} - 2640q^{14} - 6366q^{15} + 6096q^{17} + 12648q^{18} + 7170q^{19} + 2112q^{20} - 3996q^{21} - 4944q^{22} - 4476q^{23} - 192q^{24} - 12120q^{25} - 1320q^{26} + 7887q^{27} + 6816q^{28} - 1566q^{29} - 6546q^{31} + 5955q^{33} - 9168q^{34} + 46524q^{35} + 528q^{36} + 20052q^{37} - 6756q^{38} - 28956q^{39} - 3249q^{41} + 17712q^{42} + 16890q^{43} + 21504q^{44} - 66114q^{45} - 45600q^{46} - 136794q^{47} - 16896q^{48} - 62355q^{49} - 90996q^{50} + 48009q^{51} + 3936q^{52} + 9180q^{53} + 138420q^{54} + 100458q^{55} + 66816q^{56} + 411072q^{57} + 64416q^{58} + 292569q^{59} - 9696q^{60} - 87474q^{61} - 43272q^{62} - 358188q^{63} - 110592q^{64} - 283320q^{65} - 258612q^{66} - 385341q^{67} - 30384q^{68} - 144162q^{69} + 9168q^{70} + 493638q^{71} + 92544q^{72} + 411954q^{73} - 111240q^{74} + 37920q^{76} + 127380q^{77} + 437928q^{78} + 12318q^{79} - 32469q^{81} - 311220q^{82} - 350070q^{83} - 231264q^{84} - 273264q^{85} - 133248q^{86} - 193638q^{87} - 46464q^{88} + 94464q^{89} + 609456q^{90} - 407580q^{91} + 358368q^{92} + 574278q^{93} + 149328q^{94} + 1342920q^{95} + 749811q^{97} + 134784q^{98} - 412095q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.6.e.a \(24\) \(6.095\) None \(0\) \(18\) \(0\) \(438\)
38.6.e.b \(30\) \(6.095\) None \(0\) \(15\) \(0\) \(-84\)

Decomposition of \(S_{6}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)