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

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

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

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
38.6.e.a 38.e 19.e $24$ $6.095$ None \(0\) \(18\) \(0\) \(438\) $\mathrm{SU}(2)[C_{9}]$
38.6.e.b 38.e 19.e $30$ $6.095$ None \(0\) \(15\) \(0\) \(-84\) $\mathrm{SU}(2)[C_{9}]$

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

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