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Properties

Label 38.9.d
Level $38$
Weight $9$
Character orbit 38.d
Rep. character $\chi_{38}(27,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $24$
Newform subspaces $1$
Sturm bound $45$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 38.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(45\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(38, [\chi])\).

Total New Old
Modular forms 84 24 60
Cusp forms 76 24 52
Eisenstein series 8 0 8

Trace form

\( 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9} + O(q^{10}) \) \( 24 q + 168 q^{3} + 1536 q^{4} - 558 q^{5} + 896 q^{6} + 11992 q^{7} + 18448 q^{9} + 33516 q^{11} + 60870 q^{13} - 71424 q^{14} - 351930 q^{15} - 196608 q^{16} + 3546 q^{17} - 727738 q^{19} - 142848 q^{20} - 674568 q^{21} - 681600 q^{22} + 726 q^{23} - 114688 q^{24} - 277874 q^{25} - 960000 q^{26} + 767488 q^{28} - 254286 q^{29} - 71168 q^{30} - 2796150 q^{33} - 2740224 q^{34} - 690672 q^{35} - 2361344 q^{36} - 6829056 q^{38} - 1599924 q^{39} - 5153976 q^{41} + 4153600 q^{42} + 5692338 q^{43} + 2145024 q^{44} + 42653840 q^{45} + 11113938 q^{47} - 2752512 q^{48} + 17359944 q^{49} + 62169786 q^{51} + 7791360 q^{52} + 10399050 q^{53} - 24215680 q^{54} + 40181572 q^{55} - 27798558 q^{57} - 10126848 q^{58} - 58809492 q^{59} - 45047040 q^{60} - 45012614 q^{61} + 5892096 q^{62} + 62488724 q^{63} - 50331648 q^{64} + 45107968 q^{66} - 93677268 q^{67} + 907776 q^{68} - 291840 q^{70} + 5993046 q^{71} + 11698176 q^{72} + 23359860 q^{73} - 31474944 q^{74} - 1303552 q^{76} + 35611680 q^{77} + 94099200 q^{78} - 93221166 q^{79} - 9142272 q^{80} - 115510580 q^{81} + 6074880 q^{82} - 194283156 q^{83} - 15300674 q^{85} + 58611456 q^{86} + 89779380 q^{87} - 49833126 q^{89} - 63377664 q^{90} - 101275308 q^{91} - 92928 q^{92} - 157549992 q^{93} - 87570126 q^{95} - 29360128 q^{96} - 178814556 q^{97} - 88409088 q^{98} - 54444376 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{9}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
38.9.d.a 38.d 19.d $24$ $15.480$ None \(0\) \(168\) \(-558\) \(11992\) $\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{9}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)