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Properties

Label 38.5.d
Level $38$
Weight $5$
Character orbit 38.d
Rep. character $\chi_{38}(27,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $16$
Newform subspaces $1$
Sturm bound $25$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
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: \(25\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(38, [\chi])\).

Total New Old
Modular forms 44 16 28
Cusp forms 36 16 20
Eisenstein series 8 0 8

Trace form

\( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9} + O(q^{10}) \) \( 16 q - 12 q^{3} + 64 q^{4} - 18 q^{5} - 16 q^{6} + 72 q^{7} + 352 q^{9} - 84 q^{11} + 450 q^{13} + 288 q^{14} - 390 q^{15} - 512 q^{16} + 606 q^{17} - 306 q^{19} - 288 q^{20} - 2160 q^{21} - 1680 q^{22} - 54 q^{23} + 128 q^{24} - 434 q^{25} + 1344 q^{26} + 288 q^{28} - 4914 q^{29} + 2752 q^{30} + 7890 q^{33} - 1536 q^{34} + 2328 q^{35} - 2816 q^{36} + 1344 q^{38} + 7620 q^{39} - 1692 q^{41} + 2080 q^{42} - 7402 q^{43} - 336 q^{44} - 16720 q^{45} + 3198 q^{47} + 768 q^{48} + 24816 q^{49} + 10710 q^{51} + 3600 q^{52} + 3870 q^{53} - 16 q^{54} - 13588 q^{55} + 3702 q^{57} - 1728 q^{58} - 18288 q^{59} - 3120 q^{60} - 6522 q^{61} - 6144 q^{62} - 15676 q^{63} - 8192 q^{64} + 4960 q^{66} - 30168 q^{67} + 9696 q^{68} + 15360 q^{70} + 35874 q^{71} + 5376 q^{72} - 8080 q^{73} - 9120 q^{74} + 480 q^{76} + 34560 q^{77} - 46560 q^{78} - 30738 q^{79} - 1152 q^{80} - 30920 q^{81} + 6720 q^{82} - 1476 q^{83} + 33626 q^{85} + 288 q^{86} + 113100 q^{87} + 19782 q^{89} + 44256 q^{90} - 34260 q^{91} + 432 q^{92} - 4272 q^{93} - 23706 q^{95} + 2048 q^{96} - 9936 q^{97} + 12672 q^{98} + 3848 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
38.5.d.a 38.d 19.d $16$ $3.928$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-12\) \(-18\) \(72\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{5}+\beta _{9})q^{2}+(-1+\beta _{3})q^{3}+8\beta _{7}q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)