Properties

Label 38.8.e
Level $38$
Weight $8$
Character orbit 38.e
Rep. character $\chi_{38}(5,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $66$
Newform subspaces $2$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
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: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(38, [\chi])\).

Total New Old
Modular forms 222 66 156
Cusp forms 198 66 132
Eisenstein series 24 0 24

Trace form

\( 66q - 39q^{3} + 1032q^{6} - 1182q^{7} + 1536q^{8} - 1677q^{9} + O(q^{10}) \) \( 66q - 39q^{3} + 1032q^{6} - 1182q^{7} + 1536q^{8} - 1677q^{9} + 11586q^{11} - 49464q^{13} + 26976q^{14} + 109410q^{15} - 151824q^{17} - 256848q^{18} - 54246q^{19} + 768q^{20} + 101412q^{21} + 232320q^{22} + 243924q^{23} + 66048q^{24} - 646824q^{25} - 169968q^{26} + 203151q^{27} + 300672q^{28} - 899946q^{29} + 141366q^{31} + 1169529q^{33} + 170592q^{34} + 937860q^{35} - 107328q^{36} - 1508004q^{37} - 617832q^{38} + 1487220q^{39} + 494157q^{41} - 977184q^{42} + 4192962q^{43} - 221184q^{44} - 2121030q^{45} - 364800q^{46} - 1335210q^{47} + 319488q^{48} - 6445785q^{49} + 5928744q^{50} + 9043041q^{51} + 10368q^{52} + 2034492q^{53} + 896040q^{54} - 7378326q^{55} - 4909056q^{56} - 12115488q^{57} - 2854848q^{58} - 6390831q^{59} + 1150080q^{60} + 16037106q^{61} + 6348816q^{62} + 3663876q^{63} - 8650752q^{64} + 11988480q^{65} - 440088q^{66} + 418347q^{67} + 1300416q^{68} - 1612422q^{69} - 1805280q^{70} - 14190498q^{71} + 4641792q^{72} - 9870690q^{73} - 3567024q^{74} + 2053248q^{76} + 33000396q^{77} - 11977104q^{78} - 19536114q^{79} - 46133223q^{81} - 3259224q^{82} + 14115522q^{83} + 15048576q^{84} + 8751552q^{85} + 26557536q^{86} + 40486866q^{87} + 4088832q^{88} - 10658520q^{89} + 4171296q^{90} - 4410684q^{91} - 17966208q^{92} - 14723742q^{93} - 33954912q^{94} - 36453096q^{95} - 70997799q^{97} - 17740800q^{98} + 17017377q^{99} + O(q^{100}) \)

Decomposition of \(S_{8}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.8.e.a \(30\) \(11.871\) None \(0\) \(45\) \(0\) \(1806\)
38.8.e.b \(36\) \(11.871\) None \(0\) \(-84\) \(0\) \(-2988\)

Decomposition of \(S_{8}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{8}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)