Properties

Label 38.10.e
Level $38$
Weight $10$
Character orbit 38.e
Rep. character $\chi_{38}(5,\cdot)$
Character field $\Q(\zeta_{9})$
Dimension $90$
Newform subspaces $2$
Sturm bound $50$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
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: \(50\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(38, [\chi])\).

Total New Old
Modular forms 282 90 192
Cusp forms 258 90 168
Eisenstein series 24 0 24

Trace form

\( 90q - 219q^{3} + 4560q^{6} - 11436q^{7} - 12288q^{8} + 20805q^{9} + O(q^{10}) \) \( 90q - 219q^{3} + 4560q^{6} - 11436q^{7} - 12288q^{8} + 20805q^{9} - 22596q^{11} - 124416q^{12} + 373014q^{13} + 193728q^{14} - 1114176q^{15} + 2130090q^{17} + 2718624q^{18} + 3104982q^{19} - 872448q^{20} - 8253738q^{21} - 3975936q^{22} - 5339532q^{23} + 1167360q^{24} + 18934260q^{25} - 1147296q^{26} - 9159261q^{27} + 1488384q^{28} + 18350388q^{29} + 2615190q^{31} - 18138567q^{33} - 319680q^{34} - 4456146q^{35} + 5326080q^{36} + 69738420q^{37} - 40163472q^{38} - 73267932q^{39} - 33950949q^{41} + 15660864q^{42} + 140463276q^{43} - 16809984q^{44} + 42856866q^{45} - 23232000q^{46} + 280493580q^{47} + 28704768q^{48} - 142532535q^{49} - 246449616q^{50} - 256360335q^{51} - 141161472q^{52} - 244750782q^{53} + 5545872q^{54} + 493500528q^{55} + 329170944q^{56} + 512355660q^{57} + 103047552q^{58} - 247376757q^{59} - 166388736q^{60} - 717568098q^{61} - 376369632q^{62} - 225437622q^{63} - 754974720q^{64} + 76903230q^{65} + 930585648q^{66} + 1376150385q^{67} + 278354688q^{68} - 696062304q^{69} - 1447925952q^{70} - 1744555950q^{71} + 40132608q^{72} + 1380900810q^{73} + 309873888q^{74} + 2657812500q^{75} - 235451904q^{76} + 426872076q^{77} - 1076816928q^{78} - 2723006472q^{79} + 2045417583q^{81} + 2465868336q^{82} + 1266060108q^{83} - 102749184q^{84} - 498757524q^{85} - 365688384q^{86} - 1158620358q^{87} - 359817216q^{88} - 1215699516q^{89} - 2740985664q^{90} - 2339391108q^{91} - 171485184q^{92} + 9035460222q^{93} + 5158671168q^{94} - 1090068390q^{95} - 3216818607q^{97} + 1403099136q^{98} - 5695561353q^{99} + O(q^{100}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
38.10.e.a \(42\) \(19.571\) None \(0\) \(-252\) \(0\) \(14373\)
38.10.e.b \(48\) \(19.571\) None \(0\) \(33\) \(0\) \(-25809\)

Decomposition of \(S_{10}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{10}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)