Properties

Label 38.10.c
Level $38$
Weight $10$
Character orbit 38.c
Rep. character $\chi_{38}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $30$
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.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
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 94 30 64
Cusp forms 86 30 56
Eisenstein series 8 0 8

Trace form

\( 30q - 16q^{2} + 235q^{3} - 3840q^{4} + 568q^{5} - 1520q^{6} + 7396q^{7} + 8192q^{8} - 105350q^{9} + O(q^{10}) \) \( 30q - 16q^{2} + 235q^{3} - 3840q^{4} + 568q^{5} - 1520q^{6} + 7396q^{7} + 8192q^{8} - 105350q^{9} - 20000q^{10} + 122338q^{11} - 120320q^{12} + 5740q^{13} - 96q^{14} - 225416q^{15} - 983040q^{16} - 297600q^{17} + 24896q^{18} - 475453q^{19} - 290816q^{20} - 2168094q^{21} - 728208q^{22} + 3033226q^{23} - 389120q^{24} - 5707675q^{25} + 227392q^{26} - 18777458q^{27} - 946688q^{28} - 12081772q^{29} - 7360448q^{30} - 10048264q^{31} - 1048576q^{32} - 21419863q^{33} - 14798944q^{34} + 549300q^{35} - 26969600q^{36} - 39957600q^{37} + 41372800q^{38} + 42499536q^{39} - 5120000q^{40} - 3830539q^{41} + 4575968q^{42} - 78838078q^{43} - 15659264q^{44} + 11443592q^{45} + 123694848q^{46} + 94483300q^{47} + 15400960q^{48} - 14575250q^{49} + 29132128q^{50} - 145322624q^{51} + 1469440q^{52} - 55309760q^{53} + 120238000q^{54} + 279192290q^{55} + 49152q^{56} + 345672342q^{57} - 61550656q^{58} + 162438825q^{59} - 57706496q^{60} - 172532532q^{61} - 218279296q^{62} + 194824816q^{63} + 503316480q^{64} + 1050651524q^{65} + 99767568q^{66} + 66058131q^{67} + 152371200q^{68} + 494974940q^{69} - 73929024q^{70} - 505786964q^{71} - 3186688q^{72} + 258568831q^{73} + 209803520q^{74} - 2938701630q^{75} + 188076800q^{76} + 1049155980q^{77} - 266901728q^{78} - 174908218q^{79} + 37224448q^{80} - 1437564203q^{81} - 175340048q^{82} + 859531050q^{83} + 1110064128q^{84} + 341139450q^{85} - 1896209920q^{86} - 4626897064q^{87} + 372842496q^{88} - 2096857812q^{89} - 1336160896q^{90} - 1425369636q^{91} + 776505856q^{92} - 517502372q^{93} + 839179200q^{94} + 2405958962q^{95} + 199229440q^{96} - 362913935q^{97} - 1156672400q^{98} + 1722533338q^{99} + O(q^{100}) \)

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.c.a \(14\) \(19.571\) \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(112\) \(165\) \(909\) \(3692\) \(q+(2^{4}-2^{4}\beta _{2})q^{2}+(24-\beta _{1}-24\beta _{2}+\cdots)q^{3}+\cdots\)
38.10.c.b \(16\) \(19.571\) \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-128\) \(70\) \(-341\) \(3704\) \(q+(-2^{4}+2^{4}\beta _{2})q^{2}+(9-\beta _{1}-9\beta _{2}+\cdots)q^{3}+\cdots\)

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

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