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Properties

Label 38.4.c
Level $38$
Weight $4$
Character orbit 38.c
Rep. character $\chi_{38}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $10$
Newform subspaces $3$
Sturm bound $20$
Trace bound $3$

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Defining parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 38.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 3 \)
Sturm bound: \(20\)
Trace bound: \(3\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(38, [\chi])\).

Total New Old
Modular forms 34 10 24
Cusp forms 26 10 16
Eisenstein series 8 0 8

Trace form

\( 10 q + 2 q^{2} - 5 q^{3} - 20 q^{4} + 8 q^{5} + 10 q^{6} + 4 q^{7} - 16 q^{8} - 50 q^{9} + O(q^{10}) \) \( 10 q + 2 q^{2} - 5 q^{3} - 20 q^{4} + 8 q^{5} + 10 q^{6} + 4 q^{7} - 16 q^{8} - 50 q^{9} + 20 q^{10} + 34 q^{11} + 40 q^{12} + 172 q^{13} + 100 q^{14} - 152 q^{15} - 80 q^{16} - 184 q^{17} - 232 q^{18} + 59 q^{19} - 64 q^{20} + 30 q^{21} - 18 q^{22} + 58 q^{23} + 40 q^{24} - 241 q^{25} + 344 q^{26} + 718 q^{27} - 8 q^{28} + 28 q^{29} - 8 q^{30} - 168 q^{31} + 32 q^{32} + 299 q^{33} - 164 q^{34} + 108 q^{35} - 200 q^{36} - 1072 q^{37} + 360 q^{38} - 2496 q^{39} + 80 q^{40} + 711 q^{41} + 740 q^{42} + 114 q^{43} - 68 q^{44} + 3224 q^{45} + 144 q^{46} + 868 q^{47} - 80 q^{48} - 550 q^{49} - 1740 q^{50} + 544 q^{51} + 688 q^{52} - 1032 q^{53} + 718 q^{54} - 1742 q^{55} - 800 q^{56} + 330 q^{57} - 1112 q^{58} + 113 q^{59} - 608 q^{60} - 412 q^{61} - 32 q^{62} - 920 q^{63} + 640 q^{64} - 452 q^{65} - 498 q^{66} + 347 q^{67} + 1472 q^{68} - 76 q^{69} + 552 q^{70} + 1428 q^{71} + 464 q^{72} - 203 q^{73} + 320 q^{74} + 3234 q^{75} + 332 q^{76} - 604 q^{77} - 596 q^{78} + 1638 q^{79} + 128 q^{80} + 55 q^{81} - 478 q^{82} - 1142 q^{83} - 240 q^{84} - 618 q^{85} + 520 q^{86} - 3880 q^{87} + 144 q^{88} + 2156 q^{89} + 3152 q^{90} - 740 q^{91} + 232 q^{92} - 1988 q^{93} - 5400 q^{94} + 2266 q^{95} - 320 q^{96} + 571 q^{97} - 2158 q^{98} - 3158 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(38, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
38.4.c.a 38.c 19.c $2$ $2.242$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-5\) \(-3\) \(-64\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+(-5+5\zeta_{6})q^{3}+\cdots\)
38.4.c.b 38.c 19.c $2$ $2.242$ \(\Q(\sqrt{-3}) \) None \(-2\) \(5\) \(12\) \(16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+(5-5\zeta_{6})q^{3}-4\zeta_{6}q^{4}+\cdots\)
38.4.c.c 38.c 19.c $6$ $2.242$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(6\) \(-5\) \(-1\) \(52\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\beta _{4})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{4}+\cdots)q^{3}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(38, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(38, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)