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Properties

Label 19.4.c
Level $19$
Weight $4$
Character orbit 19.c
Rep. character $\chi_{19}(7,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $8$
Newform subspaces $2$
Sturm bound $6$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 19.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 2 \)
Sturm bound: \(6\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(19, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 8 8 0
Eisenstein series 4 4 0

Trace form

\( 8 q - 3 q^{2} - 2 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 12 q^{7} + 18 q^{8} - 4 q^{9} + O(q^{10}) \) \( 8 q - 3 q^{2} - 2 q^{3} - 7 q^{4} - 5 q^{5} - q^{6} + 12 q^{7} + 18 q^{8} - 4 q^{9} - 32 q^{10} - 10 q^{11} + 42 q^{12} - 73 q^{13} - 142 q^{14} + 91 q^{15} - 43 q^{16} + 187 q^{17} + 60 q^{18} - 139 q^{19} + 668 q^{20} - 130 q^{21} - 121 q^{22} - 115 q^{23} - 39 q^{24} + 75 q^{25} - 320 q^{26} - 212 q^{27} - 454 q^{28} - 137 q^{29} - 128 q^{30} + 576 q^{31} - 465 q^{32} - 737 q^{33} + 916 q^{34} - 324 q^{35} + 938 q^{36} + 1260 q^{37} - 498 q^{38} + 1962 q^{39} - 690 q^{40} - 278 q^{41} - 266 q^{42} + 43 q^{43} + 433 q^{44} - 1772 q^{45} - 1012 q^{46} - 537 q^{47} + 39 q^{48} - 760 q^{49} + 1270 q^{50} - 805 q^{51} - 1074 q^{52} + 623 q^{53} + 53 q^{54} + 1170 q^{55} + 2076 q^{56} - 717 q^{57} + 3352 q^{58} - 316 q^{59} - 1006 q^{60} - 1077 q^{61} - 496 q^{62} + 912 q^{63} - 2602 q^{64} + 186 q^{65} - 863 q^{66} + 184 q^{67} - 1540 q^{68} + 1542 q^{69} - 1908 q^{70} - 1995 q^{71} + 1854 q^{72} - 116 q^{73} + 908 q^{74} + 3014 q^{75} + 1583 q^{76} + 1364 q^{77} - 748 q^{78} + 483 q^{79} + 470 q^{80} + 104 q^{81} - 143 q^{82} - 890 q^{83} - 828 q^{84} + 1575 q^{85} + 654 q^{86} - 1710 q^{87} - 1470 q^{88} - 713 q^{89} + 1588 q^{90} - 1356 q^{91} + 1408 q^{92} - 792 q^{93} - 2184 q^{94} - 2143 q^{95} + 286 q^{96} + 870 q^{97} - 2491 q^{98} - 1642 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
19.4.c.a 19.c 19.c $4$ $1.121$ \(\Q(\sqrt{-3}, \sqrt{55})\) None \(-2\) \(0\) \(14\) \(-28\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}+(7+7\beta _{2})q^{4}+\cdots\)
19.4.c.b 19.c 19.c $4$ $1.121$ \(\Q(\sqrt{-3}, \sqrt{73})\) None \(-1\) \(-2\) \(-19\) \(40\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(-11+\beta _{1}+10\beta _{2}+\cdots)q^{4}+\cdots\)