Properties

Label 19.7.d
Level $19$
Weight $7$
Character orbit 19.d
Rep. character $\chi_{19}(8,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $18$
Newform subspaces $1$
Sturm bound $11$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 19 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 19.d (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(11\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(19, [\chi])\).

Total New Old
Modular forms 22 22 0
Cusp forms 18 18 0
Eisenstein series 4 4 0

Trace form

\( 18q - 3q^{2} + 27q^{3} + 189q^{4} - 57q^{5} - 371q^{6} - 260q^{7} + 2390q^{9} + O(q^{10}) \) \( 18q - 3q^{2} + 27q^{3} + 189q^{4} - 57q^{5} - 371q^{6} - 260q^{7} + 2390q^{9} + 1680q^{10} + 1400q^{11} + 417q^{13} - 9858q^{14} - 12483q^{15} - 1395q^{16} + 14251q^{17} - 3952q^{19} + 26308q^{20} + 18222q^{21} - 52899q^{22} - 8905q^{23} - 2855q^{24} + 4918q^{25} + 4132q^{26} + 29368q^{28} - 88203q^{29} - 2336q^{30} + 226191q^{32} + 178728q^{33} - 45930q^{34} - 112598q^{35} + 70914q^{36} - 121486q^{38} - 80318q^{39} - 278256q^{40} - 167901q^{41} - 97796q^{42} - 31509q^{43} + 195391q^{44} + 204092q^{45} + 142263q^{47} - 505623q^{48} + 459318q^{49} + 143853q^{51} + 408750q^{52} - 109767q^{53} + 161081q^{54} - 309578q^{55} - 223687q^{57} + 894852q^{58} - 670197q^{59} - 211002q^{60} + 408559q^{61} - 436084q^{62} - 324688q^{63} - 2281026q^{64} + 760991q^{66} + 114183q^{67} + 3401236q^{68} + 539202q^{70} + 717297q^{71} - 212694q^{72} - 182727q^{73} - 1538850q^{74} + 1694819q^{76} + 1644696q^{77} - 3770190q^{78} - 214683q^{79} - 633946q^{80} - 3056957q^{81} - 2094801q^{82} - 1396816q^{83} + 164605q^{85} - 4326126q^{86} + 6408842q^{87} + 1181181q^{89} + 10325442q^{90} + 1082394q^{91} - 693188q^{92} - 4462972q^{93} + 2240803q^{95} + 6840726q^{96} - 4361889q^{97} - 1898997q^{98} - 1649132q^{99} + O(q^{100}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(19, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
19.7.d.a \(18\) \(4.371\) \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None \(-3\) \(27\) \(-57\) \(-260\) \(q+(\beta _{1}-\beta _{3})q^{2}+(2+\beta _{2}-\beta _{7})q^{3}+(21+\cdots)q^{4}+\cdots\)