Properties

Label 152.4.p
Level $152$
Weight $4$
Character orbit 152.p
Rep. character $\chi_{152}(45,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $116$
Newform subspaces $1$
Sturm bound $80$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 152.p (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(80\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(152, [\chi])\).

Total New Old
Modular forms 124 124 0
Cusp forms 116 116 0
Eisenstein series 8 8 0

Trace form

\( 116q - q^{2} - 7q^{4} - 11q^{6} - 8q^{7} - 46q^{8} + 484q^{9} + O(q^{10}) \) \( 116q - q^{2} - 7q^{4} - 11q^{6} - 8q^{7} - 46q^{8} + 484q^{9} - 44q^{10} - 58q^{12} + 24q^{14} - 230q^{15} - 67q^{16} - 2q^{17} + 196q^{18} - 840q^{20} + 137q^{22} - 2q^{23} + 77q^{24} + 1248q^{25} + 492q^{26} - 96q^{28} - 904q^{30} + 208q^{31} - 431q^{32} - 180q^{33} + 224q^{34} - 84q^{36} + 1552q^{38} - 116q^{39} - 58q^{40} - 22q^{41} - 568q^{42} - 89q^{44} - 1852q^{46} + 202q^{47} - 89q^{48} + 5220q^{49} - 942q^{50} + 232q^{52} - 231q^{54} + 248q^{55} - 2296q^{56} - 398q^{57} - 3620q^{58} - 1378q^{60} + 614q^{62} - 796q^{63} + 1550q^{64} - 508q^{65} - 797q^{66} + 1860q^{68} - 2968q^{70} + 1986q^{71} - 1596q^{72} - 218q^{73} + 2490q^{74} - 4697q^{76} + 1254q^{78} + 1250q^{79} + 3136q^{80} - 3810q^{81} - 169q^{82} + 4136q^{84} - 2360q^{86} - 1404q^{87} + 4434q^{88} - 2q^{89} + 1378q^{90} - 1958q^{92} - 4608q^{94} + 438q^{95} + 3410q^{96} - 1586q^{97} + 55q^{98} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
152.4.p.a \(116\) \(8.968\) None \(-1\) \(0\) \(0\) \(-8\)