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Properties

Label 152.3.u
Level $152$
Weight $3$
Character orbit 152.u
Rep. character $\chi_{152}(35,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $228$
Newform subspaces $2$
Sturm bound $60$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 152.u (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(60\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(152, [\chi])\).

Total New Old
Modular forms 252 252 0
Cusp forms 228 228 0
Eisenstein series 24 24 0

Trace form

\( 228 q - 6 q^{2} - 12 q^{3} - 12 q^{4} - 24 q^{6} - 3 q^{8} - 12 q^{9} + O(q^{10}) \) \( 228 q - 6 q^{2} - 12 q^{3} - 12 q^{4} - 24 q^{6} - 3 q^{8} - 12 q^{9} - 9 q^{10} - 6 q^{11} - 3 q^{12} + 27 q^{14} - 48 q^{16} - 12 q^{17} - 12 q^{18} - 12 q^{19} - 42 q^{20} + 6 q^{22} - 84 q^{24} - 12 q^{25} + 69 q^{26} - 6 q^{27} + 108 q^{28} - 30 q^{30} + 39 q^{32} + 42 q^{33} - 72 q^{34} - 162 q^{35} + 9 q^{36} + 42 q^{38} - 72 q^{40} + 60 q^{41} + 219 q^{42} - 12 q^{43} - 267 q^{44} + 132 q^{46} - 561 q^{48} + 540 q^{49} + 114 q^{50} - 300 q^{51} - 21 q^{52} - 33 q^{54} - 306 q^{56} - 12 q^{57} + 60 q^{58} - 12 q^{59} - 42 q^{60} - 468 q^{62} - 213 q^{64} - 6 q^{65} - 12 q^{67} - 60 q^{68} - 261 q^{70} - 42 q^{72} + 228 q^{73} - 219 q^{74} - 696 q^{75} + 42 q^{76} + 291 q^{78} - 9 q^{80} - 126 q^{81} + 489 q^{82} - 6 q^{83} + 27 q^{84} + 444 q^{86} + 693 q^{88} - 12 q^{89} + 1014 q^{90} - 306 q^{91} + 336 q^{92} + 1074 q^{94} - 726 q^{96} - 12 q^{97} + 831 q^{98} + 474 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.3.u.a 152.u 152.u $12$ $4.142$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) \(0\) \(6\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q+(-2\beta _{1}+2\beta _{5})q^{2}+(\beta _{3}+\beta _{4}-\beta _{6}+\cdots)q^{3}+\cdots\)
152.3.u.b 152.u 152.u $216$ $4.142$ None \(-6\) \(-18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$