Properties

Label 152.5.s
Level $152$
Weight $5$
Character orbit 152.s
Rep. character $\chi_{152}(13,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $468$
Newform subspaces $1$
Sturm bound $100$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 152.s (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(100\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(152, [\chi])\).

Total New Old
Modular forms 492 492 0
Cusp forms 468 468 0
Eisenstein series 24 24 0

Trace form

\( 468 q - 6 q^{2} + 36 q^{4} - 60 q^{6} - 6 q^{7} - 9 q^{8} - 12 q^{9} + O(q^{10}) \) \( 468 q - 6 q^{2} + 36 q^{4} - 60 q^{6} - 6 q^{7} - 9 q^{8} - 12 q^{9} - 153 q^{10} - 9 q^{12} - 93 q^{14} - 12 q^{15} - 720 q^{16} - 12 q^{17} - 1182 q^{20} - 54 q^{22} - 12 q^{23} + 2652 q^{24} - 12 q^{25} - 3099 q^{26} - 3288 q^{28} - 5820 q^{30} - 18 q^{31} + 4269 q^{32} - 498 q^{33} - 3708 q^{34} + 9033 q^{36} - 4146 q^{38} - 24 q^{39} - 7212 q^{40} - 3324 q^{41} + 24321 q^{42} - 1143 q^{44} + 4446 q^{46} - 8652 q^{47} + 29523 q^{48} - 67920 q^{49} - 24228 q^{50} + 12579 q^{52} + 7353 q^{54} - 3762 q^{55} - 12 q^{57} - 8292 q^{58} - 3168 q^{60} - 7704 q^{62} + 14394 q^{63} + 8271 q^{64} - 18 q^{65} + 14508 q^{66} + 22776 q^{68} + 25665 q^{70} - 12 q^{71} + 18150 q^{72} + 11028 q^{73} + 48723 q^{74} + 8706 q^{76} + 2565 q^{78} - 12 q^{79} - 39633 q^{80} - 5238 q^{81} - 72231 q^{82} - 84573 q^{84} + 24888 q^{86} - 6 q^{87} - 6561 q^{88} - 12 q^{89} + 110298 q^{90} + 64128 q^{92} - 60492 q^{95} + 98622 q^{96} - 12 q^{97} - 5121 q^{98} + O(q^{100}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.5.s.a 152.s 152.s $468$ $15.712$ None \(-6\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{18}]$