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Properties

Label 152.3.r
Level $152$
Weight $3$
Character orbit 152.r
Rep. character $\chi_{152}(33,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $60$
Newform subspaces $1$
Sturm bound $60$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 152.r (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 1 \)
Sturm bound: \(60\)
Trace bound: \(0\)

Dimensions

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

Total New Old
Modular forms 264 60 204
Cusp forms 216 60 156
Eisenstein series 48 0 48

Trace form

\( 60 q + 6 q^{3} + 18 q^{9} + O(q^{10}) \) \( 60 q + 6 q^{3} + 18 q^{9} + 12 q^{13} + 24 q^{15} + 24 q^{17} + 48 q^{19} - 36 q^{21} - 72 q^{23} - 48 q^{25} + 90 q^{27} + 96 q^{29} + 108 q^{31} + 234 q^{33} - 12 q^{35} - 72 q^{39} - 30 q^{41} - 336 q^{43} - 144 q^{45} - 144 q^{47} - 282 q^{49} - 126 q^{51} - 36 q^{53} - 144 q^{55} - 336 q^{57} + 246 q^{59} - 60 q^{61} - 360 q^{63} - 540 q^{65} - 606 q^{67} - 180 q^{71} + 24 q^{73} + 72 q^{77} + 288 q^{79} + 642 q^{81} + 432 q^{83} - 120 q^{85} + 684 q^{87} + 324 q^{89} + 720 q^{91} + 648 q^{93} + 1080 q^{95} + 6 q^{97} + 246 q^{99} + O(q^{100}) \)

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.r.a 152.r 19.f $60$ $4.142$ None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$

Decomposition of \(S_{3}^{\mathrm{old}}(152, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(152, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 2}\)