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Properties

Label 153.2.r
Level $153$
Weight $2$
Character orbit 153.r
Rep. character $\chi_{153}(25,\cdot)$
Character field $\Q(\zeta_{24})$
Dimension $128$
Newform subspaces $1$
Sturm bound $36$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 153 = 3^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 153.r (of order \(24\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 153 \)
Character field: \(\Q(\zeta_{24})\)
Newform subspaces: \( 1 \)
Sturm bound: \(36\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(153, [\chi])\).

Total New Old
Modular forms 160 160 0
Cusp forms 128 128 0
Eisenstein series 32 32 0

Trace form

\( 128 q - 4 q^{2} - 8 q^{3} - 4 q^{5} - 8 q^{6} - 4 q^{7} - 32 q^{8} - 20 q^{9} - 16 q^{10} - 44 q^{12} - 4 q^{14} - 4 q^{15} + 32 q^{16} - 16 q^{17} - 16 q^{19} - 36 q^{20} - 4 q^{22} + 8 q^{23} + 28 q^{24}+ \cdots + 44 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(153, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
153.2.r.a 153.r 153.r $128$ $1.222$ None 153.2.r.a \(-4\) \(-8\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{24}]$