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Properties

Label 153.2.n
Level $153$
Weight $2$
Character orbit 153.n
Rep. character $\chi_{153}(4,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $64$
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.n (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 153 \)
Character field: \(\Q(\zeta_{12})\)
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 80 80 0
Cusp forms 64 64 0
Eisenstein series 16 16 0

Trace form

\( 64 q - 6 q^{3} + 24 q^{4} - 2 q^{5} - 10 q^{6} - 2 q^{7} - 16 q^{10} - 24 q^{12} - 4 q^{13} - 16 q^{16} - 8 q^{17} - 8 q^{18} + 18 q^{20} - 16 q^{21} - 4 q^{22} - 8 q^{23} - 2 q^{24} - 10 q^{29} - 36 q^{30}+ \cdots + 6 q^{99}+O(q^{100}) \) 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.n.a 153.n 153.n $64$ $1.222$ None 153.2.n.a \(0\) \(-6\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{12}]$