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Properties

Label 152.2.v
Level $152$
Weight $2$
Character orbit 152.v
Rep. character $\chi_{152}(3,\cdot)$
Character field $\Q(\zeta_{18})$
Dimension $108$
Newform subspaces $2$
Sturm bound $40$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 152 = 2^{3} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 152.v (of order \(18\) and degree \(6\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 152 \)
Character field: \(\Q(\zeta_{18})\)
Newform subspaces: \( 2 \)
Sturm bound: \(40\)
Trace bound: \(1\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(152, [\chi])\).

Total New Old
Modular forms 132 132 0
Cusp forms 108 108 0
Eisenstein series 24 24 0

Trace form

\( 108 q - 6 q^{2} - 12 q^{3} - 12 q^{4} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 6 q^{11} - 9 q^{12} - 21 q^{14} - 12 q^{17} - 12 q^{19} + 18 q^{20} - 36 q^{24} - 12 q^{25} + 21 q^{26} - 18 q^{27} - 36 q^{28} - 6 q^{30}+ \cdots + 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{2}^{\mathrm{new}}(152, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
152.2.v.a 152.v 152.v $12$ $1.214$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-2}) \) 152.2.v.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{U}(1)[D_{18}]$ \(q-\beta _{11}q^{2}+(\beta _{1}+\beta _{3}-\beta _{6}-\beta _{9}+\beta _{10}+\cdots)q^{3}+\cdots\)
152.2.v.b 152.v 152.v $96$ $1.214$ None 152.2.v.b \(-6\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{18}]$